{
  "edition": "0.14",
  "date": "2026-10-14",
  "status": "SCOPED_DEPENDENCY_REGISTER_COMPLETE__GLOBAL_PROOF_DAG_OPEN",
  "physical_promotion": 0,
  "review": "Constructor source audit; independent human proof review pending",
  "scope": "Explicit premises and evaluation gates for the displayed polarity and single-cell action/clock targets. Completeness is by target declaration, not the full 448-row research ledger. Edition 0.4 adds the finite response-source refinement; no native response law is supplied. Edition 0.5 adds RSP-1 prepared candidate results; native identification remains open. Edition0.6 adds explicit realization assumptions and no-go classes; the overall native bridge stays open. Edition0.7 adds a supplied finite-window joint carrier and explicit resource/clock premises. Native realization and global proof DAG remain open. Edition0.8 supplies a continuous word lift, engineered path metrics and scoped operator obstructions. Native admission and global proof DAG stay open. Edition0.9 tests frozen native spectral classes and distinguishes generator residual from endpoint error. No new native or physical admission follows. Edition0.10 distinguishes source metric conventions and adds scoped invariant/Gram/glued family obstructions. Native parameter selection remains OPEN. Edition0.11 tests source subdivision separately for norm, boundary and generator, and adds a conditional changed-metric existence theorem. Source selection and physical interpretation remain OPEN. Edition0.12 classifies metric/observable selection freedom and derives a unique conditional selector from explicit additional premises. Native adoption remains OPEN. Edition0.13 tests regrouping the same retained refinement sequence and transports calibrated detail pairings. Different-history covariance, native selection and physical implementation remain OPEN. Edition0.14 compares star and barycentric histories under conditional metrics, distinguishes full symmetry from spectral capacity, and retains a source/excitation gate.",
  "propagation_policy": "Hypothetical premise-change drill. Descendants are PENDING_REDERIVATION for reuse; stored scientific statuses are unchanged. Conditional theorem statements retain their explicitly declared premises.",
  "source_baseline_site_commit": "a0f81529c75f123f76c6348843ff7ce63a34300c",
  "repository_freshness_commit": "4b9c1f7ba03f76324b792f389517161d2bc47e05",
  "nodes": [
    {
      "id": "P-DEF",
      "branch": "polarity",
      "title": "Typed pair variables",
      "status": "SOURCE_DECLARED",
      "objects": "Theta,q,T,L,omega on three pair addresses",
      "conclusion": "q=1−Theta; omega=T AND L. These binary response and viability masks are different objects.",
      "citations": [
        {
          "source_id": "E04",
          "section": "§2",
          "anchor_text": "omega",
          "snapshot_sha256": "0243b70b3077ad58303ffad4f13d73fdc32bbe55fd204e52d2877c36318f4553"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "P-ADM",
      "branch": "polarity",
      "title": "Admissible response domain",
      "status": "SOURCE_DECLARED",
      "objects": "Binary masks",
      "conclusion": "omega ≤ q ≤ T coordinatewise; five admissible triples per address.",
      "citations": [
        {
          "source_id": "E04",
          "section": "§2",
          "anchor_text": "admissible",
          "snapshot_sha256": "0243b70b3077ad58303ffad4f13d73fdc32bbe55fd204e52d2877c36318f4553"
        }
      ],
      "dependencies": [
        "P-DEF"
      ],
      "ledger_ids": []
    },
    {
      "id": "P-IDLE",
      "branch": "polarity",
      "title": "Idle-response decomposition",
      "status": "EXACT_CONDITIONAL",
      "objects": "h=q−omega",
      "conclusion": "h is binary, nonnegative and supported on intact-null addresses; q=omega+h with disjoint support.",
      "citations": [
        {
          "source_id": "C0963",
          "section": "declared_source_variables / exact_response_form",
          "anchor_text": "q = omega OR h",
          "snapshot_sha256": "6da081eec3922f361d4e616673b0f994eed9471c050e818e8b98b80b46e9d2bc"
        }
      ],
      "dependencies": [
        "P-ADM"
      ],
      "ledger_ids": []
    },
    {
      "id": "P-RANK",
      "branch": "polarity",
      "title": "Finite continuation spaces",
      "status": "SOURCE_DECLARED",
      "objects": "F: L− → L+",
      "conclusion": "Declare finite spaces with dimensions |omega−| and |omega+|. No causal source is inferred from their dimensions.",
      "citations": [
        {
          "source_id": "C0884",
          "section": "§2",
          "anchor_text": "finite-dimensional continuation map",
          "snapshot_sha256": "027b1d033ef17e7d9946b18cd577b5e370e7c9319bf439a6ba689249f71971b5"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "P-INDEX",
      "branch": "polarity",
      "title": "Rank-nullity index",
      "status": "EXACT_CONDITIONAL",
      "objects": "ind Fomega",
      "conclusion": "ind Fomega=|omega−|−|omega+| for any linear map on the declared spaces. The rank cancels.",
      "citations": [
        {
          "source_id": "C0884",
          "section": "§2",
          "anchor_text": "Rank-nullity",
          "snapshot_sha256": "027b1d033ef17e7d9946b18cd577b5e370e7c9319bf439a6ba689249f71971b5"
        }
      ],
      "dependencies": [
        "P-RANK"
      ],
      "ledger_ids": []
    },
    {
      "id": "P-BUDGET",
      "branch": "polarity",
      "title": "Full Hamming budget",
      "status": "EXACT_CONDITIONAL",
      "objects": "muTheta",
      "conclusion": "muTheta=|Theta+|−|Theta−|=|q−|−|q+|. Cardinalities are invariant under pair-frame permutations.",
      "citations": [
        {
          "source_id": "C0957",
          "section": "Theorem",
          "anchor_text": "Hamming event budget",
          "snapshot_sha256": "6ea514e6f5af3cbce082605d2575259748aa22e976be5a4d8dfec5855824fae1"
        }
      ],
      "dependencies": [
        "P-DEF"
      ],
      "ledger_ids": []
    },
    {
      "id": "P-CORRECT",
      "branch": "polarity",
      "title": "Idle-corrected identity",
      "status": "EXACT_CONDITIONAL",
      "objects": "muTheta,ind Fomega,nu_h",
      "conclusion": "muTheta=ind Fomega+|h−|−|h+|. This is an identity on ordered admissible states, not an endpoint predictor.",
      "citations": [
        {
          "source_id": "C0957",
          "section": "Theorem",
          "anchor_text": "residual idle-response index",
          "snapshot_sha256": "6ea514e6f5af3cbce082605d2575259748aa22e976be5a4d8dfec5855824fae1"
        }
      ],
      "dependencies": [
        "P-IDLE",
        "P-INDEX",
        "P-BUDGET"
      ],
      "ledger_ids": []
    },
    {
      "id": "P-EQUAL",
      "branch": "polarity",
      "title": "Index equals full budget iff idle totals match",
      "status": "EXACT_CONDITIONAL",
      "objects": "Equal idle cardinalities",
      "conclusion": "muTheta=ind Fomega iff |h−|=|h+|. Equal idle totals need not mean either mask is zero.",
      "citations": [
        {
          "source_id": "C0957",
          "section": "Theorem / decomposition",
          "anchor_text": "mu_\\Theta=\\operatorname{ind}F_\\omega+\\nu_h",
          "snapshot_sha256": "6ea514e6f5af3cbce082605d2575259748aa22e976be5a4d8dfec5855824fae1"
        }
      ],
      "dependencies": [
        "P-CORRECT"
      ],
      "ledger_ids": []
    },
    {
      "id": "P-PRIOR",
      "branch": "polarity",
      "title": "Saturated prior premise",
      "status": "CONSTITUTIVE_PREMISE",
      "objects": "h−=000",
      "conclusion": "This is an additional premise for the saturated-prior corollary, not a consequence of rank-nullity.",
      "citations": [
        {
          "source_id": "C0957",
          "section": "Saturated-prior corollary",
          "anchor_text": "h^-=0",
          "snapshot_sha256": "6ea514e6f5af3cbce082605d2575259748aa22e976be5a4d8dfec5855824fae1"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "P-SAT",
      "branch": "polarity",
      "title": "Saturated-prior corollary",
      "status": "EXACT_CONDITIONAL",
      "objects": "muTheta=ind Fomega−|h+|",
      "conclusion": "With h−=0, index-only equality holds iff h+=0. Using that equality to prove no-idle response is circular.",
      "citations": [
        {
          "source_id": "C0957",
          "section": "Saturated-prior corollary",
          "anchor_text": "circularity firewall",
          "snapshot_sha256": "6ea514e6f5af3cbce082605d2575259748aa22e976be5a4d8dfec5855824fae1"
        }
      ],
      "dependencies": [
        "P-CORRECT",
        "P-PRIOR"
      ],
      "ledger_ids": []
    },
    {
      "id": "P-NOIDLE",
      "branch": "polarity",
      "title": "POC-1 no-idle response",
      "status": "CANDIDATE",
      "objects": "h+=000; q+=omega+",
      "conclusion": "A candidate constitutive law needing an independent source; it is not proved by demanding index-only equality.",
      "citations": [
        {
          "source_id": "C0963",
          "section": "minimum_missing_object / admissible_reopen_routes",
          "anchor_text": "h=000",
          "snapshot_sha256": "6da081eec3922f361d4e616673b0f994eed9471c050e818e8b98b80b46e9d2bc"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "P-ADDRESS",
      "branch": "polarity",
      "title": "Binding no-idle address",
      "status": "EXACT_CONDITIONAL",
      "objects": "Theta+=1−omega+",
      "conclusion": "If POC-1 binds the response, the final address is fixed. A competing burden minimizer cannot freely choose a different final address.",
      "citations": [
        {
          "source_id": "E04",
          "section": "§3",
          "anchor_text": "address-selector",
          "snapshot_sha256": "0243b70b3077ad58303ffad4f13d73fdc32bbe55fd204e52d2877c36318f4553"
        }
      ],
      "dependencies": [
        "P-DEF",
        "P-NOIDLE"
      ],
      "ledger_ids": []
    },
    {
      "id": "P-BURDEN",
      "branch": "polarity",
      "title": "Burden and integrity inputs",
      "status": "SOURCE_DECLARED",
      "objects": "T,W,k",
      "conclusion": "A supplied burden selector optimizes a target Hamming shell subject to integrity; it must also respect the chosen viability/idle-response contract.",
      "citations": [
        {
          "source_id": "C0884",
          "section": "§5",
          "anchor_text": "three-pair address selector",
          "snapshot_sha256": "027b1d033ef17e7d9946b18cd577b5e370e7c9319bf439a6ba689249f71971b5"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "P-SHELL",
      "branch": "polarity",
      "title": "Conditional shell optimizer",
      "status": "EXACT_CONDITIONAL",
      "objects": "argmin on a declared finite shell",
      "conclusion": "An empty admissible shell returns infeasible; a tied optimum holds unresolved symmetry. The historical integrity-only shell is not automatically compatible with binding POC-1.",
      "citations": [
        {
          "source_id": "C0884",
          "section": "§5",
          "anchor_text": "HOLD_UNRESOLVED_SYMMETRY",
          "snapshot_sha256": "027b1d033ef17e7d9946b18cd577b5e370e7c9319bf439a6ba689249f71971b5"
        }
      ],
      "dependencies": [
        "P-BURDEN"
      ],
      "ledger_ids": []
    },
    {
      "id": "P-CONFLICT",
      "branch": "polarity",
      "title": "Two final selectors can conflict",
      "status": "EXACT_NO_GO",
      "objects": "T=111,L=100,W=(2,8,10)",
      "conclusion": "POC-1 gives Theta=011 (cost 18); integrity-only k=2 minimization gives 110 (cost 10), violating omega≤q. Adding viability fixes this example.",
      "citations": [
        {
          "source_id": "E04",
          "section": "§3",
          "anchor_text": "18",
          "snapshot_sha256": "0243b70b3077ad58303ffad4f13d73fdc32bbe55fd204e52d2877c36318f4553"
        }
      ],
      "dependencies": [
        "P-ADM",
        "P-ADDRESS",
        "P-SHELL"
      ],
      "ledger_ids": []
    },
    {
      "id": "P-FRAME",
      "branch": "polarity",
      "title": "Frame-alignment receipt",
      "status": "OPEN",
      "objects": "Oriented C1 transport; old Theta and omega",
      "conclusion": "A native address prediction requires an independently obtained relative-frame receipt and aligned prior address masks. Count identities alone do not provide this receipt.",
      "citations": [
        {
          "source_id": "E04",
          "section": "§5",
          "anchor_text": "frame",
          "snapshot_sha256": "0243b70b3077ad58303ffad4f13d73fdc32bbe55fd204e52d2877c36318f4553"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "P-SOURCE",
      "branch": "polarity",
      "title": "Native pre-event viability source",
      "status": "OPEN",
      "objects": "L−,L+,T from target-hidden pre-state",
      "conclusion": "Finite rank-nullity does not construct independently sourced obligation spaces from native evolution.",
      "citations": [
        {
          "source_id": "C0884",
          "section": "§9",
          "anchor_text": "native pre-event mechanism",
          "snapshot_sha256": "027b1d033ef17e7d9946b18cd577b5e370e7c9319bf439a6ba689249f71971b5"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "P-HSOURCE",
      "branch": "polarity",
      "title": "Independent idle-response source",
      "status": "OPEN",
      "objects": "h before endpoint release",
      "conclusion": "Supply typed gate dynamics, an independent silence theorem, an authenticated pre-event receipt or blinded response discrimination. Endpoint-inferred h is forbidden.",
      "citations": [
        {
          "source_id": "C0963",
          "section": "minimum_missing_object",
          "anchor_text": "before endpoint release",
          "snapshot_sha256": "6da081eec3922f361d4e616673b0f994eed9471c050e818e8b98b80b46e9d2bc"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "P-PREDICT",
      "branch": "polarity",
      "title": "Native address/polarity prediction",
      "status": "OPEN",
      "objects": "Declared complete pre-event packet",
      "conclusion": "A predictive model needs independently generated viable and idle response data, the address-frame receipt, and a consistent final selector. Exact endpoint identities do not close these gates.",
      "citations": [
        {
          "source_id": "E04",
          "section": "§§2–5",
          "anchor_text": "pre-event",
          "snapshot_sha256": "0243b70b3077ad58303ffad4f13d73fdc32bbe55fd204e52d2877c36318f4553"
        }
      ],
      "dependencies": [
        "P-SOURCE",
        "P-HSOURCE",
        "P-FRAME",
        "P-CORRECT",
        "P-SHELL"
      ],
      "ledger_ids": []
    },
    {
      "id": "P-SCORE",
      "branch": "polarity",
      "title": "Eligible independent score",
      "status": "SOURCE_BLOCKED",
      "objects": "Frozen scorer + target-hidden native episode",
      "conclusion": "No new empirical score is issued by this graph. Original scorer custody, source admission and eligible target-hidden episodes remain required.",
      "citations": [
        {
          "source_id": "R35",
          "section": "Object and scope / scoring gate",
          "anchor_text": "SOURCE_INCOMPLETE_NO_SCORE",
          "snapshot_sha256": "7924f1d2acc7a8419ae1a70ef3a44e8d776fea32e4ca9141f857ef9b06bc331a"
        }
      ],
      "dependencies": [
        "P-PREDICT"
      ],
      "ledger_ids": []
    },
    {
      "id": "P-FLUX",
      "branch": "polarity",
      "title": "Fixed-K flux witness",
      "status": "SOURCE_DECLARED",
      "objects": "s_a=pi/12,s_b=pi/6",
      "conclusion": "Unchanged viable obligation gives zero index/budget; edge support rises by 3/8 (one pair 1/8).",
      "citations": [
        {
          "source_id": "E04",
          "section": "§4",
          "anchor_text": "EXACT fixed-K counterexample",
          "snapshot_sha256": "0243b70b3077ad58303ffad4f13d73fdc32bbe55fd204e52d2877c36318f4553"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "P-FLUX-NOGO",
      "branch": "polarity",
      "title": "Universal flux-index equality fails",
      "status": "EXACT_NO_GO",
      "objects": "signed support diagnostic versus integer index",
      "conclusion": "The witness disproves universal equality on this admitted domain. A diagnostic under a new restricted contract remains a separate possibility.",
      "citations": [
        {
          "source_id": "E04",
          "section": "§4",
          "anchor_text": "counterexample",
          "snapshot_sha256": "0243b70b3077ad58303ffad4f13d73fdc32bbe55fd204e52d2877c36318f4553"
        }
      ],
      "dependencies": [
        "P-FLUX"
      ],
      "ledger_ids": []
    },
    {
      "id": "A-UNIT",
      "branch": "action-scale",
      "title": "Typed action unit",
      "status": "SOURCE_DECLARED",
      "objects": "B0 masslike; a0 length; tau0 time",
      "conclusion": "A0=B0 a0²/tau0 has action dimensions. This definition supplies no measured value.",
      "citations": [
        {
          "source_id": "E11",
          "section": "§2",
          "anchor_text": "B_0",
          "snapshot_sha256": "2d41cee743acbaee4b7ae2101ee32a96c5eca8904bc1ff4ea12bd35c21065331"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "A-METRIC",
      "branch": "action-scale",
      "title": "Unit chain metric and active sector",
      "status": "SOURCE_DECLARED",
      "objects": "Filled K4, Euclidean norm, P2",
      "conclusion": "Fix the declared unit metric and active nonharmonic sector. Changing this carrier or metric requires rederiving its generator and action geometry.",
      "citations": [
        {
          "source_id": "C0579",
          "section": "Theorem / source anchors",
          "anchor_text": "Euclidean chain norm",
          "snapshot_sha256": "ef3bb744995b2cca8087c7ae1718a40a0526cbae314254b2a9ebc5ba6dce2fae"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "A-CARRIER",
      "branch": "action-scale",
      "title": "Single-cell spectral identity",
      "status": "SOURCE_DECLARED",
      "objects": "A^T=−A; A²=−4P2",
      "conclusion": "The active frequency is 2 in native parameter s; the harmonic component is static. This source-supplied finite identity is not independently reproofed here.",
      "citations": [
        {
          "source_id": "C0906",
          "section": "§1",
          "anchor_text": "Exact carrier",
          "snapshot_sha256": "4e5cdc41c1fd93f69b8d80aeb557f5cfdf8b3b335b320ef4b2028bc1b08c6739"
        }
      ],
      "dependencies": [
        "A-METRIC"
      ],
      "ledger_ids": []
    },
    {
      "id": "A-J",
      "branch": "action-scale",
      "title": "Active complex structure",
      "status": "EXACT_CONDITIONAL",
      "objects": "J=A/2; J²=−I",
      "conclusion": "The active restriction is an orthogonal complex structure; the induced symplectic convention is fixed by this norm.",
      "citations": [
        {
          "source_id": "C0579",
          "section": "Theorem",
          "anchor_text": "orthogonal complex structure",
          "snapshot_sha256": "ef3bb744995b2cca8087c7ae1718a40a0526cbae314254b2a9ebc5ba6dce2fae"
        }
      ],
      "dependencies": [
        "A-CARRIER"
      ],
      "ledger_ids": []
    },
    {
      "id": "A-PHASE",
      "branch": "action-scale",
      "title": "Lifted phase history",
      "status": "SOURCE_DECLARED",
      "objects": "a=||x||²; Delta phi tilde",
      "conclusion": "Retain winding in lifted phase, with phase rate 2 in native parameter. Endpoint phase modulo 2pi discards this history.",
      "citations": [
        {
          "source_id": "C0906",
          "section": "§§1,3",
          "anchor_text": "Endpoint phase alone",
          "snapshot_sha256": "4e5cdc41c1fd93f69b8d80aeb557f5cfdf8b3b335b320ef4b2028bc1b08c6739"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "A-ACTION",
      "branch": "action-scale",
      "title": "Single-sector lifted action",
      "status": "EXACT_CONDITIONAL",
      "objects": "I_Hodge=(a/2) Delta phi tilde",
      "conclusion": "With the declared symplectic normalization, accumulated native action is S=A0(a/2)Delta phi tilde. It varies continuously with support a.",
      "citations": [
        {
          "source_id": "C0906",
          "section": "§1",
          "anchor_text": "lifted Hodge action",
          "snapshot_sha256": "4e5cdc41c1fd93f69b8d80aeb557f5cfdf8b3b335b320ef4b2028bc1b08c6739"
        }
      ],
      "dependencies": [
        "A-J",
        "A-PHASE",
        "A-UNIT"
      ],
      "ledger_ids": [
        "O09"
      ]
    },
    {
      "id": "A-SCALE",
      "branch": "action-scale",
      "title": "Specific action-phase scale",
      "status": "EXACT_CONDITIONAL",
      "objects": "S/(a Delta phi tilde)=A0/2",
      "conclusion": "For a>0 and nonzero lifted phase, the ratio is independent of amplitude. It is not yet physical hbar.",
      "citations": [
        {
          "source_id": "C0906",
          "section": "§2",
          "anchor_text": "amplitude-independent",
          "snapshot_sha256": "4e5cdc41c1fd93f69b8d80aeb557f5cfdf8b3b335b320ef4b2028bc1b08c6739"
        }
      ],
      "dependencies": [
        "A-ACTION"
      ],
      "ledger_ids": []
    },
    {
      "id": "A-NORM",
      "branch": "action-scale",
      "title": "Normalized representative",
      "status": "CONVENTION",
      "objects": "a=1 on an explicitly normalized ray",
      "conclusion": "Normalizing a representative does not prove native support quantization or physical quantum identity.",
      "citations": [
        {
          "source_id": "C0906",
          "section": "§5",
          "anchor_text": "normalized representative",
          "snapshot_sha256": "4e5cdc41c1fd93f69b8d80aeb557f5cfdf8b3b335b320ef4b2028bc1b08c6739"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "A-REC",
      "branch": "action-scale",
      "title": "Normalized recurrence action",
      "status": "EXACT_CONDITIONAL",
      "objects": "Delta phi tilde=2pi; S=pi A0",
      "conclusion": "One single-cell recurrence has native interval pi; its normalized circulation is pi A0. This is not a universal glued-carrier recurrence.",
      "citations": [
        {
          "source_id": "C0906",
          "section": "§§3,5",
          "anchor_text": "One recurrence",
          "snapshot_sha256": "4e5cdc41c1fd93f69b8d80aeb557f5cfdf8b3b335b320ef4b2028bc1b08c6739"
        }
      ],
      "dependencies": [
        "A-ACTION",
        "A-NORM",
        "A-CARRIER"
      ],
      "ledger_ids": []
    },
    {
      "id": "A-END",
      "branch": "action-scale",
      "title": "Endpoint versus history comparison",
      "status": "SOURCE_DECLARED",
      "objects": "Same endpoint: zero winding and one winding",
      "conclusion": "Admit both a zero-duration history and a nonzero full-cycle active orbit at the same endpoint with a>0.",
      "citations": [
        {
          "source_id": "C0906",
          "section": "§3",
          "anchor_text": "2\\pi n\\equiv0",
          "snapshot_sha256": "4e5cdc41c1fd93f69b8d80aeb557f5cfdf8b3b335b320ef4b2028bc1b08c6739"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "A-END-NOGO",
      "branch": "action-scale",
      "title": "Endpoint-only accumulated action no-go",
      "status": "EXACT_NO_GO",
      "objects": "Endpoint defect delta(U) versus lifted action",
      "conclusion": "Zero winding has action 0; one full active winding has pi a A0 at the same endpoint. An endpoint-only scalar cannot encode both.",
      "citations": [
        {
          "source_id": "C0906",
          "section": "§3",
          "anchor_text": "generally nonzero",
          "snapshot_sha256": "4e5cdc41c1fd93f69b8d80aeb557f5cfdf8b3b335b320ef4b2028bc1b08c6739"
        }
      ],
      "dependencies": [
        "A-END",
        "A-ACTION"
      ],
      "ledger_ids": [
        "G05",
        "O09"
      ]
    },
    {
      "id": "A-G05",
      "branch": "action-scale",
      "title": "Universal scalar alias retired",
      "status": "RETIRED",
      "objects": "kappa_loop^master",
      "conclusion": "The ledger retires a universal scalar alias. A restricted alias needs a new sufficiency/proportionality and carrier-stability certificate.",
      "citations": [
        {
          "source_id": "L65",
          "section": "G05",
          "anchor_text": "RETIRED FROM MAINLINE AS UNIVERSAL SCALAR",
          "snapshot_sha256": "a74d3b63a68237b56a5e56221c8d17385f3b029ffaf2b82fde2b0ce71303ab14"
        }
      ],
      "dependencies": [],
      "ledger_ids": [
        "G05"
      ]
    },
    {
      "id": "A-ALG",
      "branch": "action-scale",
      "title": "Conditional scalar-family algebra",
      "status": "PRESERVED_CONDITIONAL",
      "objects": "Supplied scalar on a declared operator family",
      "conclusion": "Retiring a universal native alias does not invalidate algebra conditional on a supplied scalar. No specific scalar-family operator is reproofed in this graph.",
      "citations": [
        {
          "source_id": "REC02",
          "section": "ARA01",
          "anchor_text": "Conditional scalar-family algebra survives",
          "snapshot_sha256": "fc74e96093e5892a56e148e13fc4735fa3c49b206096282ada73d32e8e996cd9"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "A-CERT",
      "branch": "action-scale",
      "title": "Restricted scalar sufficiency certificate",
      "status": "OPEN",
      "objects": "Sufficient history compression; stable proportionality",
      "conclusion": "A declared compression must retain O09 history and have carrier-stable proportionality before any restricted native scalar identification.",
      "citations": [
        {
          "source_id": "L65",
          "section": "G05 next_gate",
          "anchor_text": "sufficient for O09",
          "snapshot_sha256": "a74d3b63a68237b56a5e56221c8d17385f3b029ffaf2b82fde2b0ce71303ab14"
        }
      ],
      "dependencies": [],
      "ledger_ids": [
        "G05",
        "O09"
      ]
    },
    {
      "id": "A-ALIAS",
      "branch": "action-scale",
      "title": "Restricted native scalar identification",
      "status": "OPEN",
      "objects": "Declared restricted domain only",
      "conclusion": "This conditional reopening route needs both valid scalar-family algebra and the separate sufficiency certificate. It does not revive the universal alias.",
      "citations": [
        {
          "source_id": "L65",
          "section": "G05",
          "anchor_text": "restricted scalar aliases",
          "snapshot_sha256": "a74d3b63a68237b56a5e56221c8d17385f3b029ffaf2b82fde2b0ce71303ab14"
        }
      ],
      "dependencies": [
        "A-ALG",
        "A-CERT"
      ],
      "ledger_ids": [
        "G05"
      ]
    },
    {
      "id": "A-ETA",
      "branch": "action-scale",
      "title": "Unambiguous current ratio",
      "status": "SOURCE_DECLARED",
      "objects": "eta_A=A0/hbar",
      "conclusion": "Current ratio direction is A0/hbar. Historical bare xi_hbar used reciprocal conventions and must remain typed.",
      "citations": [
        {
          "source_id": "L65",
          "section": "G06",
          "anchor_text": "current canonical ratio is eta_A=A0/hbar",
          "snapshot_sha256": "a74d3b63a68237b56a5e56221c8d17385f3b029ffaf2b82fde2b0ce71303ab14"
        }
      ],
      "dependencies": [
        "A-UNIT"
      ],
      "ledger_ids": [
        "G06"
      ]
    },
    {
      "id": "A-QPB",
      "branch": "action-scale",
      "title": "QPB-1 physical correspondence candidate",
      "status": "CANDIDATE",
      "objects": "Physical hbar=A0/2; eta_A=2",
      "conclusion": "Identifying the specific native action-phase scale with physical hbar is a candidate correspondence, not a theorem from internal geometry.",
      "citations": [
        {
          "source_id": "C0883",
          "section": "Frozen prediction",
          "anchor_text": "Frozen prediction",
          "snapshot_sha256": "29442a9bedd0beafa14abc1b56a89077d0ebb1a25541441ae6e23fdcf09bd50a"
        }
      ],
      "dependencies": [
        "A-SCALE",
        "A-ETA"
      ],
      "ledger_ids": []
    },
    {
      "id": "A-ANCHOR",
      "branch": "action-scale",
      "title": "Independent physical A0 anchor",
      "status": "OPEN",
      "objects": "Physical A0, source-derived uncertainty",
      "conclusion": "Freeze an independently constructed action anchor excluding hbar, h, Planck units, known action targets and fitting to 2. No such data is supplied here.",
      "citations": [
        {
          "source_id": "C0883",
          "section": "Lawful future test",
          "anchor_text": "independently constructed physical",
          "snapshot_sha256": "29442a9bedd0beafa14abc1b56a89077d0ebb1a25541441ae6e23fdcf09bd50a"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "A-QPB-TEST",
      "branch": "action-scale",
      "title": "Prospective QPB-1 comparison",
      "status": "OPEN",
      "objects": "eta_obs=A0_indep/hbar",
      "conclusion": "Only after freezing the independent anchor compare with 2 under source-derived uncertainty; PASS, FAIL, indeterminate and invalid-source are distinct verdicts.",
      "citations": [
        {
          "source_id": "C0883",
          "section": "Verdicts",
          "anchor_text": "QPB1_FAIL",
          "snapshot_sha256": "29442a9bedd0beafa14abc1b56a89077d0ebb1a25541441ae6e23fdcf09bd50a"
        }
      ],
      "dependencies": [
        "A-QPB",
        "A-ANCHOR"
      ],
      "ledger_ids": []
    },
    {
      "id": "A-SPEED",
      "branch": "action-scale",
      "title": "Speed/action identities",
      "status": "EXACT_CONDITIONAL",
      "objects": "c_speed=a0/tau0; A0=B0 c_speed² tau0",
      "conclusion": "Even fixed A0 and c_speed determine B0 tau0, not B0 and tau0 separately.",
      "citations": [
        {
          "source_id": "E11",
          "section": "§2",
          "anchor_text": "c",
          "snapshot_sha256": "2d41cee743acbaee4b7ae2101ee32a96c5eca8904bc1ff4ea12bd35c21065331"
        }
      ],
      "dependencies": [
        "A-UNIT"
      ],
      "ledger_ids": []
    },
    {
      "id": "A-GAUGE",
      "branch": "action-scale",
      "title": "Physical clock scale gauge",
      "status": "EXACT_CONDITIONAL",
      "objects": "lambda>0",
      "conclusion": "(a0,tau0,B0)→(lambda a0,lambda tau0,B0/lambda) fixes speed and action, while physical frequency scales as 1/lambda and G_SI as lambda².",
      "citations": [
        {
          "source_id": "E11",
          "section": "§§3–4",
          "anchor_text": "Scale-gauge theorem",
          "snapshot_sha256": "2d41cee743acbaee4b7ae2101ee32a96c5eca8904bc1ff4ea12bd35c21065331"
        }
      ],
      "dependencies": [
        "A-SPEED"
      ],
      "ledger_ids": []
    },
    {
      "id": "A-ANCHOR-NOGO",
      "branch": "action-scale",
      "title": "Action anchor alone cannot set seconds",
      "status": "EXACT_NO_GO",
      "objects": "A0 invariant under lambda",
      "conclusion": "An independent action anchor can test eta_A but is invariant under the residual clock gauge. It cannot alone identify absolute tau0. This is an explicit algebraic consequence of E11.",
      "citations": [
        {
          "source_id": "E11",
          "section": "§§3,9",
          "anchor_text": "What can break the scale gauge?",
          "snapshot_sha256": "2d41cee743acbaee4b7ae2101ee32a96c5eca8904bc1ff4ea12bd35c21065331"
        }
      ],
      "dependencies": [
        "A-GAUGE"
      ],
      "ledger_ids": []
    },
    {
      "id": "A-CLOCK-ANCHOR",
      "branch": "action-scale",
      "title": "Independent scale-sensitive anchor",
      "status": "OPEN",
      "objects": "Identified mass, length or time observable",
      "conclusion": "Supply a lawful physical observable that changes under lambda, an independently identified carrier and a unique map to native units. Merely supplying A0 or a dimensionless ratio is insufficient.",
      "citations": [
        {
          "source_id": "E11",
          "section": "§9",
          "anchor_text": "What can break the scale gauge?",
          "snapshot_sha256": "2d41cee743acbaee4b7ae2101ee32a96c5eca8904bc1ff4ea12bd35c21065331"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "A-CLOCK",
      "branch": "action-scale",
      "title": "Absolute physical clock",
      "status": "OPEN",
      "objects": "tau0 in seconds",
      "conclusion": "Absolute seconds require a source-complete, scale-sensitive physical correspondence. Native period pi or event coordinate 3/4 is not that anchor.",
      "citations": [
        {
          "source_id": "E11",
          "section": "§§5,8–9",
          "anchor_text": "Strongest lawful clock bridge",
          "snapshot_sha256": "2d41cee743acbaee4b7ae2101ee32a96c5eca8904bc1ff4ea12bd35c21065331"
        }
      ],
      "dependencies": [
        "A-CLOCK-ANCHOR",
        "A-GAUGE"
      ],
      "ledger_ids": []
    },
    {
      "id": "G-HISTORY",
      "branch": "action-scale",
      "title": "Same local canonical history",
      "status": "CONSTITUTIVE_PREMISE",
      "objects": "Genesis and Hodge active local plane",
      "conclusion": "Assume the typed GH-1 balanced coordinate map represents the same local canonical history. c_bridge is a coordinate normalization, distinct from c_speed.",
      "citations": [
        {
          "source_id": "E13",
          "section": "§§4–5",
          "anchor_text": "same local canonical history",
          "snapshot_sha256": "909a193d046ea7e560bc83f044cb942c74a39f93ac929a6486073d0792cf8082"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "G-STATIONARY",
      "branch": "action-scale",
      "title": "Stationary Genesis local carrier",
      "status": "CONSTITUTIVE_PREMISE",
      "objects": "omega_G constant locally",
      "conclusion": "Use a locally stationary harmonic Genesis mode and its declared historical action/time units hbar_d,tau_d; neither is identified with physical hbar or seconds.",
      "citations": [
        {
          "source_id": "E13",
          "section": "§§1–3",
          "anchor_text": "locally stationary Genesis",
          "snapshot_sha256": "909a193d046ea7e560bc83f044cb942c74a39f93ac929a6486073d0792cf8082"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "G-EVENT",
      "branch": "action-scale",
      "title": "GH-2 active event geometry",
      "status": "SOURCE_DECLARED",
      "objects": "delta_H²=(3/4)c_bridge² Delta a_G²",
      "conclusion": "The active event length is a typed source object, not an independently fixed physical length.",
      "citations": [
        {
          "source_id": "E13",
          "section": "§6",
          "anchor_text": "exact GH-2 event geometry",
          "snapshot_sha256": "909a193d046ea7e560bc83f044cb942c74a39f93ac929a6486073d0792cf8082"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "G-LOCAL",
      "branch": "action-scale",
      "title": "Conditional Genesis–Hodge ratios",
      "status": "EXACT_CONDITIONAL",
      "objects": "A0/hbar_d=3omega_G/(4delta_H²); tau0/tau_d=2/omega_G",
      "conclusion": "The product is 3/(2delta_H²). Local harmonic action areas and recurrence periods match under the same-history canonical intertwiner. No absolute units follow.",
      "citations": [
        {
          "source_id": "E13",
          "section": "§§5–11",
          "anchor_text": "Conditional canonical identity theorem",
          "snapshot_sha256": "909a193d046ea7e560bc83f044cb942c74a39f93ac929a6486073d0792cf8082"
        }
      ],
      "dependencies": [
        "G-HISTORY",
        "G-STATIONARY",
        "G-EVENT",
        "A-J",
        "A-UNIT"
      ],
      "ledger_ids": []
    },
    {
      "id": "G-VARY",
      "branch": "action-scale",
      "title": "Nonstationary history domain",
      "status": "DOMAIN_PREMISE",
      "objects": "omega_G(t) assumes unequal values",
      "conclusion": "The no-go is conditional on a history with varying local frequency; it does not assert every Genesis history is nonstationary.",
      "citations": [
        {
          "source_id": "E13",
          "section": "§12",
          "anchor_text": "omega_G(t)",
          "snapshot_sha256": "909a193d046ea7e560bc83f044cb942c74a39f93ac929a6486073d0792cf8082"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "G-CONST",
      "branch": "action-scale",
      "title": "Constant unit-ratio requirement",
      "status": "DOMAIN_PREMISE",
      "objects": "One constant tau0/tau_d across the whole history",
      "conclusion": "A proposed global identification uses one constant ratio rather than a newly supplied varying clock law.",
      "citations": [
        {
          "source_id": "E13",
          "section": "§12",
          "anchor_text": "single constant ratio",
          "snapshot_sha256": "909a193d046ea7e560bc83f044cb942c74a39f93ac929a6486073d0792cf8082"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "G-GLOBAL-NOGO",
      "branch": "action-scale",
      "title": "Nonstationary global clock no-go",
      "status": "EXACT_NO_GO",
      "objects": "omega_G(t) varying; constant unit ratio",
      "conclusion": "One constant tau0/tau_d cannot equal 2/omega_G(t) at all times if the historical frequency varies. A new stationary/effective-clock theorem would be needed.",
      "citations": [
        {
          "source_id": "E13",
          "section": "§12",
          "anchor_text": "single constant ratio",
          "snapshot_sha256": "909a193d046ea7e560bc83f044cb942c74a39f93ac929a6486073d0792cf8082"
        }
      ],
      "dependencies": [
        "G-VARY",
        "G-CONST"
      ],
      "ledger_ids": []
    },
    {
      "id": "R-I",
      "branch": "polarity",
      "title": "Intact-null potential domain",
      "status": "SOURCE_DECLARED",
      "objects": "I=T AND NOT L; i=|I|",
      "conclusion": "I marks potential idle response addresses; h is the actual response. Prospective T,L must be independently sourced.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§1",
          "anchor_text": "I is the intact-null potential mask",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
        }
      ],
      "dependencies": [
        "P-ADM"
      ],
      "ledger_ids": []
    },
    {
      "id": "R-FIBER",
      "branch": "polarity",
      "title": "Exact response fiber",
      "status": "EXACT_CONDITIONAL",
      "objects": "q=omega+h; h≤I",
      "conclusion": "Every admitted response corresponds to one subset of I. There are exactly 2^i responses.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§2",
          "anchor_text": "response fiber has exactly 2^i",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
        }
      ],
      "dependencies": [
        "R-I",
        "P-IDLE"
      ],
      "ledger_ids": []
    },
    {
      "id": "R-COUNT",
      "branch": "polarity",
      "title": "Count-conditioned address fiber",
      "status": "EXACT_CONDITIONAL",
      "objects": "|h|=j; binomial(i,j)",
      "conclusion": "An independently sourced idle count fixes a budget but generally leaves binomial(i,j) address masks.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§§2–3",
          "anchor_text": "binomial(i,j)",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
        }
      ],
      "dependencies": [
        "R-FIBER",
        "P-CORRECT"
      ],
      "ledger_ids": []
    },
    {
      "id": "R-REDUCED",
      "branch": "polarity",
      "title": "Reduced equivariant rule domain",
      "status": "DOMAIN_PREMISE",
      "objects": "Only (T,L); all pair-permutation equivariance",
      "conclusion": "These symmetry conclusions apply to a rule with no additional distinguishing pre-event state. Extra burdens, memory or source receipts require a larger declared carrier.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§4",
          "anchor_text": "using only (T,L)",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
        }
      ],
      "dependencies": [
        "R-I"
      ],
      "ledger_ids": []
    },
    {
      "id": "R-DETERMINISTIC",
      "branch": "polarity",
      "title": "Reduced deterministic selector restriction",
      "status": "EXACT_CONDITIONAL",
      "objects": "h=0 or h=I",
      "conclusion": "For a deterministic equivariant selector based only on (T,L), the intact-null stabilizer forces a constant mask. Intermediate j cannot be selected for i≥2.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§4",
          "anchor_text": "must be constant",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
        }
      ],
      "dependencies": [
        "R-FIBER",
        "R-REDUCED"
      ],
      "ledger_ids": []
    },
    {
      "id": "R-KERNEL",
      "branch": "polarity",
      "title": "Invariant stochastic response kernels",
      "status": "EXACT_CONDITIONAL",
      "objects": "P(h)=p_j/binomial(i,j), j=|h|",
      "conclusion": "Invariant kernels have i+1 cardinality-orbit weights summing to 1. Symmetry leaves i free probability parameters. It does not set an event rate.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§4",
          "anchor_text": "one probability p_j",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
        }
      ],
      "dependencies": [
        "R-FIBER",
        "R-REDUCED"
      ],
      "ledger_ids": []
    },
    {
      "id": "R-UNIQUE-NOGO",
      "branch": "polarity",
      "title": "Admission does not select a response law",
      "status": "EXACT_NO_GO",
      "objects": "i>0; h=0 versus h=I",
      "conclusion": "Two admitted equivariant responses share the same reduced (T,L) but have budgets differing by i. This is finite-domain underidentification, not a physical realization claim.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§3",
          "anchor_text": "both h=000 and h=I",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
        }
      ],
      "dependencies": [
        "R-FIBER",
        "P-CORRECT"
      ],
      "ledger_ids": []
    },
    {
      "id": "R-PACKET",
      "branch": "polarity",
      "title": "Source-complete prospective packet",
      "status": "OPEN",
      "objects": "Independent prospective viability, idle choice, frame and event/null program",
      "conclusion": "The contract narrows the missing source objects and supplies a structural validator. It does not generate a native packet or establish eligible scorer custody.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§5",
          "anchor_text": "complete prospective packet",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
        }
      ],
      "dependencies": [
        "R-COUNT",
        "P-SOURCE",
        "P-HSOURCE",
        "P-FRAME"
      ],
      "ledger_ids": []
    },
    {
      "id": "SP-STATE",
      "branch": "polarity",
      "title": "RSP-1 prepared finite carrier",
      "status": "CANDIDATE",
      "objects": "T,L_cache,q,r,finite bank,cursor,frozen branch",
      "conclusion": "Fixed integrity and labeled identity frame; admitted prior cache independent of current stock. Tokens have no HD/physical identification.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§2",
          "anchor_text": "Complete prepared state",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "SP-DRIVE",
      "branch": "polarity",
      "title": "Demand-inhibited stock source",
      "status": "CANDIDATE",
      "objects": "L+=T 1[r>0](1−q_old), r+=r−omega+",
      "conclusion": "The chosen generator produces prospective source masks from the complete prepared state. It is a new source-interface completion.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§3",
          "anchor_text": "demand-inhibited",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ],
      "dependencies": [
        "SP-STATE"
      ],
      "ledger_ids": []
    },
    {
      "id": "SP-CLOSE",
      "branch": "polarity",
      "title": "Close-on-idle candidate branch",
      "status": "CANDIDATE",
      "objects": "q+=T+L+, h+=0",
      "conclusion": "The source C map is lawful on supplied prospective masks; its adoption in RSP-1 is a frozen candidate choice.",
      "citations": [
        {
          "source_id": "C0593",
          "section": "Close-vs-Hold theorem",
          "anchor_text": "C(q^-,T^+,L^+)",
          "snapshot_sha256": "a6843a3c799ea1b408f13fe5c2a594c906778c60a28de756fe2a1658890a3163"
        }
      ],
      "dependencies": [
        "SP-DRIVE"
      ],
      "ledger_ids": []
    },
    {
      "id": "SP-HOLD",
      "branch": "polarity",
      "title": "Hold-open candidate branch",
      "status": "CANDIDATE",
      "objects": "q+=omega+ OR(T q_old); h+=I+ q_old",
      "conclusion": "The source H map is lawful and uses the current intact-null domain. It is not selected natively.",
      "citations": [
        {
          "source_id": "C0593",
          "section": "Close-vs-Hold theorem",
          "anchor_text": "H(q^-,T^+,L^+)",
          "snapshot_sha256": "a6843a3c799ea1b408f13fe5c2a594c906778c60a28de756fe2a1658890a3163"
        }
      ],
      "dependencies": [
        "SP-DRIVE",
        "SP-STATE"
      ],
      "ledger_ids": []
    },
    {
      "id": "SP-BANK",
      "branch": "polarity",
      "title": "Finite preloaded renewal rule",
      "status": "CANDIDATE",
      "objects": "quiescent load + cursor advance",
      "conclusion": "At r=q=L_cache=0 load one prepared packet. Zero packets advance the cursor. This is prepared supply, not endogenous production.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§3",
          "anchor_text": "RENEWAL_ONLY",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ],
      "dependencies": [
        "SP-STATE"
      ],
      "ledger_ids": []
    },
    {
      "id": "SP-STOP",
      "branch": "polarity",
      "title": "Full-state commit and stopping rule",
      "status": "CANDIDATE",
      "objects": "Commit hidden null changes; HALT iff X+=X",
      "conclusion": "Response-null and zero net budget do not justify stopping. Exhaustion and latching/stranding are separate model outcomes.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§4",
          "anchor_text": "complete successor X+ equals X",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ],
      "dependencies": [
        "SP-STATE",
        "SP-BANK"
      ],
      "ledger_ids": []
    },
    {
      "id": "SP-STOCK",
      "branch": "polarity",
      "title": "Exact token-accounting law",
      "status": "EXACT_CONDITIONAL",
      "objects": "S=active stock + unspent bank",
      "conclusion": "Renewal preserves S and inspection consumes exactly |omega+|. This counts prepared tokens, not joules or chain support.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§5",
          "anchor_text": "Renewal preserves S",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ],
      "dependencies": [
        "SP-DRIVE",
        "SP-BANK"
      ],
      "ledger_ids": []
    },
    {
      "id": "SP-TERM",
      "branch": "polarity",
      "title": "Strict potential and finite termination",
      "status": "EXACT_CONDITIONAL",
      "objects": "V=4S+2|q|+|L_cache|+(B−k)",
      "conclusion": "Every committed tick strictly reduces the integer potential for either frozen branch. The episode reaches a full model fixed point within V_initial changes.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§5",
          "anchor_text": "Every committed tick strictly decreases V",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ],
      "dependencies": [
        "SP-STOCK",
        "SP-CLOSE",
        "SP-HOLD",
        "SP-STOP"
      ],
      "ledger_ids": []
    },
    {
      "id": "SP-C-DURATION",
      "branch": "polarity",
      "title": "Exact close duration and pulse balance",
      "status": "EXACT_CONDITIONAL",
      "objects": "D_C=D0+(B−k)+2sum max b",
      "conclusion": "C spends all prepared stock; openings=S_initial and closures=S_initial+|q_initial|. Includes broken-cache cleanup and zero refills.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§6",
          "anchor_text": "exact number of committed C ticks",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ],
      "dependencies": [
        "SP-CLOSE",
        "SP-DRIVE",
        "SP-BANK",
        "SP-STOP"
      ],
      "ledger_ids": []
    },
    {
      "id": "SP-H-LATCH",
      "branch": "polarity",
      "title": "Hold-branch finite latch bound",
      "status": "EXACT_CONDITIONAL",
      "objects": "D_H≤(B−k)+2+delta",
      "conclusion": "H can latch with unused active and queued stock. The C exhaustion theorem cannot be reused for H.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§7",
          "anchor_text": "H never closes",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ],
      "dependencies": [
        "SP-HOLD",
        "SP-DRIVE",
        "SP-BANK",
        "SP-STOP"
      ],
      "ledger_ids": []
    },
    {
      "id": "SP-PROJECTION",
      "branch": "polarity",
      "title": "Theta-only RSP source no-go",
      "status": "EXACT_NO_GO",
      "objects": "Same q,L,T; different hidden r",
      "conclusion": "The candidate is deterministic on its complete state; its Theta-only projection can give different next endpoints. This does not identify native hidden variables.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§7",
          "anchor_text": "projection onto Theta alone",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ],
      "dependencies": [
        "SP-STATE",
        "SP-DRIVE",
        "SP-CLOSE"
      ],
      "ledger_ids": []
    },
    {
      "id": "SP-HD-BRIDGE",
      "branch": "polarity",
      "title": "HD-to-RSP realization",
      "status": "OPEN",
      "objects": "R^(HD), edge transport versus R^(RSP), fixed flags",
      "conclusion": "A source-authenticated carrier/observable map or obstruction theorem is needed before attributing programme outputs to native UD.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§8",
          "anchor_text": "no proved identification",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ],
      "dependencies": [
        "SP-STATE",
        "SP-DRIVE"
      ],
      "ledger_ids": []
    },
    {
      "id": "HR-EXACT",
      "branch": "polarity",
      "title": "Exact complete-state realization contract",
      "status": "DOMAIN_PREMISE",
      "objects": "phi U=F phi on declared D",
      "conclusion": "A state-only decoder includes resource, cache, bank/cursor and branch. Theta-only agreement is weaker.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§1",
          "anchor_text": "complete RSP successor",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "HR-SURJ",
      "branch": "polarity",
      "title": "Two-sided invariant source domain",
      "status": "DOMAIN_PREMISE",
      "objects": "U:D→D surjective",
      "conclusion": "A closed Hodge step is invertible on a two-sided invariant carrier or norm sphere. A forward initialization restriction can fail surjectivity.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§2",
          "anchor_text": "U is surjective",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "HR-FINITE",
      "branch": "polarity",
      "title": "Finite decoded preparation",
      "status": "DOMAIN_PREMISE",
      "objects": "phi(D) finite",
      "conclusion": "Fix a bounded finite RSP prepared register family; arbitrary unbounded preparations need a separate contract.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§§2–3",
          "anchor_text": "decoded image M=phi(D) is finite",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ],
      "dependencies": [
        "SP-STATE"
      ],
      "ledger_ids": []
    },
    {
      "id": "HR-FINITE-NOGO",
      "branch": "polarity",
      "title": "Reversible finite-factor obstruction",
      "status": "EXACT_NO_GO",
      "objects": "phi(D)⊂Fix F",
      "conclusion": "A surjective source makes F surjective on its finite image; strict target descent permits only fixed cycles. No continuity or common period is required.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§2",
          "anchor_text": "A surjective map on a finite set",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ],
      "dependencies": [
        "HR-EXACT",
        "HR-SURJ",
        "HR-FINITE",
        "SP-TERM"
      ],
      "ledger_ids": []
    },
    {
      "id": "HR-UNIFORM",
      "branch": "polarity",
      "title": "Common finite settling bound",
      "status": "DOMAIN_PREMISE",
      "objects": "One N across phi(D)",
      "conclusion": "This may replace finite image, but unbounded stock/bank preparations do not necessarily have one common bound.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§3",
          "anchor_text": "common finite settling bound",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "HR-UNIFORM-NOGO",
      "branch": "polarity",
      "title": "Uniform-settling factor obstruction",
      "status": "EXACT_NO_GO",
      "objects": "Every decoded state is fixed",
      "conclusion": "Surjectivity and F^N(phi(D))=phi(D) force fixed image when the whole image settles uniformly.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§3",
          "anchor_text": "Finite image can be replaced",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ],
      "dependencies": [
        "HR-EXACT",
        "HR-SURJ",
        "HR-UNIFORM"
      ],
      "ledger_ids": []
    },
    {
      "id": "HR-PERIOD",
      "branch": "polarity",
      "title": "Finite-order source sample",
      "status": "DOMAIN_PREMISE",
      "objects": "U^m=id",
      "conclusion": "Rational delta/pi gives finite order on unit-metric filled K4. The sampling interval remains a declared internal choice.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§4",
          "anchor_text": "U^m=id",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "HR-PERIOD-NOGO",
      "branch": "polarity",
      "title": "Finite-order absorbing-factor obstruction",
      "status": "EXACT_NO_GO",
      "objects": "Periodic decoded target states must be fixed",
      "conclusion": "This needs neither finite image nor continuity: exact periodicity plus strict descent excludes all nonfixed decoded points.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§4",
          "anchor_text": "F^m(phi(x))=phi(x)",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ],
      "dependencies": [
        "HR-EXACT",
        "HR-PERIOD",
        "SP-TERM"
      ],
      "ledger_ids": []
    },
    {
      "id": "HR-SKEW",
      "branch": "polarity",
      "title": "Declared closed skew Hodge flow",
      "status": "SOURCE_DECLARED",
      "objects": "U_delta=exp(delta A), A^T=−A",
      "conclusion": "The fixed-complex finite generator conserves norm and gives reversible orthogonal samples. No physical energy or native event clock follows.",
      "citations": [
        {
          "source_id": "PI",
          "section": "T4.3",
          "anchor_text": "standard skew-flow conservation",
          "snapshot_sha256": "23a62d17d88076589e4904973c166e086c03352629e620913e4bb3897eb275ab"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "HR-RECURRENCE",
      "branch": "polarity",
      "title": "Forward recurrence of closed samples",
      "status": "EXACT_CONDITIONAL",
      "objects": "Arbitrarily late U^n x→x",
      "conclusion": "A finite spectral torus has simultaneous phase returns. Irrational glued frequencies remove a common exact period, not approximate recurrence.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§5",
          "anchor_text": "Simultaneous phase approximation",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ],
      "dependencies": [
        "HR-SKEW"
      ],
      "ledger_ids": []
    },
    {
      "id": "HR-STABLE",
      "branch": "polarity",
      "title": "Stable complete-state decoding",
      "status": "DOMAIN_PREMISE",
      "objects": "Near returns decode to the same complete state",
      "conclusion": "Local constancy or continuity into a discrete register carrier suffices. Exact-zero positivity gates need not satisfy this at boundary points.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§5",
          "anchor_text": "return-stable at x",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "HR-ROBUST-NOGO",
      "branch": "polarity",
      "title": "Recurrent robust-factor obstruction",
      "status": "EXACT_NO_GO",
      "objects": "Only fixed decoded initial state",
      "conclusion": "Exact intertwining and stable recurrence conflict with any irreversible drop of the RSP ranking potential.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§5",
          "anchor_text": "contradicting exact intertwining",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ],
      "dependencies": [
        "HR-EXACT",
        "HR-RECURRENCE",
        "HR-STABLE",
        "SP-TERM"
      ],
      "ledger_ids": []
    },
    {
      "id": "HR-NORM-ID",
      "branch": "polarity",
      "title": "Stock/total-norm identification",
      "status": "DOMAIN_PREMISE",
      "objects": "S_RSP=g(c^T c)",
      "conclusion": "This is an additional proposed bridge, not a source theorem; local readouts can vary even when total norm does not.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§6",
          "anchor_text": "specifically identified",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "HR-NORM-NOGO",
      "branch": "polarity",
      "title": "Conserved-stock alias excludes consumption",
      "status": "EXACT_NO_GO",
      "objects": "No change of a conserved total-norm stock alias",
      "conclusion": "Only the stated conserved-observable identification is blocked on consuming ticks. No universal decoder impossibility follows from norm alone.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§6",
          "anchor_text": "forbids a token-consuming inspection",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ],
      "dependencies": [
        "HR-NORM-ID",
        "HR-SKEW",
        "SP-STOCK",
        "HR-EXACT"
      ],
      "ledger_ids": []
    },
    {
      "id": "HR-WINDOW",
      "branch": "polarity",
      "title": "Prepared finite lookup window",
      "status": "CANDIDATE",
      "objects": "Distinct native samples; lookup chosen from RSP trace",
      "conclusion": "A selected trajectory can be encoded before wrap. Decoder selection, preparation, clock and capture are additional source debts.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§7",
          "anchor_text": "PREPARED lookup",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "HR-WRAP",
      "branch": "polarity",
      "title": "Exact quarter-turn wrap failure",
      "status": "EXACT_CONDITIONAL",
      "objects": "v→u→−v→−u→v; decoded s0,s1,s2,s2",
      "conclusion": "Both branch lookups match three edges and fail at the fourth. This validates a window encoding and refutes its global absorbing-factor extension.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§7",
          "anchor_text": "The first three native transitions",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ],
      "dependencies": [
        "HR-WINDOW",
        "HR-SKEW",
        "A-CARRIER",
        "SP-DRIVE",
        "SP-TERM"
      ],
      "ledger_ids": []
    },
    {
      "id": "HR-LATENT",
      "branch": "polarity",
      "title": "Original HD instantaneous latent witness",
      "status": "SOURCE_DECLARED",
      "objects": "R_e=c1,e²(c0,i²+c0,j²); L_p=1[sum R_e>0]",
      "conclusion": "This chain-polynomial positivity receipt is distinct from the prepared RSP stock/cache source.",
      "citations": [
        {
          "source_id": "C0926",
          "section": "§4.6",
          "anchor_text": "R_e=c_{1,e}^2",
          "snapshot_sha256": "6927d2f2871f280bcf6f5740e7cc8407225f0e21f734f809c97bdc32846e514c"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "HR-LATENT-MISMATCH",
      "branch": "polarity",
      "title": "Direct HD latent alias fails in the lookup",
      "status": "EXACT_CONDITIONAL",
      "objects": "All quarter samples have L_HD=000; phi(u) cache L=100",
      "conclusion": "Directly identifying cached L with the instantaneous original HD witness does not reproduce this prepared first update. This says nothing about a separately sourced history/coupling map.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§7",
          "anchor_text": "lookup is also distinct",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ],
      "dependencies": [
        "HR-LATENT",
        "HR-WINDOW",
        "A-CARRIER"
      ],
      "ledger_ids": []
    },
    {
      "id": "JC-MAP",
      "branch": "polarity",
      "title": "Total encoded target and receipt tables",
      "status": "DOMAIN_PREMISE",
      "objects": "Finite S; e:S↔Z_d; f total; rho:Z_d→Z_m",
      "conclusion": "Complete states and deterministic receipts are supplied, with no modular label holes. The example compiles one RSP trajectory closure.",
      "citations": [
        {
          "source_id": "JC01",
          "section": "§1",
          "anchor_text": "Every modular label",
          "snapshot_sha256": "d2642a6d5f03986e83cc6ab47198de289769fd3204c26e5b903ba3a81b52b911"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "JC-TAPS",
      "branch": "polarity",
      "title": "Fresh per-tick state and receipt taps",
      "status": "DOMAIN_PREMISE",
      "objects": "H_i=0,R_i=0 at first use",
      "conclusion": "Freshness is a complete prepared resource hypothesis. A work reset alone does not clear history or receipts.",
      "citations": [
        {
          "source_id": "JC01",
          "section": "§3",
          "anchor_text": "For a fresh tap",
          "snapshot_sha256": "d2642a6d5f03986e83cc6ab47198de289769fd3204c26e5b903ba3a81b52b911"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "JC-BANK",
      "branch": "polarity",
      "title": "Finite independent complete donor bank",
      "status": "CANDIDATE",
      "objects": "B payloads p*; active p*; clock0",
      "conclusion": "Donors supply the full work/history/record payload. Whole-bank freshness and independence cannot be replaced by good marginals.",
      "citations": [
        {
          "source_id": "JC01",
          "section": "§2",
          "anchor_text": "B independent donors",
          "snapshot_sha256": "d2642a6d5f03986e83cc6ab47198de289769fd3204c26e5b903ba3a81b52b911"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "JC-SCHEDULE",
      "branch": "polarity",
      "title": "Supplied finite master-clock schedule",
      "status": "CANDIDATE",
      "objects": "L=(B+1)(N+1), N compute slots then reset address",
      "conclusion": "Clock contains episode and donor-selection state. It advances across payload resets and wraps after the declared window.",
      "citations": [
        {
          "source_id": "JC01",
          "section": "§4",
          "anchor_text": "one fixed joint operator",
          "snapshot_sha256": "d2642a6d5f03986e83cc6ab47198de289769fd3204c26e5b903ba3a81b52b911"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "JC-GATE",
      "branch": "polarity",
      "title": "Explicit reversible successor/history/receipt gate",
      "status": "EXACT_CONDITIONAL",
      "objects": "G_i(w,h,r)=(h+f(w),w,r+rho(w))",
      "conclusion": "The inverse recovers old work from new history, so a noninjective target map still has an exact joint permutation.",
      "citations": [
        {
          "source_id": "JC01",
          "section": "§3",
          "anchor_text": "Its explicit inverse",
          "snapshot_sha256": "d2642a6d5f03986e83cc6ab47198de289769fd3204c26e5b903ba3a81b52b911"
        }
      ],
      "dependencies": [
        "JC-MAP"
      ],
      "ledger_ids": []
    },
    {
      "id": "JC-U",
      "branch": "polarity",
      "title": "One globally reversible joint step",
      "status": "EXACT_CONDITIONAL",
      "objects": "Controlled G_i/SWAP/id followed by cyclic clock shift",
      "conclusion": "Inverse decrements the clock and applies the corresponding inverse block. Valid on dirty configurations as well as preparations.",
      "citations": [
        {
          "source_id": "JC01",
          "section": "§4",
          "anchor_text": "The inverse first decrements",
          "snapshot_sha256": "d2642a6d5f03986e83cc6ab47198de289769fd3204c26e5b903ba3a81b52b911"
        }
      ],
      "dependencies": [
        "JC-GATE",
        "JC-SCHEDULE"
      ],
      "ledger_ids": []
    },
    {
      "id": "JC-WINDOW",
      "branch": "polarity",
      "title": "Exact finite-window target reproduction",
      "status": "EXACT_CONDITIONAL",
      "objects": "K=L−1=(B+1)N+B; work=f^k(0)",
      "conclusion": "B+1 episodes each use N fresh taps. B swaps export full old payloads and introduce untouched donors. No wrap enters the theorem.",
      "citations": [
        {
          "source_id": "JC01",
          "section": "§5",
          "anchor_text": "Theorem JC.1",
          "snapshot_sha256": "d2642a6d5f03986e83cc6ab47198de289769fd3204c26e5b903ba3a81b52b911"
        }
      ],
      "dependencies": [
        "JC-U",
        "JC-TAPS",
        "JC-BANK",
        "JC-SCHEDULE"
      ],
      "ledger_ids": []
    },
    {
      "id": "JC-PIV-EXPORT",
      "branch": "polarity",
      "title": "Primary complete correlation-export identity",
      "status": "SOURCE_DECLARED",
      "objects": "SWAP_AD(rho_AY⊗sigma_D)=sigma_A⊗rho_DY",
      "conclusion": "Paper IV supplies the matched-register identity with independent complete donor. Physical energy matching is a separate premise.",
      "citations": [
        {
          "source_id": "PIV",
          "section": "§8.1 IV.12",
          "anchor_text": "Every old $A/Y$ correlation",
          "snapshot_sha256": "18ba71180c42249dda68d6649552c44f78fa8819e84ace7c9c54e7818f4287d8"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "JC-EXPORT",
      "branch": "polarity",
      "title": "Outgoing records retain old correlations",
      "status": "EXACT_CONDITIONAL",
      "objects": "Consumed D_j becomes complete outgoing payload",
      "conclusion": "Old work, histories, records and spectator correlations are exported by SWAP; no discard or success conditioning.",
      "citations": [
        {
          "source_id": "JC01",
          "section": "§5",
          "anchor_text": "Outgoing record cells are not",
          "snapshot_sha256": "d2642a6d5f03986e83cc6ab47198de289769fd3204c26e5b903ba3a81b52b911"
        }
      ],
      "dependencies": [
        "JC-PIV-EXPORT",
        "JC-BANK",
        "JC-SCHEDULE"
      ],
      "ledger_ids": []
    },
    {
      "id": "JC-CAPACITY",
      "branch": "polarity",
      "title": "Full register capacity and reset count",
      "status": "EXACT_CONDITIONAL",
      "objects": "D=d^(N+1)m^N, dim J=L D^(B+1)",
      "conclusion": "Allocated state/receipt cells, clock addresses and B resets are explicit. Capacity is not an entropy, heat or minimal-memory claim.",
      "citations": [
        {
          "source_id": "JC01",
          "section": "§6",
          "anchor_text": "allocated capacity",
          "snapshot_sha256": "d2642a6d5f03986e83cc6ab47198de289769fd3204c26e5b903ba3a81b52b911"
        }
      ],
      "dependencies": [
        "JC-MAP",
        "JC-BANK",
        "JC-SCHEDULE"
      ],
      "ledger_ids": []
    },
    {
      "id": "JC-COLLISION",
      "branch": "polarity",
      "title": "Many-to-one map needs retained distinctions",
      "status": "EXACT_CONDITIONAL",
      "objects": "Auxiliary dimension≥max_y |f^-1(y)|",
      "conclusion": "Fresh common auxiliaries plus reversible implementation require orthogonal outputs somewhere when work outputs coincide. Not an N log d optimal memory theorem.",
      "citations": [
        {
          "source_id": "JC01",
          "section": "§6",
          "anchor_text": "narrow collision bound",
          "snapshot_sha256": "d2642a6d5f03986e83cc6ab47198de289769fd3204c26e5b903ba3a81b52b911"
        }
      ],
      "dependencies": [
        "JC-MAP"
      ],
      "ledger_ids": []
    },
    {
      "id": "JC-TOKENS",
      "branch": "polarity",
      "title": "RSP work-register stock ledger",
      "status": "EXACT_CONDITIONAL",
      "objects": "Active + unspent donor + outgoing remaining stock",
      "conclusion": "RSP compute consumes exactly its receipt count; payload SWAP preserves work-register total. Historical label copies are nonspendable descriptions.",
      "citations": [
        {
          "source_id": "JC01",
          "section": "§6",
          "anchor_text": "nonspendable descriptions",
          "snapshot_sha256": "d2642a6d5f03986e83cc6ab47198de289769fd3204c26e5b903ba3a81b52b911"
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      ],
      "dependencies": [
        "SP-STOCK",
        "JC-WINDOW",
        "JC-EXPORT"
      ],
      "ledger_ids": []
    },
    {
      "id": "JC-WRAP",
      "branch": "polarity",
      "title": "Clock wrap does not restore fresh resources",
      "status": "EXACT_CONDITIONAL",
      "objects": "Post-window dirty-tap counterexample",
      "conclusion": "A cyclic step remains unitary. Freshness/target law is no longer guaranteed; the actual C/H example fails at the second dirty compute.",
      "citations": [
        {
          "source_id": "JC01",
          "section": "§7",
          "anchor_text": "the second gives",
          "snapshot_sha256": "d2642a6d5f03986e83cc6ab47198de289769fd3204c26e5b903ba3a81b52b911"
        }
      ],
      "dependencies": [
        "JC-GATE",
        "JC-SCHEDULE",
        "JC-MAP"
      ],
      "ledger_ids": []
    },
    {
      "id": "JC-RESET",
      "branch": "polarity",
      "title": "Complete restart requires a larger supplied donor",
      "status": "OPEN",
      "objects": "Fresh dim J donor; full SWAP exports clock and entire bank",
      "conclusion": "A payload swap does not reset the master clock. Full-resource re-preparation has an algebraic sufficient resource but no acquired source or implemented autonomous exchange.",
      "citations": [
        {
          "source_id": "JC01",
          "section": "§7",
          "anchor_text": "fresh matched donor J",
          "snapshot_sha256": "d2642a6d5f03986e83cc6ab47198de289769fd3204c26e5b903ba3a81b52b911"
        }
      ],
      "dependencies": [
        "JC-CAPACITY",
        "JC-EXPORT"
      ],
      "ledger_ids": []
    },
    {
      "id": "JC-ERROR",
      "branch": "polarity",
      "title": "Conditional full-bank error composition",
      "status": "EXACT_CONDITIONAL",
      "objects": "D_tr≤min(1,epsilon_bank+sum epsilon_t)",
      "conclusion": "Requires complete-bank admission and matching full-domain uniformly bounded channels. No experimental numeric budget is supplied.",
      "citations": [
        {
          "source_id": "JC01",
          "section": "§8",
          "anchor_text": "telescoping full-domain comparison",
          "snapshot_sha256": "d2642a6d5f03986e83cc6ab47198de289769fd3204c26e5b903ba3a81b52b911"
        }
      ],
      "dependencies": [
        "JC-BANK",
        "JC-U"
      ],
      "ledger_ids": []
    },
    {
      "id": "JC-NATIVE",
      "branch": "polarity",
      "title": "Native finite-window apparatus realization",
      "status": "OPEN",
      "objects": "Native operator, source prep, time/energy, detection, restart",
      "conclusion": "A supplied reversible schedule constructs a mathematical larger carrier. It does not derive Hodge coupling, physical fuel, SI clock or source-selected prediction.",
      "citations": [
        {
          "source_id": "JC01",
          "section": "§8",
          "anchor_text": "Native Hodge→joint-carrier coupling",
          "snapshot_sha256": "d2642a6d5f03986e83cc6ab47198de289769fd3204c26e5b903ba3a81b52b911"
        }
      ],
      "dependencies": [
        "JC-SCHEDULE",
        "JC-WINDOW",
        "JC-RESET"
      ],
      "ledger_ids": []
    },
    {
      "id": "PC-WORD",
      "branch": "polarity",
      "title": "Owned complete payload word",
      "status": "DOMAIN_PREMISE",
      "objects": "K compute/reset gates; all donors/history retained",
      "conclusion": "Original cyclic shifts and final wrap are omitted; total payload permutations define the supplied finite word.",
      "citations": [
        {
          "source_id": "PC01",
          "section": "§1",
          "anchor_text": "Remove the original cyclic clock shift",
          "snapshot_sha256": "45b69deefe6f370ece8dc7e010e9df21796ffa7f9beee34217d8d708334627a3"
        }
      ],
      "dependencies": [
        "JC-GATE",
        "JC-U"
      ],
      "ledger_ids": []
    },
    {
      "id": "PC-SPIN",
      "branch": "polarity",
      "title": "Primary supplied history-clock theorem",
      "status": "SOURCE_DECLARED",
      "objects": "Square-root path clock and prefix dressing",
      "conclusion": "Paper IV IV.4 supplies conditional perfect transfer, coherent history and return; gate synthesis and native clocks remain supplied.",
      "citations": [
        {
          "source_id": "PIV",
          "section": "§4 IV.4",
          "anchor_text": "Theorem IV.4",
          "snapshot_sha256": "18ba71180c42249dda68d6649552c44f78fa8819e84ace7c9c54e7818f4287d8"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "PC-H",
      "branch": "polarity",
      "title": "Candidate constant dressed Hamiltonian",
      "status": "CANDIDATE",
      "objects": "H_p=W(H_C⊗I)W†; Hbar=0",
      "conclusion": "Zero comparison work generator meets commutation. This is supplied apparatus and does not recover a native tetrahedral source.",
      "citations": [
        {
          "source_id": "PC01",
          "section": "§2",
          "anchor_text": "These are exact definitions",
          "snapshot_sha256": "45b69deefe6f370ece8dc7e010e9df21796ffa7f9beee34217d8d708334627a3"
        }
      ],
      "dependencies": [
        "PC-WORD",
        "PC-SPIN"
      ],
      "ledger_ids": []
    },
    {
      "id": "PC-END",
      "branch": "polarity",
      "title": "Complete endpoint and projective return",
      "status": "EXACT_CONDITIONAL",
      "objects": "At T clockn/Q_n; at2T (-1)^n I",
      "conclusion": "Every input/spectator follows coherent prefixes; all outgoing record exchanges are reversed at complete return.",
      "citations": [
        {
          "source_id": "PC01",
          "section": "§2",
          "anchor_text": "Theorem PC.1",
          "snapshot_sha256": "45b69deefe6f370ece8dc7e010e9df21796ffa7f9beee34217d8d708334627a3"
        }
      ],
      "dependencies": [
        "PC-H",
        "PC-SPIN"
      ],
      "ledger_ids": []
    },
    {
      "id": "PC-METRIC",
      "branch": "polarity",
      "title": "Authored positive rational path metrics",
      "status": "CANDIDATE",
      "objects": "a0=1; b_r=a_r/left²; a_next=b_r right²",
      "conclusion": "Unit-rate metrics are chosen from the engineered clock. They are not a native geometry selection or a physical normalization.",
      "citations": [
        {
          "source_id": "PC01",
          "section": "§3",
          "anchor_text": "All a_r,b_r are positive rational",
          "snapshot_sha256": "45b69deefe6f370ece8dc7e010e9df21796ffa7f9beee34217d8d708334627a3"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "PC-PATH",
      "branch": "polarity",
      "title": "Exact engineered weighted-path Hodge form",
      "status": "EXACT_CONDITIONAL",
      "objects": "S=diag(i^j); S H_p S†=W(iκA_path⊗I)W†",
      "conclusion": "Even word has Q disjoint ordinary path components. Current basis-permutation gates preserve literal two-endpoint incidence.",
      "citations": [
        {
          "source_id": "PC01",
          "section": "§3",
          "anchor_text": "Theorem PC.2",
          "snapshot_sha256": "45b69deefe6f370ece8dc7e010e9df21796ffa7f9beee34217d8d708334627a3"
        }
      ],
      "dependencies": [
        "PC-METRIC",
        "PC-H",
        "PC-WORD"
      ],
      "ledger_ids": []
    },
    {
      "id": "PC-ODD",
      "branch": "polarity",
      "title": "Odd-word full-carrier harmonic obstruction",
      "status": "EXACT_NO_GO",
      "objects": "Odd spin has no zero mode; ordinary full Hodge has b0≥1",
      "conclusion": "Kernel mismatch excludes entire-carrier unitary equivalence. Restrictions, augmentation or active-subspace embeddings are outside this theorem.",
      "citations": [
        {
          "source_id": "PC01",
          "section": "§4",
          "anchor_text": "Theorem PC.3",
          "snapshot_sha256": "45b69deefe6f370ece8dc7e010e9df21796ffa7f9beee34217d8d708334627a3"
        }
      ],
      "dependencies": [
        "PC-END"
      ],
      "ledger_ids": []
    },
    {
      "id": "PC-PAD",
      "branch": "polarity",
      "title": "Identity padding preserves terminal payload",
      "status": "EXACT_CONDITIONAL",
      "objects": "Odd K→even n=K+1; +1 address",
      "conclusion": "A supplied identity makes the path representation available without extra payload donor or history cells. Clock dimension/norm/variance change.",
      "citations": [
        {
          "source_id": "PC01",
          "section": "§4",
          "anchor_text": "Identity padding changes odd K",
          "snapshot_sha256": "45b69deefe6f370ece8dc7e010e9df21796ffa7f9beee34217d8d708334627a3"
        }
      ],
      "dependencies": [
        "PC-WORD",
        "PC-ODD",
        "PC-PATH"
      ],
      "ledger_ids": []
    },
    {
      "id": "PC-TET-NOGO",
      "branch": "polarity",
      "title": "Single-frequency tetrahedron excludes full clock embedding",
      "status": "EXACT_NO_GO",
      "objects": "Even n≥4 frequencies2κ,4κ versus native positive2",
      "conclusion": "Exact isometry intertwining must preserve distinct eigenvalues. This does not exclude other weighted/glued complexes or weak finite-window comparison.",
      "citations": [
        {
          "source_id": "PC01",
          "section": "§4",
          "anchor_text": "Theorem PC.4",
          "snapshot_sha256": "45b69deefe6f370ece8dc7e010e9df21796ffa7f9beee34217d8d708334627a3"
        }
      ],
      "dependencies": [
        "PC-END",
        "A-CARRIER"
      ],
      "ledger_ids": []
    },
    {
      "id": "PC-RESOURCES",
      "branch": "polarity",
      "title": "Continuous clock/data/reset ledger",
      "status": "EXACT_CONDITIONAL",
      "objects": "(n+1)Q, normκn, varianceκ²n",
      "conclusion": "Padding adds an address sector, not a payload donor; intermediate resources belong to coherent conditional prefixes. Zero mean is not free preparation.",
      "citations": [
        {
          "source_id": "PC01",
          "section": "§5",
          "anchor_text": "Complete dimension becomes",
          "snapshot_sha256": "45b69deefe6f370ece8dc7e010e9df21796ffa7f9beee34217d8d708334627a3"
        }
      ],
      "dependencies": [
        "JC-CAPACITY",
        "PC-H",
        "PC-PAD"
      ],
      "ledger_ids": []
    },
    {
      "id": "PC-DIST",
      "branch": "polarity",
      "title": "Exact mixed-state complete terminal distance",
      "status": "EXACT_CONDITIONAL",
      "objects": "D_tr=sqrt(1−sin^(2n)(κt))",
      "conclusion": "Scalar overlap of the two isometries gives the equality for arbitrary mixed input and spectators; marginal terminal probability is a different type.",
      "citations": [
        {
          "source_id": "PC01",
          "section": "§5",
          "anchor_text": "Mixed-state proof",
          "snapshot_sha256": "45b69deefe6f370ece8dc7e010e9df21796ffa7f9beee34217d8d708334627a3"
        }
      ],
      "dependencies": [
        "PC-END"
      ],
      "ledger_ids": []
    },
    {
      "id": "PC-ERROR",
      "branch": "polarity",
      "title": "Owned supply/operator/jitter comparison",
      "status": "EXACT_CONDITIONAL",
      "objects": "eps_supply+sqrt(n)κσ+r(t)",
      "conclusion": "Requires full input admission and a residual on matching joint domain. Controls are protocol assumptions, not certified errors or theory constants.",
      "citations": [
        {
          "source_id": "PC01",
          "section": "§5",
          "anchor_text": "complete supplied input",
          "snapshot_sha256": "45b69deefe6f370ece8dc7e010e9df21796ffa7f9beee34217d8d708334627a3"
        }
      ],
      "dependencies": [
        "PC-DIST",
        "PC-H"
      ],
      "ledger_ids": []
    },
    {
      "id": "PC-ENCODE",
      "branch": "polarity",
      "title": "Native operator and full isometry premise",
      "status": "DOMAIN_PREMISE",
      "objects": "H_nat Hermitian; E†E=I; complete retained domain",
      "conclusion": "Source-defined geometry, metric, encoding and preparation must be supplied before fitting outputs. No concrete accepted E is available.",
      "citations": [
        {
          "source_id": "PC01",
          "section": "§6",
          "anchor_text": "Specify an isometry E",
          "snapshot_sha256": "45b69deefe6f370ece8dc7e010e9df21796ffa7f9beee34217d8d708334627a3"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "PC-ADMISSION",
      "branch": "polarity",
      "title": "Native isometry residual bounds propagation",
      "status": "EXACT_CONDITIONAL",
      "objects": "eta=norm(H_nat E−E H_p); mismatch≤|t|eta",
      "conclusion": "Duhamel comparison does not require encoded-subspace invariance; residual0 does establish it. No numerical native residual is certified.",
      "citations": [
        {
          "source_id": "PC01",
          "section": "§6",
          "anchor_text": "This does not assume",
          "snapshot_sha256": "45b69deefe6f370ece8dc7e010e9df21796ffa7f9beee34217d8d708334627a3"
        }
      ],
      "dependencies": [
        "PC-ENCODE",
        "PC-H"
      ],
      "ledger_ids": []
    },
    {
      "id": "PC-NATIVE",
      "branch": "polarity",
      "title": "Source-defined enlarged native realization",
      "status": "OPEN",
      "objects": "Native complex/metric/E/supply/clock/readout",
      "conclusion": "Engineered path form is not native selection. Single tetrahedron exact class excluded; other source classes require the full operator-admission receipt.",
      "citations": [
        {
          "source_id": "PC01",
          "section": "§6",
          "anchor_text": "concrete falsifiable operator-admission target",
          "snapshot_sha256": "45b69deefe6f370ece8dc7e010e9df21796ffa7f9beee34217d8d708334627a3"
        }
      ],
      "dependencies": [
        "PC-ADMISSION",
        "PC-TET-NOGO",
        "PC-ERROR"
      ],
      "ledger_ids": []
    },
    {
      "id": "PC-RETENTION",
      "branch": "polarity",
      "title": "Protected records beyond the completion window",
      "status": "OPEN",
      "objects": "Capture/isolation contact and fresh output supply",
      "conclusion": "The closed constant clock coherently returns all records. Permanent output isolation is not delivered by endpoint perfect transfer.",
      "citations": [
        {
          "source_id": "PC01",
          "section": "§2",
          "anchor_text": "Protected output needs",
          "snapshot_sha256": "45b69deefe6f370ece8dc7e010e9df21796ffa7f9beee34217d8d708334627a3"
        }
      ],
      "dependencies": [
        "PC-END",
        "JC-EXPORT"
      ],
      "ledger_ids": []
    },
    {
      "id": "NA-GLUED-SOURCE",
      "branch": "polarity",
      "title": "Primary glued unit-metric spectra",
      "status": "SOURCE_DECLARED",
      "objects": "Kminus:lambda(lambda²+3)^4(lambda²+5)^7; Kplus:lambda(lambda²+2)^2(lambda²+5)^11",
      "conclusion": "Paper I source spectra use unique-simplex bases and unit metrics; graph counts alone are not these operators.",
      "citations": [
        {
          "source_id": "PI",
          "section": "§6.3 T6.4",
          "anchor_text": "Theorem T6.4",
          "snapshot_sha256": "23a62d17d88076589e4904973c166e086c03352629e620913e4bb3897eb275ab"
        }
      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "NA-CLASSES",
      "branch": "polarity",
      "title": "Frozen unit-metric native spectra",
      "status": "SOURCE_DECLARED",
      "objects": "Delta3:0,±2; Kminus:0,±sqrt3,±sqrt5; Kplus:0,±sqrt2,±sqrt5",
      "conclusion": "Only identical common-rate disconnected copies are in this class. Additional operators, metrics and unequal rates require new source premises.",
      "citations": [
        {
          "source_id": "NA01",
          "section": "§1",
          "anchor_text": "Use r identical disconnected copies",
          "snapshot_sha256": "c83efb28a57904d0e019bd3c0ad29535993e9a0eb9484a3739a85e6c4c73231d"
        }
      ],
      "dependencies": [
        "A-CARRIER",
        "NA-GLUED-SOURCE"
      ],
      "ledger_ids": []
    },
    {
      "id": "NA-DIM",
      "branch": "polarity",
      "title": "Complete native-domain dimension gate",
      "status": "EXACT_CONDITIONAL",
      "objects": "dim native≥(n+1)Q",
      "conclusion": "A complete isometry includes all clock/work/history/receipt/bank factors. One original carrier cannot host the default full register dimension.",
      "citations": [
        {
          "source_id": "NA01",
          "section": "§1",
          "anchor_text": "A complete isometry E requires",
          "snapshot_sha256": "c83efb28a57904d0e019bd3c0ad29535993e9a0eb9484a3739a85e6c4c73231d"
        }
      ],
      "dependencies": [
        "PC-RESOURCES",
        "NA-CLASSES"
      ],
      "ledger_ids": []
    },
    {
      "id": "NA-SPECTRAL",
      "branch": "polarity",
      "title": "Necessary nearest-spectrum residual bound",
      "status": "EXACT_CONDITIONAL",
      "objects": "eta≥maxlambda dist(lambda,specHnative)",
      "conclusion": "An isometry preserves eigenvector norm; finite Hermitian spectral distance bounds the residual without invariant-image assumptions.",
      "citations": [
        {
          "source_id": "NA01",
          "section": "§2",
          "anchor_text": "Theorem NA.1",
          "snapshot_sha256": "c83efb28a57904d0e019bd3c0ad29535993e9a0eb9484a3739a85e6c4c73231d"
        }
      ],
      "dependencies": [
        "PC-ENCODE",
        "PC-END",
        "NA-CLASSES"
      ],
      "ledger_ids": []
    },
    {
      "id": "NA-MULT",
      "branch": "polarity",
      "title": "Eigenvalue multiplicity refines admission",
      "status": "EXACT_CONDITIONAL",
      "objects": "Qth nearest distance per target eigenvalue",
      "conclusion": "A Q-dimensional image requires enough near eigenvectors; a fixed-copy/source encoding can have a larger residual than the nearest-spectrum floor.",
      "citations": [
        {
          "source_id": "NA01",
          "section": "§2",
          "anchor_text": "safe stronger bound",
          "snapshot_sha256": "c83efb28a57904d0e019bd3c0ad29535993e9a0eb9484a3739a85e6c4c73231d"
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      ],
      "dependencies": [
        "NA-SPECTRAL",
        "PC-END"
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      "ledger_ids": []
    },
    {
      "id": "NA-SCALE",
      "branch": "polarity",
      "title": "Free common-rate comparison relaxation",
      "status": "CANDIDATE",
      "objects": "x=gamma/kappa; no source parameter selected",
      "conclusion": "The native class is given free scale adjustment for a strongest obstruction test. Optimizing x does not acquire native rates, metrics or encoded preparation.",
      "citations": [
        {
          "source_id": "NA01",
          "section": "§3",
          "anchor_text": "deliberate relaxation",
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      "ledger_ids": []
    },
    {
      "id": "NA-MIN",
      "branch": "polarity",
      "title": "Exact three n10 spectral minima",
      "status": "EXACT_CONDITIONAL",
      "objects": "3;7sqrt15−25;2",
      "conclusion": "Elementary lower certificates and attainable centre assignments agree with exact ordered-partition enumeration. Optimal scales may form a union, not a convex hull.",
      "citations": [
        {
          "source_id": "NA01",
          "section": "§3",
          "anchor_text": "Theorem NA.2",
          "snapshot_sha256": "c83efb28a57904d0e019bd3c0ad29535993e9a0eb9484a3739a85e6c4c73231d"
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      ],
      "dependencies": [
        "NA-SPECTRAL",
        "NA-SCALE",
        "NA-CLASSES"
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      "ledger_ids": []
    },
    {
      "id": "NA-UNION",
      "branch": "polarity",
      "title": "Disconnected exact scale solutions retained",
      "status": "EXACT_CONDITIONAL",
      "objects": "n2: high centre2 or2/rho",
      "conclusion": "An interval hull would invent unproved exact scales. The solver retains every optimal interval component and its partition certificates.",
      "citations": [
        {
          "source_id": "NA01",
          "section": "§3",
          "anchor_text": "Optimal intervals are retained",
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      "dependencies": [
        "NA-MIN",
        "PC-END"
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      "ledger_ids": []
    },
    {
      "id": "NA-SHARP",
      "branch": "polarity",
      "title": "Unrestricted-copy residual floors are sharp",
      "status": "EXACT_CONDITIONAL",
      "objects": "3Q copies and free eigenbasis E attain all n10 floors",
      "conclusion": "Source multiplicities accommodate orthogonal images. No minimal-copy, local, degree-preserving or source-selected encoding claim follows.",
      "citations": [
        {
          "source_id": "NA01",
          "section": "§4",
          "anchor_text": "These minima can be attained",
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      "dependencies": [
        "NA-MIN",
        "NA-CLASSES",
        "NA-SCALE"
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      "ledger_ids": []
    },
    {
      "id": "NA-NOGO",
      "branch": "polarity",
      "title": "All three fixed classes exclude full exact clock embedding",
      "status": "EXACT_NO_GO",
      "objects": "Even n≥4:positive target ratio2 versus fixed native spectra",
      "conclusion": "Common-rate identical copies preserve the single frequency or irrational two-frequency ratio. Weaker endpoints and different operators are outside the theorem.",
      "citations": [
        {
          "source_id": "NA01",
          "section": "§5",
          "anchor_text": "Theorem NA.3",
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        "PC-END",
        "NA-CLASSES"
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      "ledger_ids": []
    },
    {
      "id": "NA-TIME",
      "branch": "polarity",
      "title": "Slowdown does not reduce integrated residual floor",
      "status": "EXACT_CONDITIONAL",
      "objects": "Teta≥pi minb/2 atT=pi/(2kappa)",
      "conclusion": "Common source/programme slowdown cancels from this sufficient budget. This is not an actual error or failure-probability lower bound.",
      "citations": [
        {
          "source_id": "NA01",
          "section": "§5",
          "anchor_text": "dimensionless requirement",
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      "dependencies": [
        "NA-MIN",
        "PC-END",
        "PC-ADMISSION"
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      "ledger_ids": []
    },
    {
      "id": "NA-ALIAS",
      "branch": "polarity",
      "title": "Complete endpoint alias with nonzero generator residual",
      "status": "EXACT_CONDITIONAL",
      "objects": "5Q tetra copies; endpoint exact;eta8kappa",
      "conclusion": "A supplied eigenphase encoding matches the full endpoint channel yet differs during propagation. The full-generator no-go remains valid.",
      "citations": [
        {
          "source_id": "NA01",
          "section": "§6",
          "anchor_text": "Theorem NA.4",
          "snapshot_sha256": "c83efb28a57904d0e019bd3c0ad29535993e9a0eb9484a3739a85e6c4c73231d"
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      "dependencies": [
        "NA-CLASSES",
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        "PC-ENCODE"
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      "ledger_ids": []
    },
    {
      "id": "NA-ERROR-TYPE",
      "branch": "polarity",
      "title": "Residual budget is not actual endpoint error",
      "status": "EXACT_NO_GO",
      "objects": "Cannot infer error≥c fromTeta≥c",
      "conclusion": "The exact endpoint alias refutes that inference, even for full encoded channel agreement with arbitrary spectators.",
      "citations": [
        {
          "source_id": "NA01",
          "section": "§5",
          "anchor_text": "Crucial type distinction",
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        "NA-TIME",
        "NA-ALIAS"
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      "ledger_ids": []
    },
    {
      "id": "NA-NEXT",
      "branch": "polarity",
      "title": "Revised native admission frontier",
      "status": "OPEN",
      "objects": "Different source operator or explicitly weaker contract",
      "conclusion": "New geometry/metric/rates require a source law; alternatively declare a prepared-window/endpoint comparison with full preparation/readout/retention. No promotion from scale fit.",
      "citations": [
        {
          "source_id": "NA01",
          "section": "§7",
          "anchor_text": "The next native target must",
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        "NA-NOGO",
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        "NA-ALIAS"
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      "id": "MF-CONTRACT",
      "branch": "polarity",
      "title": "Complete fixed-origin identical-copy comparison",
      "status": "CANDIDATE",
      "objects": "Hnative E=E Hprogramme; Hnative=iγÂ",
      "conclusion": "Same metric/geometry/coefficients in every uncoupled copy; common rate and unrestricted complete isometry are comparison relaxations.",
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        {
          "source_id": "MF01",
          "section": "§1",
          "anchor_text": "Copies share the same metric",
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      "dependencies": [
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        "PC-END"
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      "ledger_ids": []
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      "id": "MF-S4-SOURCE",
      "branch": "polarity",
      "title": "Primary three-channel skew classification",
      "status": "SOURCE_DECLARED",
      "objects": "λ(λ²+4a²)³(λ²+4b²)³(λ²+4c²)",
      "conclusion": "Three real skew channels are not the full complex Hermitian equivariant family.",
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        {
          "source_id": "C0190",
          "section": "C0190",
          "anchor_text": "A(a,b,c)",
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      "id": "MF-CONVENTIONS",
      "branch": "polarity",
      "title": "Metric-adjoint and mass whitening crosswalk",
      "status": "EXACT_CONDITIONAL",
      "objects": "tk=√(gprev/gcurrent) versus1/√(gprev*gcurrent)",
      "conclusion": "Fixed boundaries with their changed adjoint and G ċ=A0c define different operators. Common metric scaling distinguishes their rates.",
      "citations": [
        {
          "source_id": "MF01",
          "section": "§2",
          "anchor_text": "Fixed-boundary metric-adjoint convention",
          "snapshot_sha256": "883df604c517c929ebba7063ebcad5d14aba35d5fdcdb0fdb5e43e41ed79695f"
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        {
          "source_id": "C0496",
          "section": "§9 convention repair",
          "anchor_text": "whitening",
          "snapshot_sha256": "05200f695017e1e4a381af0eac824df7410c6b570e856b94fe0c92b12e4567ac"
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    {
      "id": "MF-S4",
      "branch": "polarity",
      "title": "Invariant metric normalization preserves three bands",
      "status": "EXACT_CONDITIONAL",
      "objects": "G invariant SPD; L equivariant G-skew",
      "conclusion": "G½ commutes with the signed action; normalized real skew family still has at most three positive bands.",
      "citations": [
        {
          "source_id": "MF01",
          "section": "§3",
          "anchor_text": "Theorem MF.1",
          "snapshot_sha256": "883df604c517c929ebba7063ebcad5d14aba35d5fdcdb0fdb5e43e41ed79695f"
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      "dependencies": [
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    },
    {
      "id": "MF-DEGREE",
      "branch": "polarity",
      "title": "Degree-isotropic ratio-metric spectra",
      "status": "EXACT_CONDITIONAL",
      "objects": "2√(g0/g1),2√(g1/g2),2√(g2/g3)",
      "conclusion": "Signed multiplicities3,3,1; algebraic parameterization does not choose a native metric.",
      "citations": [
        {
          "source_id": "MF01",
          "section": "§3",
          "anchor_text": "For degree-isotropic fixed-boundary metrics",
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      "dependencies": [
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        "MF-S4"
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      "id": "MF-NOGO",
      "branch": "polarity",
      "title": "Three-band full-generator exclusion",
      "status": "EXACT_NO_GO",
      "objects": "Even n≥8; identical same-parameter copies",
      "conclusion": "Copies do not create a fourth positive band. Larger carriers and symmetry-breaking metrics are outside this result.",
      "citations": [
        {
          "source_id": "MF01",
          "section": "§3",
          "anchor_text": "Corollary MF.2",
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      "dependencies": [
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        "MF-CONTRACT"
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      "ledger_ids": []
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    {
      "id": "MF-RESIDUAL",
      "branch": "polarity",
      "title": "Exact free three-center residual relaxation",
      "status": "EXACT_CONDITIONAL",
      "objects": "rM=min{integer r≥0:M≤floor(r/2)+3(r+1)}",
      "conclusion": "Default η/κ≥1; relaxed centers3,7,10 attain it. No native coefficients or endpoint-error lower bound follows.",
      "citations": [
        {
          "source_id": "MF01",
          "section": "§4",
          "anchor_text": "Theorem MF.3",
          "snapshot_sha256": "883df604c517c929ebba7063ebcad5d14aba35d5fdcdb0fdb5e43e41ed79695f"
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      "dependencies": [
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        "MF-CONTRACT"
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      "ledger_ids": []
    },
    {
      "id": "MF-GRAM",
      "branch": "polarity",
      "title": "Source coordinate-defined Gram candidates",
      "status": "CANDIDATE",
      "objects": "q>0,p=1/2; five positive factors u,v,x,y,z",
      "conclusion": "Rules A/B are source-authored alternative geometric metrics. Nonregular geometry breaks fixed fullS4 invariance.",
      "citations": [
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          "source_id": "MF01",
          "section": "§5",
          "anchor_text": "C0173 declares the fixed tetrahedron coordinates",
          "snapshot_sha256": "883df604c517c929ebba7063ebcad5d14aba35d5fdcdb0fdb5e43e41ed79695f"
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        {
          "source_id": "C0173",
          "section": "Disposition",
          "anchor_text": "Neither is selected as canonical UD dynamics.",
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    },
    {
      "id": "MF-GRAM-ID",
      "branch": "polarity",
      "title": "Gram scale-invariant band relation",
      "status": "EXACT_CONDITIONAL",
      "objects": "u/v+x/y=2",
      "conclusion": "The identity survives any common positive rate and is not a frequency-count argument.",
      "citations": [
        {
          "source_id": "MF01",
          "section": "§5",
          "anchor_text": "u/v+x/y=2/(a+1)",
          "snapshot_sha256": "883df604c517c929ebba7063ebcad5d14aba35d5fdcdb0fdb5e43e41ed79695f"
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      "branch": "polarity",
      "title": "Five-band Gram default-clock exclusion",
      "status": "EXACT_NO_GO",
      "objects": "n10:120 squared-target assignments, zero hits",
      "conclusion": "Allq>0 in RuleA/B exclude full default-generator admission; n≥12 fails band count. n8 remains unresolved. Relation gap is not an operator/error bound.",
      "citations": [
        {
          "source_id": "MF01",
          "section": "§5",
          "anchor_text": "Theorem MF.4",
          "snapshot_sha256": "883df604c517c929ebba7063ebcad5d14aba35d5fdcdb0fdb5e43e41ed79695f"
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      "dependencies": [
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        "MF-CONTRACT"
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    },
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      "branch": "polarity",
      "title": "Source degree-weighted glued spectral families",
      "status": "CANDIDATE",
      "objects": "Kminus6bands; Kplus5bands",
      "conclusion": "Declared degree groups have irrational paired ratios and unselected coefficients; arbitrary simplex-dependent metrics are outside this family.",
      "citations": [
        {
          "source_id": "MF01",
          "section": "§6",
          "anchor_text": "Kminus has per-degree paired bands",
          "snapshot_sha256": "883df604c517c929ebba7063ebcad5d14aba35d5fdcdb0fdb5e43e41ed79695f"
        },
        {
          "source_id": "C0473",
          "section": "Degree-weighted source family",
          "anchor_text": "WEIGHTED-HODGE CONTROL FAMILY",
          "snapshot_sha256": "d979a0e5d77e78eee5ea996045e9cc9acaf02ecb0c03ddc24c01533e0db7140a"
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      ],
      "dependencies": [],
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    },
    {
      "id": "MF-GLUED-NOGO",
      "branch": "polarity",
      "title": "Weighted glued commensurability exclusion",
      "status": "EXACT_NO_GO",
      "objects": "Even n≥8:at most3 distinct grid matches",
      "conclusion": "Each degree group matches at most one integer-grid frequency, even when the source has five/six bands.",
      "citations": [
        {
          "source_id": "MF01",
          "section": "§6",
          "anchor_text": "Theorem MF.5",
          "snapshot_sha256": "883df604c517c929ebba7063ebcad5d14aba35d5fdcdb0fdb5e43e41ed79695f"
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      "dependencies": [
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        "MF-CONTRACT"
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      "ledger_ids": []
    },
    {
      "id": "MF-FRONTIER",
      "branch": "polarity",
      "title": "Revised source-operator admission frontier",
      "status": "OPEN",
      "objects": "Heterogeneous/coupled carriers, different complexes or weaker contract",
      "conclusion": "Native law, complete encoding, acquisition, protected export and restart accounting still require declared source premises and fresh tests.",
      "citations": [
        {
          "source_id": "MF01",
          "section": "§7",
          "anchor_text": "The revised frontier is a source-defined",
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        "MF-GRAM-NOGO",
        "MF-GLUED-NOGO",
        "MF-RESIDUAL",
        "JC-RESET"
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    },
    {
      "id": "SG-SOURCE",
      "branch": "polarity",
      "title": "Source ordinary barycentric subdivision",
      "status": "SOURCE_DECLARED",
      "objects": "S:C(Δ³)→C(sdΔ³)",
      "conclusion": "The dated source map has15→149 chain coordinates and exact factorial Gram factors; it selects no cross-event metric.",
      "citations": [
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          "source_id": "R31",
          "section": "R31 §4",
          "anchor_text": "ordinary oriented barycentric",
          "snapshot_sha256": "668f2b1a6f4173575ce5073d66a726ac0ab1a360f23ec3e60f5b18a5b9d7e056"
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      "dependencies": [],
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    },
    {
      "id": "SG-GRAM",
      "branch": "polarity",
      "title": "Recovered boundary and factorial Gram identities",
      "status": "EXACT_CONDITIONAL",
      "objects": "B′S=SB; SᵀS=diag(1,2,6,24)",
      "conclusion": "The degree-dependent norm factors are not one universal sqrt2 normalization.",
      "citations": [
        {
          "source_id": "SG01",
          "section": "§2",
          "anchor_text": "Theorem SG.1",
          "snapshot_sha256": "0125d4649c7b914650da93b5e94d0d6a1f25fde272e6f239f0295bcc66319109"
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      ],
      "dependencies": [
        "SG-SOURCE"
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      "ledger_ids": []
    },
    {
      "id": "SG-EUCLIDEAN",
      "branch": "polarity",
      "title": "Original Euclidean strict-interface exclusion",
      "status": "EXACT_NO_GO",
      "objects": "old/new vertex incidence3/7; generator defect squared7",
      "conclusion": "Unit singleton readout, contraction and unchanged unit-incidence generator remain incompatible.",
      "citations": [
        {
          "source_id": "SG01",
          "section": "§2",
          "anchor_text": "R34's no-go",
          "snapshot_sha256": "0125d4649c7b914650da93b5e94d0d6a1f25fde272e6f239f0295bcc66319109"
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        {
          "source_id": "R34",
          "section": "§2 strict contract",
          "anchor_text": "a contradiction.",
          "snapshot_sha256": "93b5632f2fe38efd678ec52676dab81676a7c5b1f5324fc8a7ad110aa4f24d1f"
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      ],
      "dependencies": [
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      "ledger_ids": []
    },
    {
      "id": "SG-NORMALIZATIONS",
      "branch": "polarity",
      "title": "Distinct scalar and factorial negative controls",
      "status": "EXACT_CONDITIONAL",
      "objects": "S/√24; degree-normalized U; Hdiag=I/(k+1)!",
      "conclusion": "Boundary/norm/generator gates remain separate; naive metric defect squared11, bounded defect7/24, normalized edge boundary defect3−2√2.",
      "citations": [
        {
          "source_id": "SG01",
          "section": "§3",
          "anchor_text": "Naive metric alternative",
          "snapshot_sha256": "0125d4649c7b914650da93b5e94d0d6a1f25fde272e6f239f0295bcc66319109"
        },
        {
          "source_id": "R33",
          "section": "§2 bounded source family",
          "anchor_text": "T_k={S_k",
          "snapshot_sha256": "59080e03ad825c7bd0464b0830b4d2837a194240de7c3421cab967d170bd9a74"
        }
      ],
      "dependencies": [
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        "MF-CONVENTIONS"
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      "ledger_ids": []
    },
    {
      "id": "SG-R",
      "branch": "polarity",
      "title": "Authored affine barycentric retraction",
      "status": "CANDIDATE",
      "objects": "Rflag=exterior product of face barycenters",
      "conclusion": "No clock spectrum or physical target selects this authored coarse readout. Source selection is open.",
      "citations": [
        {
          "source_id": "SG01",
          "section": "§4",
          "anchor_text": "The new conditional branch starts",
          "snapshot_sha256": "0125d4649c7b914650da93b5e94d0d6a1f25fde272e6f239f0295bcc66319109"
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      ],
      "dependencies": [],
      "ledger_ids": []
    },
    {
      "id": "SG-RETRACT",
      "branch": "polarity",
      "title": "Exact chain left inverse and decomposition",
      "status": "EXACT_CONDITIONAL",
      "objects": "RB′=BR; RS=I;Q=I−SR",
      "conclusion": "Affine augmentation and signed barycentric determinants give a boundary-invariant direct sum imS⊕kerR.",
      "citations": [
        {
          "source_id": "SG01",
          "section": "§4",
          "anchor_text": "Theorem SG.2",
          "snapshot_sha256": "0125d4649c7b914650da93b5e94d0d6a1f25fde272e6f239f0295bcc66319109"
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      "dependencies": [
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        "SG-R"
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      "ledger_ids": []
    },
    {
      "id": "SG-H",
      "branch": "polarity",
      "title": "Authored positive complement metric family",
      "status": "CANDIDATE",
      "objects": "H=RᵀGR+QᵀWQ;G,W SPD",
      "conclusion": "Pairing changes after subdivision. Complement weights and local/physical identification are unselected.",
      "citations": [
        {
          "source_id": "SG01",
          "section": "§5",
          "anchor_text": "H=Rᵀ G R+Qᵀ W Q.",
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          "source_id": "C0243",
          "section": "Metric/source distinction",
          "anchor_text": "A coordinate change transports the adjoint",
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    {
      "id": "SG-SPD",
      "branch": "polarity",
      "title": "Metric positive definiteness and isometry",
      "status": "EXACT_CONDITIONAL",
      "objects": "HS=RᵀG;SᵀHS=G",
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        {
          "source_id": "SG01",
          "section": "§5",
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      "id": "SG-DYNAMICS",
      "branch": "polarity",
      "title": "Weighted-adjoint generator intertwining",
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      "objects": "A′H S=S A_G; same internal rate",
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        {
          "source_id": "SG01",
          "section": "§5",
          "anchor_text": "Since H is invertible",
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      "title": "Fine complement and full-state accounting",
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      "objects": "134 direct-sum directions;dims11,44,56,23",
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        {
          "source_id": "SG01",
          "section": "§6",
          "anchor_text": "Here134 is a",
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      "id": "SG-LOCAL",
      "branch": "polarity",
      "title": "Dense metric does not inherit local simplex stocks",
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      "conclusion": "Source Q170/Q171/Q172 nonnegative simplex stocks and local current rules do not transfer automatically to this conditional metric.",
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          "source_id": "SG01",
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      "branch": "polarity",
      "title": "No universal sqrt2 law from these identities",
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      "objects": "factorial1,2,6,24; F²(r)=r; arbitrary skew rate",
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          "source_id": "SG01",
          "section": "§7",
          "anchor_text": "For the specifically rotated rectangle-halving map",
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      "id": "SG-NEXT",
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          "source_id": "SG01",
          "section": "§8",
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          "section": "§1",
          "anchor_text": "Theorem MS.1",
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          "source_id": "MS01",
          "section": "§2",
          "anchor_text": "Require SᵀHS=G",
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      "title": "All compatible metrics induce chain retractions",
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      "conclusion": "This necessary and sufficient classification exposes two unselected ingredients beyond the source map.",
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          "source_id": "MS01",
          "section": "§2",
          "anchor_text": "Theorem MS.2",
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          "source_id": "MS01",
          "section": "§3",
          "anchor_text": "In particular H1 gives2",
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      "title": "Code calibration does not select a positive observable",
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      "objects": "Kλ coarse-equivalent; fine values1/2,5/4,2",
      "conclusion": "Even at fixedH1, positive norm-bounded observations can differ on retained complementary information.",
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          "source_id": "MS01",
          "section": "§3",
          "anchor_text": "Even fix H1.",
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      "title": "Any diagonal fine metric fails ordinary generator inheritance",
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      "objects": "Other-end flag coefficient0 versus1",
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          "source_id": "MS01",
          "section": "§4",
          "anchor_text": "Theorem MS.3",
          "snapshot_sha256": "e07baad19d01bafbb7f93a0222610b208b5c84c59f97f85c6d143c471979ce76"
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      "title": "Explicit candidate selector premises A/B/C",
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      "conclusion": "These are added constitutive/measurement premises, not recovered native laws or parameter-free optimization consequences.",
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          "source_id": "MS01",
          "section": "§5",
          "anchor_text": "The following is an explicit",
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        {
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          "section": "§5 added optimization law",
          "anchor_text": "Parameter-free optimization still adds a law",
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      "id": "MS-SELECT-H",
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      "title": "Unique conditional retraction and metric",
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      "objects": "R affine;H*=RᵀGR+QᵀQ",
      "conclusion": "Face-local normalized covariance plus exterior consistency fixesR; calibrated orthogonal split uniquely fixesH*.",
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          "source_id": "MS01",
          "section": "§5",
          "anchor_text": "Theorem MS.4",
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      "branch": "polarity",
      "title": "Unique complement-blind positive observable",
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      "objects": "K_U=RᵀD_U R",
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      "citations": [
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          "source_id": "MS01",
          "section": "§5",
          "anchor_text": "Theorem MS.5",
          "snapshot_sha256": "e07baad19d01bafbb7f93a0222610b208b5c84c59f97f85c6d143c471979ce76"
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      "branch": "polarity",
      "title": "Complete coarse plus complement support receipts",
      "status": "EXACT_CONDITIONAL",
      "objects": "15 source simplex effects+1 complement; sumH*",
      "conclusion": "Barycenter fractions1/8,1/8,3/4 retain the complementary outcome; no physical measurement or Born-law claim.",
      "citations": [
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          "source_id": "MS01",
          "section": "§6",
          "anchor_text": "Σσ K_σ+K_comp=H*.",
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      "dependencies": [
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      "branch": "polarity",
      "title": "Decoded coarse stocks inherit the source current",
      "status": "EXACT_CONDITIONAL",
      "objects": "R A′H*=A_G R; Q170 on decodedRx",
      "conclusion": "Recovered continuity is coarse-first observation, not additive fine-simplex stock or a selection of C0559 local-first ordering.",
      "citations": [
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          "source_id": "MS01",
          "section": "§6",
          "anchor_text": "The retraction is the metric adjoint",
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          "section": "Ordering source audit",
          "anchor_text": "leaves coefficient selection open",
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    },
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      "branch": "polarity",
      "title": "Native cross-refinement selector remains open",
      "status": "OPEN",
      "objects": "Source-authored adoption/calibration of A/B/C or alternative interface",
      "conclusion": "Current source fidelity selects fixed-carrier objects; dense metric and observer order are uniquely determined only after extra candidate commitments.",
      "citations": [
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          "section": "§7",
          "anchor_text": "The outstanding gate is",
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      "dependencies": [
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      "id": "RT-CONTRACT",
      "branch": "polarity",
      "title": "Additional retained-sequence grouping requirement",
      "status": "CANDIDATE",
      "objects": "SameS/R sequence; inherited details retained",
      "conclusion": "This grouping condition is new; one-step conditional uniqueness did not assert it. Different refinement histories are outside the test.",
      "citations": [
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          "section": "§1",
          "anchor_text": "New **candidate requirement:",
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      "branch": "polarity",
      "title": "Exact two-level chain and detail decomposition",
      "status": "EXACT_CONDITIONAL",
      "objects": "x=S20c+S21z1+z2;Q20=Q21+S21Q10R21",
      "conclusion": "Retractions recover each component; ordinary subdivision preserves every boundary map.",
      "citations": [
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          "source_id": "RT01",
          "section": "§2",
          "anchor_text": "Theorem RT.1",
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      "title": "Sequential inherited-detail pairing",
      "status": "EXACT_CONDITIONAL",
      "objects": "H2seq=R20ᵀG0R20+(Q10R21)ᵀ(Q10R21)+Q21ᵀQ21",
      "conclusion": "The two-step unit residual rule retains the intermediate calibration and all fine directions.",
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          "section": "§3",
          "anchor_text": "Its squared norm is",
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          "section": "§5 one-step selector",
          "anchor_text": "Theorem MS.4",
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      "title": "Fresh composite unit calibration",
      "status": "CANDIDATE",
      "objects": "H2fresh=R20ᵀG0R20+Q20ᵀQ20",
      "conclusion": "This is a different declaration about the same final detail coordinates. It still preserves original coarse norm and generator.",
      "citations": [
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          "section": "§3",
          "anchor_text": "In contrast, applying fresh unit calibration",
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      "title": "Unit final calibration does not preserve inherited detail norms",
      "status": "EXACT_NO_GO",
      "objects": "Squared detail ratios1,2,6,24 by degree",
      "conclusion": "Sequential/fresh metrics differ on retained positive-degree details; the one-step theorem and coarse-image dynamics remain intact.",
      "citations": [
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          "section": "§3",
          "anchor_text": "Theorem RT.2",
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      "title": "Induced composite complement pairing",
      "status": "EXACT_CONDITIONAL",
      "objects": "W20=(Q10R21)ᵀ(Q10R21)+Q21ᵀQ21",
      "conclusion": "Positive onkerR20, semidefinite onambient and zero onthe coarse image. An SPD ambient extension keeps the same complement restriction.",
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          "section": "§4",
          "anchor_text": "Theorem RT.3",
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      "title": "Retain and transport each detail pairing",
      "status": "CANDIDATE",
      "objects": "Composemaps; carrydeclaredWj; no calibration reset",
      "conclusion": "This added tower rule fixes bookkeeping for a retained sequence, without selecting a native history or physical norm.",
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          "section": "§4",
          "anchor_text": "**Candidate rule:",
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      "title": "Grouping-coherent calibrated hierarchy",
      "status": "EXACT_CONDITIONAL",
      "objects": "HL=coarse form+sumL_jᵀW_jL_j",
      "conclusion": "Unique positive hierarchical norm and inherited adjoints for the same retained maps/pairings. Different histories still need comparison laws.",
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          "section": "§4",
          "anchor_text": "For L retained levels",
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      "title": "Associative coarse observable pullback",
      "status": "EXACT_CONDITIONAL",
      "objects": "K20=R21ᵀ(R10ᵀD R10)R21",
      "conclusion": "Absolute coarse stocks compose under both metrics; their fractions can differ because full detail denominators differ.",
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          "section": "§5",
          "anchor_text": "Theorem RT.4",
          "snapshot_sha256": "f11f009ba7bd7f8d572c5f84271d0f00533a54aa7834f5c25e3f230160aae239"
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      "title": "Seventeen complete support effects",
      "status": "EXACT_CONDITIONAL",
      "objects": "15source projectors+old detail+new detail=sumH2seq",
      "conclusion": "Mixed edge witnessfractions1/3,2/3,0 retain both detail outcomes. No physical detector or Born law is acquired.",
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          "section": "§5",
          "anchor_text": "These17 positive quadratic effects",
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      "branch": "polarity",
      "title": "Full barycentric coordinate growth",
      "status": "EXACT_CONDITIONAL",
      "objects": "15→149→2745→61649→1455585",
      "conclusion": "First two refinement matrices are sparse regenerated. Later counts follow exact strict-flag recurrence; directions are not qubits or implementation minima.",
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          "section": "§6",
          "anchor_text": "For a finite3-complex",
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        "SG-SOURCE"
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      "ledger_ids": []
    },
    {
      "id": "RT-RESOURCES",
      "branch": "polarity",
      "title": "Finite whole-chain hierarchy dimension gate",
      "status": "EXACT_CONDITIONAL",
      "objects": "15+134+2596=2745; fixedbudget limits this full tower",
      "conclusion": "Fine details remain in a direct-sum state; dimensions supply no clock, event, initialization, protected export or free reset.",
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        {
          "source_id": "RT01",
          "section": "§6",
          "anchor_text": "With a separately supplied finite",
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    },
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      "branch": "polarity",
      "title": "Hierarchy adoption and different-history frontier",
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      "conclusion": "Associativity for one retained sequence does not select its constitutive source, detector, alternative history covariance or growth law.",
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        {
          "source_id": "RT01",
          "section": "§7",
          "anchor_text": "The next source gate is",
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      "id": "HC-CONTRACT",
      "branch": "polarity",
      "title": "Fixed metric, rate and whole-carrier comparison",
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      "objects": "Star29; bary149; affine/exteriorR; unitdetailH",
      "conclusion": "This is a new conditional comparison contract, not native selection.",
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        {
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          "anchor_text": "conditional unit-detail calibration",
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      "id": "HC-STAR",
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      "title": "Center-star exact weighted spectrum",
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      "objects": "Details(1,4,6,3); seven√5pairs",
      "conclusion": "λ(λ²+4)^7(λ²+5)^7 includes old coarse harmonic and dynamics.",
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        {
          "source_id": "HC01",
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          "anchor_text": "The star f-vector",
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      "dependencies": [
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      "branch": "polarity",
      "title": "Unrestricted spectral and graded capacity",
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      "objects": "Bary√5multiplicities(2,7,8,3)",
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        {
          "source_id": "HC01",
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          "anchor_text": "Theorem HC.1",
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      "title": "S4-equivariant full generator embedding fails",
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        {
          "source_id": "HC01",
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          "anchor_text": "Theorem HC.2",
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      "title": "Coarse transfer loses retained details",
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          "source_id": "HC01",
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      "branch": "polarity",
      "title": "163-direction reversible record completion",
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          "source_id": "HC01",
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      "objects": "imS reducing underH-skewA",
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        {
          "source_id": "HC01",
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      "objects": "[[A0,−C†],[C,Ad]]; externalQf",
      "conclusion": "NonzeroC entails reciprocal feedback and inheritance defect; forcing entails a typed norm-work ledger. NoC/fsource is selected.",
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          "source_id": "HC01",
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      "title": "Native excitation and history selection remain OPEN",
      "status": "OPEN",
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        {
          "source_id": "RSP01",
          "section": "§5",
          "anchor_text": "Every committed tick strictly decreases V",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ]
    },
    {
      "from": "SP-HOLD",
      "to": "SP-TERM",
      "kind": "constitutive_assumption",
      "reason": "Supplies the alternative hold branch.",
      "citations": [
        {
          "source_id": "RSP01",
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          "anchor_text": "Every committed tick strictly decreases V",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ]
    },
    {
      "from": "SP-STOP",
      "to": "SP-TERM",
      "kind": "constitutive_assumption",
      "reason": "Defines committed changes and the full terminal test.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§5",
          "anchor_text": "Every committed tick strictly decreases V",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ]
    },
    {
      "from": "SP-CLOSE",
      "to": "SP-C-DURATION",
      "kind": "constitutive_assumption",
      "reason": "The formula is branch-specific.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§6",
          "anchor_text": "exact number of committed C ticks",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ]
    },
    {
      "from": "SP-DRIVE",
      "to": "SP-C-DURATION",
      "kind": "proof_premise",
      "reason": "Defines pulse/closure feedback.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§6",
          "anchor_text": "exact number of committed C ticks",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ]
    },
    {
      "from": "SP-BANK",
      "to": "SP-C-DURATION",
      "kind": "constitutive_assumption",
      "reason": "Serializes finite refill stages.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§6",
          "anchor_text": "exact number of committed C ticks",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ]
    },
    {
      "from": "SP-STOP",
      "to": "SP-C-DURATION",
      "kind": "constitutive_assumption",
      "reason": "Excludes terminal unchanged inspection from duration.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§6",
          "anchor_text": "exact number of committed C ticks",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ]
    },
    {
      "from": "SP-HOLD",
      "to": "SP-H-LATCH",
      "kind": "constitutive_assumption",
      "reason": "Makes prior open responses persistent.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§7",
          "anchor_text": "H never closes",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ]
    },
    {
      "from": "SP-DRIVE",
      "to": "SP-H-LATCH",
      "kind": "proof_premise",
      "reason": "An open response inhibits later stock pulses.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§7",
          "anchor_text": "H never closes",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ]
    },
    {
      "from": "SP-BANK",
      "to": "SP-H-LATCH",
      "kind": "constitutive_assumption",
      "reason": "Only quiescent states can load further packets.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§7",
          "anchor_text": "H never closes",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ]
    },
    {
      "from": "SP-STOP",
      "to": "SP-H-LATCH",
      "kind": "constitutive_assumption",
      "reason": "A full fixed point is a model halt, not physical no-event.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§7",
          "anchor_text": "H never closes",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ]
    },
    {
      "from": "SP-STATE",
      "to": "SP-PROJECTION",
      "kind": "proof_premise",
      "reason": "The domain includes different stock at the same visible response.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§7",
          "anchor_text": "projection onto Theta alone",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ]
    },
    {
      "from": "SP-DRIVE",
      "to": "SP-PROJECTION",
      "kind": "proof_premise",
      "reason": "The next viability depends on stock.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§7",
          "anchor_text": "projection onto Theta alone",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ]
    },
    {
      "from": "SP-CLOSE",
      "to": "SP-PROJECTION",
      "kind": "constitutive_assumption",
      "reason": "The witness uses the close branch.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§7",
          "anchor_text": "projection onto Theta alone",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ]
    },
    {
      "from": "SP-STATE",
      "to": "SP-HD-BRIDGE",
      "kind": "proof_premise",
      "reason": "Marks prepared variables requiring realization.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§8",
          "anchor_text": "no proved identification",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ]
    },
    {
      "from": "SP-DRIVE",
      "to": "SP-HD-BRIDGE",
      "kind": "constitutive_assumption",
      "reason": "Marks the new source rule requiring justification.",
      "citations": [
        {
          "source_id": "RSP01",
          "section": "§8",
          "anchor_text": "no proved identification",
          "snapshot_sha256": "2b48098d6a477f1de5e45b27ef4f57c723486a25a684953f69b8a913beb82e4e"
        }
      ]
    },
    {
      "from": "SP-STATE",
      "to": "HR-FINITE",
      "kind": "proof_premise",
      "reason": "Defines the finite prepared carrier whose image is requested.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§§2–3",
          "anchor_text": "decoded image M=phi(D) is finite",
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      ]
    },
    {
      "from": "HR-EXACT",
      "to": "HR-FINITE-NOGO",
      "kind": "proof_premise",
      "reason": "Assumes exact state-only intertwining.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§2",
          "anchor_text": "A surjective map on a finite set",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
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      ]
    },
    {
      "from": "HR-SURJ",
      "to": "HR-FINITE-NOGO",
      "kind": "proof_premise",
      "reason": "Makes the decoded image invariant and surjective under F.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§2",
          "anchor_text": "A surjective map on a finite set",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ]
    },
    {
      "from": "HR-FINITE",
      "to": "HR-FINITE-NOGO",
      "kind": "proof_premise",
      "reason": "Turns surjectivity into a permutation.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§2",
          "anchor_text": "A surjective map on a finite set",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
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      ]
    },
    {
      "from": "SP-TERM",
      "to": "HR-FINITE-NOGO",
      "kind": "proof_premise",
      "reason": "Excludes nonfixed target cycles.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§2",
          "anchor_text": "A surjective map on a finite set",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
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      ]
    },
    {
      "from": "HR-EXACT",
      "to": "HR-UNIFORM-NOGO",
      "kind": "proof_premise",
      "reason": "Preserves the exact successor law.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§3",
          "anchor_text": "Finite image can be replaced",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ]
    },
    {
      "from": "HR-SURJ",
      "to": "HR-UNIFORM-NOGO",
      "kind": "proof_premise",
      "reason": "Makes every decoded state have source predecessors.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§3",
          "anchor_text": "Finite image can be replaced",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ]
    },
    {
      "from": "HR-UNIFORM",
      "to": "HR-UNIFORM-NOGO",
      "kind": "proof_premise",
      "reason": "Bounds settlement across the complete decoded family.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§3",
          "anchor_text": "Finite image can be replaced",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ]
    },
    {
      "from": "HR-EXACT",
      "to": "HR-PERIOD-NOGO",
      "kind": "proof_premise",
      "reason": "Transfers source iteration to target iteration.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§4",
          "anchor_text": "F^m(phi(x))=phi(x)",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ]
    },
    {
      "from": "HR-PERIOD",
      "to": "HR-PERIOD-NOGO",
      "kind": "proof_premise",
      "reason": "Returns the source point exactly.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§4",
          "anchor_text": "F^m(phi(x))=phi(x)",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ]
    },
    {
      "from": "SP-TERM",
      "to": "HR-PERIOD-NOGO",
      "kind": "proof_premise",
      "reason": "Excludes nonfixed periodic target points.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§4",
          "anchor_text": "F^m(phi(x))=phi(x)",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ]
    },
    {
      "from": "HR-SKEW",
      "to": "HR-RECURRENCE",
      "kind": "proof_premise",
      "reason": "Supplies a finite-dimensional orthogonal spectral flow.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§5",
          "anchor_text": "Simultaneous phase approximation",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ]
    },
    {
      "from": "HR-EXACT",
      "to": "HR-ROBUST-NOGO",
      "kind": "proof_premise",
      "reason": "Relates native returns to target iterates.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§5",
          "anchor_text": "contradicting exact intertwining",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ]
    },
    {
      "from": "HR-RECURRENCE",
      "to": "HR-ROBUST-NOGO",
      "kind": "proof_premise",
      "reason": "Supplies arbitrarily late source returns.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§5",
          "anchor_text": "contradicting exact intertwining",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ]
    },
    {
      "from": "HR-STABLE",
      "to": "HR-ROBUST-NOGO",
      "kind": "proof_premise",
      "reason": "Returns the whole decoded state, including hidden stock.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§5",
          "anchor_text": "contradicting exact intertwining",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ]
    },
    {
      "from": "SP-TERM",
      "to": "HR-ROBUST-NOGO",
      "kind": "proof_premise",
      "reason": "Prevents target potential from recovering its initial value.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§5",
          "anchor_text": "contradicting exact intertwining",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ]
    },
    {
      "from": "HR-NORM-ID",
      "to": "HR-NORM-NOGO",
      "kind": "proof_premise",
      "reason": "Identifies stock with a conserved total observable.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§6",
          "anchor_text": "forbids a token-consuming inspection",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ]
    },
    {
      "from": "HR-SKEW",
      "to": "HR-NORM-NOGO",
      "kind": "proof_premise",
      "reason": "Conserves the source total norm.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§6",
          "anchor_text": "forbids a token-consuming inspection",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ]
    },
    {
      "from": "SP-STOCK",
      "to": "HR-NORM-NOGO",
      "kind": "proof_premise",
      "reason": "Specifies which target ticks consume stock.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§6",
          "anchor_text": "forbids a token-consuming inspection",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ]
    },
    {
      "from": "HR-EXACT",
      "to": "HR-NORM-NOGO",
      "kind": "proof_premise",
      "reason": "Requires the identified readout to follow the successor.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§6",
          "anchor_text": "forbids a token-consuming inspection",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ]
    },
    {
      "from": "HR-WINDOW",
      "to": "HR-WRAP",
      "kind": "proof_premise",
      "reason": "Supplies the prepared lookup and restricted window.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§7",
          "anchor_text": "The first three native transitions",
          "snapshot_sha256": "150be4a8437edf0d60d1536a3baedd282686c1e163e13ca7c975427f4c4c730e"
        }
      ]
    },
    {
      "from": "HR-SKEW",
      "to": "HR-WRAP",
      "kind": "proof_premise",
      "reason": "Supplies the closed skew flow convention.",
      "citations": [
        {
          "source_id": "HR01",
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          "anchor_text": "The first three native transitions",
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        }
      ]
    },
    {
      "from": "A-CARRIER",
      "to": "HR-WRAP",
      "kind": "proof_premise",
      "reason": "Supplies the filled K4 active frequency-2 spectral identity.",
      "citations": [
        {
          "source_id": "HR01",
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          "anchor_text": "The first three native transitions",
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        }
      ]
    },
    {
      "from": "SP-DRIVE",
      "to": "HR-WRAP",
      "kind": "proof_premise",
      "reason": "Supplies the target trajectory.",
      "citations": [
        {
          "source_id": "HR01",
          "section": "§7",
          "anchor_text": "The first three native transitions",
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        }
      ]
    },
    {
      "from": "SP-TERM",
      "to": "HR-WRAP",
      "kind": "proof_premise",
      "reason": "Makes its final target state fixed.",
      "citations": [
        {
          "source_id": "HR01",
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          "anchor_text": "The first three native transitions",
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        }
      ]
    },
    {
      "from": "HR-LATENT",
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      "kind": "proof_premise",
      "reason": "Supplies the polynomial latent readout.",
      "citations": [
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          "section": "§7",
          "anchor_text": "lookup is also distinct",
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      ]
    },
    {
      "from": "HR-WINDOW",
      "to": "HR-LATENT-MISMATCH",
      "kind": "proof_premise",
      "reason": "Supplies the prepared decoded source states.",
      "citations": [
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          "anchor_text": "lookup is also distinct",
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      ]
    },
    {
      "from": "A-CARRIER",
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      "kind": "proof_premise",
      "reason": "Fixes the declared K4 active plane used by the witness.",
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          "anchor_text": "lookup is also distinct",
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      ]
    },
    {
      "from": "JC-MAP",
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      "reason": "Specifies total finite label maps and codomains.",
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          "anchor_text": "Its explicit inverse",
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    },
    {
      "from": "JC-GATE",
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      "kind": "proof_premise",
      "reason": "Makes each compute block reversible.",
      "citations": [
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          "anchor_text": "The inverse first decrements",
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      ]
    },
    {
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      "kind": "constitutive_assumption",
      "reason": "Specifies all controlled reset/identity blocks and shift.",
      "citations": [
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          "anchor_text": "The inverse first decrements",
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    },
    {
      "from": "JC-U",
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      "kind": "proof_premise",
      "reason": "Supplies each exact joint step.",
      "citations": [
        {
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          "section": "§5",
          "anchor_text": "Theorem JC.1",
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      "kind": "proof_premise",
      "reason": "Allows the projected target successor and exact receipt.",
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          "source_id": "JC01",
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    {
      "from": "JC-BANK",
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      "kind": "constitutive_assumption",
      "reason": "Supplies fresh active and donor payloads.",
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        {
          "source_id": "JC01",
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          "anchor_text": "Theorem JC.1",
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      "from": "JC-SCHEDULE",
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      "kind": "constitutive_assumption",
      "reason": "Contacts each unused cell/donor at the declared address.",
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          "source_id": "JC01",
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      "kind": "proof_premise",
      "reason": "Supplies the complete SWAP identity.",
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          "source_id": "JC01",
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          "anchor_text": "Outgoing record cells are not",
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    {
      "from": "JC-BANK",
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      "kind": "constitutive_assumption",
      "reason": "Supplies independent matched-dimension donor states.",
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        {
          "source_id": "JC01",
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          "anchor_text": "Outgoing record cells are not",
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    {
      "from": "JC-SCHEDULE",
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      "kind": "constitutive_assumption",
      "reason": "Retains each consumed donor and does not contact it again in the window.",
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          "source_id": "JC01",
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          "anchor_text": "Outgoing record cells are not",
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      "reason": "Determines state and receipt dimensions.",
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          "source_id": "JC01",
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          "anchor_text": "allocated capacity",
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      "reason": "Sets the count of retained matched payload carriers.",
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          "source_id": "JC01",
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      "from": "JC-SCHEDULE",
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      "reason": "Determines clock and number of taps.",
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          "source_id": "JC01",
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      "from": "JC-MAP",
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      "kind": "proof_premise",
      "reason": "Defines the admitted finite map and collision preimages.",
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          "source_id": "JC01",
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      "reason": "Supplies the unchanged RSP consumption/renewal accounting.",
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          "source_id": "JC01",
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    {
      "from": "JC-WINDOW",
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      "kind": "proof_premise",
      "reason": "Makes the work labels follow that map within the window.",
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    {
      "from": "JC-EXPORT",
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      "reason": "Transfers remaining work stock to retained outgoing factors.",
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          "source_id": "JC01",
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      "from": "JC-GATE",
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      "kind": "proof_premise",
      "reason": "Specifies dirty-memory modular addition.",
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          "source_id": "JC01",
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          "anchor_text": "the second gives",
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      "from": "JC-SCHEDULE",
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      "reason": "Revisits the same cells after final clock wrap.",
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          "source_id": "JC01",
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      "from": "JC-MAP",
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      "reason": "Supplies the finite C/H example tables.",
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          "source_id": "JC01",
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      "reason": "Sets the complete carrier that must be replenished.",
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          "source_id": "JC01",
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      "from": "JC-EXPORT",
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      "from": "JC-BANK",
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      "reason": "Defines the ideal complete independent supply.",
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          "source_id": "JC01",
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      "reason": "Defines ideal joint channels to compare.",
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          "source_id": "JC01",
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      "from": "JC-GATE",
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          "source_id": "PC01",
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      "from": "JC-U",
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          "source_id": "PC01",
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      "from": "PC-WORD",
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          "source_id": "PC01",
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      "from": "PC-WORD",
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      "reason": "States the full-carrier parity scope.",
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          "snapshot_sha256": "45b69deefe6f370ece8dc7e010e9df21796ffa7f9beee34217d8d708334627a3"
        }
      ]
    },
    {
      "from": "PC-END",
      "to": "PC-RETENTION",
      "kind": "proof_premise",
      "reason": "Exhibits complete projective return.",
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        {
          "source_id": "PC01",
          "section": "§2",
          "anchor_text": "Protected output needs",
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    },
    {
      "from": "JC-EXPORT",
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      "kind": "proof_premise",
      "reason": "Distinguishes correlation export from erasure or fresh supply.",
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        {
          "source_id": "PC01",
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    {
      "from": "A-CARRIER",
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      "kind": "proof_premise",
      "reason": "Supplies the unit-metric single-cell spectrum.",
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          "source_id": "NA01",
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    {
      "from": "NA-GLUED-SOURCE",
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      "kind": "proof_premise",
      "reason": "Supplies the declared glued carriers and exact spectrum.",
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          "source_id": "NA01",
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    {
      "from": "PC-RESOURCES",
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      "kind": "proof_premise",
      "reason": "Supplies retained full programme dimensions.",
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    {
      "from": "NA-CLASSES",
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      "kind": "proof_premise",
      "reason": "Supplies native chain dimensions and copy convention.",
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          "source_id": "NA01",
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    {
      "from": "PC-ENCODE",
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      "kind": "proof_premise",
      "reason": "Requires a declared Hermitian source operator and complete isometry.",
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          "source_id": "NA01",
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    {
      "from": "PC-END",
      "to": "NA-SPECTRAL",
      "kind": "proof_premise",
      "reason": "Supplies full target spectrum.",
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    {
      "from": "NA-CLASSES",
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      "reason": "Fixes the native spectral class.",
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      "from": "PC-END",
      "to": "NA-MULT",
      "kind": "proof_premise",
      "reason": "Supplies target eigenvalue multiplicityQ.",
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          "source_id": "NA01",
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    {
      "from": "NA-SPECTRAL",
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      "kind": "proof_premise",
      "reason": "Makes these spectral distances necessary residual bounds.",
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          "source_id": "NA01",
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    {
      "from": "NA-SCALE",
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      "kind": "constitutive_assumption",
      "reason": "Permits a free common rate in the relaxed comparison.",
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          "source_id": "NA01",
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    {
      "from": "NA-CLASSES",
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      "kind": "proof_premise",
      "reason": "Supplies the three fixed frequency ratios.",
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    {
      "from": "NA-MIN",
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      "kind": "proof_premise",
      "reason": "Supplies the ordered-partition method and finite exact arithmetic.",
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    {
      "from": "PC-END",
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      "kind": "proof_premise",
      "reason": "Supplies the short-clock comparison family.",
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      "from": "NA-MIN",
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      "reason": "Supplies exact rate/centre minima.",
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    {
      "from": "NA-CLASSES",
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      "kind": "proof_premise",
      "reason": "Supplies signed native eigenspace capacities.",
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    {
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      "kind": "constitutive_assumption",
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        {
          "source_id": "NA01",
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      "kind": "proof_premise",
      "reason": "Supplies frequencies2kappa and4kappa.",
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          "source_id": "NA01",
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      "reason": "Supplies native frequency count/ratio.",
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      "from": "NA-MIN",
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      "reason": "Supplies scale-independent relative floors.",
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          "source_id": "NA01",
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      "from": "PC-ENCODE",
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      "reason": "Declares isometry and complete comparison domain.",
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      "from": "NA-TIME",
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      "kind": "proof_premise",
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      "title": "UD bounded subdivision: two-event development gate v0.1",
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      "note": "The saturated-prior conditional theorem survives with its stated h−=0 premise. The binding final-address application needs rederivation."
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      "note": "Permutation-invariant cardinality identities survive; address predictions require rechecking."
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      "note": "No proof edge from a retired universal alias to conditional supplied-scalar algebra is licensed."
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      "note": "An action anchor is not a clock anchor. The clock remains open under its separate scale-sensitive gate."
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      "note": "Changing the information carrier requires rederiving the restricted symmetry result; finite response algebra survives."
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      "note": "Resource and duration claims require a new derivation; the admitted response algebra survives."
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      "changes": [
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      "note": "A close pulse/exhaustion theorem is branch-specific and cannot be transferred to the hold branch."
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      "changes": [
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      "note": "Source-null and cursor changes can be lost. Original full-state duration guarantees need rederivation."
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      "note": "Finite-order or robust-recurrence obstructions can still apply under their own assumptions."
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      "note": "This relaxes the robust-return route; it does not evade a total two-sided finite-image theorem."
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      "title": "Remove the stock/total-norm identification",
      "changes": [
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      "must_affect": [
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      "must_preserve": [
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        "HR-ROBUST-NOGO",
        "SP-STOCK"
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      "note": "Conservation no longer fixes the proposed stock readout; the factor theorems have separate assumptions."
    },
    {
      "id": "jc-fresh",
      "title": "Reuse dirty compute taps",
      "changes": [
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      "must_affect": [
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        "JC-TOKENS",
        "JC-NATIVE"
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      "must_preserve": [
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        "JC-U",
        "HR-FINITE-NOGO",
        "SP-STOCK"
      ],
      "note": "The global permutation and prior no-go persist; projected work/receipt guarantee needs fresh taps."
    },
    {
      "id": "jc-bank",
      "title": "Replace complete fresh bank by marginal checks",
      "changes": [
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      ],
      "must_affect": [
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        "JC-EXPORT",
        "JC-CAPACITY",
        "JC-ERROR",
        "JC-NATIVE"
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      "must_preserve": [
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        "JC-U",
        "HR-FINITE-NOGO"
      ],
      "note": "Whole-bank admission and count premises change; bijectivity does not require independent input states."
    },
    {
      "id": "jc-clock",
      "title": "Change master clock and reset schedule",
      "changes": [
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      "must_affect": [
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        "JC-WINDOW",
        "JC-CAPACITY",
        "JC-WRAP",
        "JC-NATIVE"
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      "must_preserve": [
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        "JC-COLLISION",
        "HR-FINITE-NOGO"
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      "note": "A new schedule needs a new finite-window and accounting proof; inverse of each local gate survives."
    },
    {
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      "title": "Change engineered path metrics",
      "changes": [
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      "must_affect": [
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        "PC-PAD",
        "PC-RESOURCES"
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      "must_preserve": [
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        "PC-ODD",
        "PC-TET-NOGO",
        "HR-FINITE-NOGO"
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      "note": "Clock theorem may remain valid; its specific ordinary path realization must be rederived."
    },
    {
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      "title": "Change the supplied word Hamiltonian",
      "changes": [
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      "must_affect": [
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        "PC-PATH",
        "PC-DIST",
        "PC-ERROR",
        "PC-NATIVE"
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      "must_preserve": [
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        "JC-WINDOW",
        "HR-FINITE-NOGO"
      ],
      "note": "The previous discrete candidate and closed-factor no-go do not inherit a changed continuous implementation."
    },
    {
      "id": "pc-encode",
      "title": "Revise native domain or isometry",
      "changes": [
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      ],
      "must_affect": [
        "PC-ADMISSION",
        "PC-NATIVE"
      ],
      "must_preserve": [
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        "PC-END",
        "PC-TET-NOGO"
      ],
      "note": "The native comparison needs new source matrices; candidate conditional math and scoped spectral obstruction survive."
    },
    {
      "id": "na-native",
      "title": "Change native metric, rates or coupled geometry",
      "changes": [
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      "must_affect": [
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        "NA-MIN",
        "NA-NOGO",
        "NA-ALIAS",
        "NA-NEXT"
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      "must_preserve": [
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        "PC-PATH",
        "HR-FINITE-NOGO"
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      "note": "Recompute class spectra/residuals. Candidate clock and previous total-factor theorem have their own premises."
    },
    {
      "id": "na-free",
      "title": "Restrict the free scale/encoding relaxation",
      "changes": [
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      "must_affect": [
        "NA-MIN",
        "NA-SHARP",
        "NA-TIME",
        "NA-NEXT"
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      "must_preserve": [
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        "NA-NOGO",
        "NA-ALIAS"
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      "note": "Free-frame optima need requalification; necessary spectral theorem and independent alias construction survive."
    },
    {
      "id": "na-isometry",
      "title": "Revise complete native-isometry premise",
      "changes": [
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      "must_affect": [
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        "NA-ALIAS",
        "NA-ERROR-TYPE",
        "NA-NEXT"
      ],
      "must_preserve": [
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        "PC-PATH",
        "HR-FINITE-NOGO"
      ],
      "note": "Full-domain residual and alias comparison require a new encoding contract."
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    {
      "id": "mf-invariant",
      "title": "Break fixed S4 metric invariance",
      "changes": [
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      "must_affect": [
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        "MF-RESIDUAL",
        "MF-FRONTIER"
      ],
      "must_preserve": [
        "MF-GRAM-NOGO",
        "MF-GLUED-NOGO",
        "PC-END",
        "NA-NOGO"
      ],
      "note": "Reclassify native bands; the separate Gram and glued identities have independent source scopes."
    },
    {
      "id": "mf-gram",
      "title": "Revise the fixed Gram rule or geometry family",
      "changes": [
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      ],
      "must_affect": [
        "MF-GRAM-ID",
        "MF-GRAM-NOGO",
        "MF-FRONTIER"
      ],
      "must_preserve": [
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        "MF-RESIDUAL",
        "NA-NOGO"
      ],
      "note": "The allq proof depends on this exact fixed-boundary diagonal family."
    },
    {
      "id": "mf-contract",
      "title": "Allow heterogeneous copies or weaken generator equality",
      "changes": [
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      ],
      "must_affect": [
        "MF-NOGO",
        "MF-RESIDUAL",
        "MF-GRAM-NOGO",
        "MF-GLUED-NOGO",
        "MF-FRONTIER"
      ],
      "must_preserve": [
        "MF-S4",
        "MF-GRAM",
        "MF-GLUED",
        "PC-END"
      ],
      "note": "Single-carrier source formulas survive; complete admission results require a new contract."
    },
    {
      "id": "sg-retraction",
      "title": "Revise the affine coarse retraction",
      "changes": [
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      ],
      "must_affect": [
        "SG-RETRACT",
        "SG-SPD",
        "SG-DYNAMICS",
        "SG-COMPLEMENT",
        "SG-NEXT"
      ],
      "must_preserve": [
        "SG-GRAM",
        "SG-EUCLIDEAN",
        "SG-NORMALIZATIONS",
        "MF-GRAM-NOGO"
      ],
      "note": "All transported metric results require the revised chain retraction; source Euclidean results retain their own premises."
    },
    {
      "id": "sg-pairing",
      "title": "Retain unit metric instead of complement metric",
      "changes": [
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      ],
      "must_affect": [
        "SG-SPD",
        "SG-DYNAMICS",
        "SG-COMPLEMENT",
        "SG-LOCAL",
        "SG-NEXT"
      ],
      "must_preserve": [
        "SG-RETRACT",
        "SG-EUCLIDEAN",
        "SG-SQRT2",
        "PC-END"
      ],
      "note": "The existence theorem is conditional on the declared changed pairing, not a repair of the original unweighted source."
    },
    {
      "id": "sg-source",
      "title": "Change the source subdivision map",
      "changes": [
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      ],
      "must_affect": [
        "SG-GRAM",
        "SG-NORMALIZATIONS",
        "SG-DYNAMICS",
        "SG-SQRT2",
        "SG-NEXT"
      ],
      "must_preserve": [
        "MF-NOGO",
        "NA-NOGO",
        "JC-WINDOW"
      ],
      "note": "Recompute subdivision/adjoint gates. Earlier native spectral and finite-window results remain scoped separately."
    },
    {
      "id": "ms-axioms",
      "title": "Withdraw residual calibration or observer blindness",
      "changes": [
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      ],
      "must_affect": [
        "MS-SELECT-H",
        "MS-SELECT-K",
        "MS-RECEIPTS",
        "MS-CURRENT",
        "MS-SOURCE-GATE"
      ],
      "must_preserve": [
        "MS-CLASSIFY",
        "MS-METRIC-NONUNIQUE",
        "MS-DIAGONAL",
        "SG-GRAM"
      ],
      "note": "Uniqueness requires the stated extra premises. Classification and source nonselection remain separate results."
    },
    {
      "id": "ms-contract",
      "title": "Weaken full coarse-generator inheritance",
      "changes": [
        "MS-CONTRACT"
      ],
      "must_affect": [
        "MS-CLASSIFY",
        "MS-METRIC-NONUNIQUE",
        "MS-SELECT-H",
        "MS-SOURCE-GATE"
      ],
      "must_preserve": [
        "MS-FIDELITY",
        "MS-SELECT-K",
        "MS-OBS-NONUNIQUE",
        "PC-END"
      ],
      "note": "Reclassify compatible metrics; separately stipulated blind-observable theorem survives."
    },
    {
      "id": "ms-stock",
      "title": "Revise the native fixed-carrier stock definition",
      "changes": [
        "MS-FIDELITY"
      ],
      "must_affect": [
        "MS-SELECT-K",
        "MS-RECEIPTS",
        "MS-CURRENT",
        "MS-SOURCE-GATE"
      ],
      "must_preserve": [
        "MS-DIAGONAL",
        "MS-METRIC-NONUNIQUE",
        "MS-CLASSIFY"
      ],
      "note": "Declared coarse region observables need a new source binding; fixed-map algebraic examples keep their stated unit-generator assumptions."
    },
    {
      "id": "rt-history",
      "title": "Change inherited detail calibration",
      "changes": [
        "RT-HISTORY"
      ],
      "must_affect": [
        "RT-ASSOCIATIVE",
        "RT-NEXT"
      ],
      "must_preserve": [
        "RT-MISMATCH",
        "RT-OBS",
        "RT-COUNTS",
        "MS-SELECT-H"
      ],
      "note": "The transported hierarchy requires a new calibration; independently scoped one-step and count theorems survive."
    },
    {
      "id": "rt-regroup",
      "title": "Remove same-sequence grouping requirement",
      "changes": [
        "RT-CONTRACT"
      ],
      "must_affect": [
        "RT-MISMATCH",
        "RT-ASSOCIATIVE",
        "RT-NEXT"
      ],
      "must_preserve": [
        "RT-STEPWISE",
        "RT-W20",
        "RT-OBS",
        "RT-COUNTS"
      ],
      "note": "The two formulas remain different, but their discrepancy is no longer a failure of a declared grouping requirement."
    },
    {
      "id": "rt-readout",
      "title": "Change the complement-blind coarse observable",
      "changes": [
        "MS-SELECT-K"
      ],
      "must_affect": [
        "RT-OBS",
        "RT-EFFECTS",
        "RT-NEXT"
      ],
      "must_preserve": [
        "RT-SPLIT",
        "RT-MISMATCH",
        "RT-COUNTS"
      ],
      "note": "Metric composition and source coordinate counts have premises separate from coarse readout."
    },
    {
      "id": "hc-contract",
      "title": "Change metric, rate or symmetry contract",
      "changes": [
        "HC-CONTRACT"
      ],
      "must_affect": [
        "HC-STAR",
        "HC-CAPACITY",
        "HC-S4",
        "HC-LOSS",
        "HC-RECORD",
        "HC-NEXT"
      ],
      "must_preserve": [
        "HC-NOSEED",
        "HC-COUPLING",
        "RT-ASSOCIATIVE"
      ],
      "note": "New full-carrier comparison requires replay; universal inherited skew no-seed result and prior same-sequence theorem survive."
    },
    {
      "id": "hc-inheritance",
      "title": "Relax exact generator inheritance",
      "changes": [
        "HC-NOSEED"
      ],
      "must_affect": [
        "HC-COUPLING",
        "HC-NEXT"
      ],
      "must_preserve": [
        "HC-CAPACITY",
        "HC-S4",
        "HC-RECORD",
        "RT-OBS"
      ],
      "note": "General coupling analysis depends on the no-seed contract, not unrelated frequency and resource checks."
    }
  ],
  "excluded_inferences": [
    {
      "from": "P-INDEX",
      "to": "P-NOIDLE",
      "reason": "Index-only equality cannot independently prove no-idle response; the idle correction must be sourced."
    },
    {
      "from": "P-INDEX",
      "to": "P-SOURCE",
      "reason": "Rank-nullity does not generate target-hidden obligation spaces."
    },
    {
      "from": "P-FLUX",
      "to": "P-PREDICT",
      "reason": "Signed support is a diagnostic; universal flux-index equality has a counterexample."
    },
    {
      "from": "A-G05",
      "to": "A-ALG",
      "reason": "Retiring a universal native alias does not retract supplied-scalar conditional algebra."
    },
    {
      "from": "A-SCALE",
      "to": "A-ETA",
      "reason": "An exact internal factor 1/2 does not supply a measured physical action correspondence."
    },
    {
      "from": "A-ANCHOR",
      "to": "A-CLOCK",
      "reason": "A0 is invariant under lambda. A separate scale-sensitive anchor is needed."
    },
    {
      "from": "G-LOCAL",
      "to": "A-CLOCK",
      "reason": "A local ratio of historically typed units gives no absolute seconds."
    },
    {
      "from": "A-REC",
      "to": "A-NORM",
      "reason": "A normalized recurrence does not prove support quantization."
    },
    {
      "from": "R-FIBER",
      "to": "P-NOIDLE",
      "reason": "Counting admissible responses does not select the no-idle law."
    },
    {
      "from": "R-PACKET",
      "to": "P-SCORE",
      "reason": "Structural receipt validation does not establish native truth, chronology authentication or empirical score eligibility."
    },
    {
      "from": "SP-TERM",
      "to": "P-PREDICT",
      "reason": "Finite prepared-register termination does not identify native Hodge/transport source laws."
    },
    {
      "from": "SP-C-DURATION",
      "to": "SP-H-LATCH",
      "reason": "Close exhaustion and pulse-duration conclusions do not apply to hold latching."
    },
    {
      "from": "SP-STOCK",
      "to": "A-ANCHOR",
      "reason": "Counting prepared tokens does not supply a physical action anchor."
    },
    {
      "from": "SP-STATE",
      "to": "P-FRAME",
      "reason": "Fixing the identity frame is a candidate restriction, not a native frame receipt."
    },
    {
      "from": "HR-WRAP",
      "to": "SP-HD-BRIDGE",
      "reason": "Matching a prepared finite trace does not supply a native predictive realization."
    },
    {
      "from": "HR-RECURRENCE",
      "to": "HR-STABLE",
      "reason": "Native recurrence does not establish complete-state decoder stability at exact positivity boundaries."
    },
    {
      "from": "HR-NORM-NOGO",
      "to": "HR-FINITE-NOGO",
      "reason": "Norm alias obstruction is separate from the reversible finite-factor theorem."
    },
    {
      "from": "JC-WINDOW",
      "to": "HR-FINITE-NOGO",
      "reason": "A prepared finite window does not supply a total two-sided absorbing factor."
    },
    {
      "from": "JC-CAPACITY",
      "to": "JC-NATIVE",
      "reason": "Register count alone gives no native apparatus, entropy/heat minimum or energy/time calibration."
    },
    {
      "from": "JC-U",
      "to": "JC-RESET",
      "reason": "Global reversibility does not acquire a fresh complete-joint donor or autonomous full restart."
    },
    {
      "from": "PC-PATH",
      "to": "PC-NATIVE",
      "reason": "Authored path metrics/prefix encoding do not establish native source selection."
    },
    {
      "from": "PC-DIST",
      "to": "PC-RETENTION",
      "reason": "Terminal-state fidelity alone does not provide permanent isolation."
    },
    {
      "from": "PC-ODD",
      "to": "PC-TET-NOGO",
      "reason": "Full-space kernel obstruction and isometric spectral embedding obstruction have different scopes."
    },
    {
      "from": "NA-TIME",
      "to": "PC-DIST",
      "reason": "A lower floor on an upper comparison budget is not an actual trace-distance lower bound."
    },
    {
      "from": "NA-SHARP",
      "to": "PC-NATIVE",
      "reason": "Unrestricted eigenbasis/copy sharpness does not acquire a source-selected native encoding."
    },
    {
      "from": "NA-ALIAS",
      "to": "NA-NOGO",
      "reason": "Exact sampled endpoint agreement does not imply exact generator intertwining."
    },
    {
      "from": "MF-RESIDUAL",
      "to": "PC-DIST",
      "reason": "A generator-budget floor does not bound actual endpoint discrepancy from below."
    },
    {
      "from": "MF-GRAM-NOGO",
      "to": "MF-NOGO",
      "reason": "The five-band Gram obstruction is a separate ratio proof, not fixedS4 invariance."
    },
    {
      "from": "MF-DEGREE",
      "to": "PC-NATIVE",
      "reason": "Algebraically realizable metric ratios do not supply a source-selected native metric or encoding."
    },
    {
      "from": "SG-DYNAMICS",
      "to": "PC-NATIVE",
      "reason": "Exact inherited old-code dynamics selects no metric law, full programme encoding or native physical bridge."
    },
    {
      "from": "SG-SPD",
      "to": "SG-EUCLIDEAN",
      "reason": "A changed target pairing does not refute the original Euclidean strict-contract theorem."
    },
    {
      "from": "SG-COMPLEMENT",
      "to": "JC-RESET",
      "reason": "A direct-sum complement is not a free reset or a tensor-factor donor bank."
    },
    {
      "from": "MS-SELECT-H",
      "to": "PC-NATIVE",
      "reason": "Conditional uniqueness after added axioms is not a source-selected native operator or physical bridge."
    },
    {
      "from": "MS-CURRENT",
      "to": "SG-LOCAL",
      "reason": "Decoded coarse continuity does not provide additive local fine stocks."
    },
    {
      "from": "MS-RECEIPTS",
      "to": "JC-RESET",
      "reason": "A retained complement outcome is not erased information or a free reset."
    },
    {
      "from": "RT-ASSOCIATIVE",
      "to": "PC-NATIVE",
      "reason": "Calibrated same-sequence regrouping does not select a native history or physical operator."
    },
    {
      "from": "RT-MISMATCH",
      "to": "MS-SELECT-H",
      "reason": "A new grouping requirement does not retract one-step uniqueness under its declared residual calibration."
    },
    {
      "from": "RT-EFFECTS",
      "to": "JC-RESET",
      "reason": "Aggregated detail observations retain rather than erase state or acquire reset resources."
    },
    {
      "from": "HC-RECORD",
      "to": "PC-NATIVE",
      "reason": "A reversible direct-sum record transfer does not acquire a native refinement event, generator or physical reset."
    }
  ],
  "target_closure": [
    {
      "target": "P-IDLE",
      "direct_premises": [
        "P-ADM"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "P-INDEX",
      "direct_premises": [
        "P-RANK"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "P-BUDGET",
      "direct_premises": [
        "P-DEF"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "P-CORRECT",
      "direct_premises": [
        "P-IDLE",
        "P-INDEX",
        "P-BUDGET"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "P-EQUAL",
      "direct_premises": [
        "P-CORRECT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "P-SAT",
      "direct_premises": [
        "P-CORRECT",
        "P-PRIOR"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "P-ADDRESS",
      "direct_premises": [
        "P-DEF",
        "P-NOIDLE"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "P-SHELL",
      "direct_premises": [
        "P-BURDEN"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "P-CONFLICT",
      "direct_premises": [
        "P-ADM",
        "P-ADDRESS",
        "P-SHELL"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "P-FLUX-NOGO",
      "direct_premises": [
        "P-FLUX"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "A-J",
      "direct_premises": [
        "A-CARRIER"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "A-ACTION",
      "direct_premises": [
        "A-J",
        "A-PHASE",
        "A-UNIT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "A-SCALE",
      "direct_premises": [
        "A-ACTION"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "A-REC",
      "direct_premises": [
        "A-ACTION",
        "A-NORM",
        "A-CARRIER"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "A-END-NOGO",
      "direct_premises": [
        "A-END",
        "A-ACTION"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "A-SPEED",
      "direct_premises": [
        "A-UNIT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "A-GAUGE",
      "direct_premises": [
        "A-SPEED"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "A-ANCHOR-NOGO",
      "direct_premises": [
        "A-GAUGE"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "G-LOCAL",
      "direct_premises": [
        "G-HISTORY",
        "G-STATIONARY",
        "G-EVENT",
        "A-J",
        "A-UNIT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "G-GLOBAL-NOGO",
      "direct_premises": [
        "G-VARY",
        "G-CONST"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "R-FIBER",
      "direct_premises": [
        "R-I",
        "P-IDLE"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "R-COUNT",
      "direct_premises": [
        "R-FIBER",
        "P-CORRECT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "R-DETERMINISTIC",
      "direct_premises": [
        "R-FIBER",
        "R-REDUCED"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "R-KERNEL",
      "direct_premises": [
        "R-FIBER",
        "R-REDUCED"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "R-UNIQUE-NOGO",
      "direct_premises": [
        "R-FIBER",
        "P-CORRECT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "SP-STOCK",
      "direct_premises": [
        "SP-DRIVE",
        "SP-BANK"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "SP-TERM",
      "direct_premises": [
        "SP-STOCK",
        "SP-CLOSE",
        "SP-HOLD",
        "SP-STOP"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "SP-C-DURATION",
      "direct_premises": [
        "SP-CLOSE",
        "SP-DRIVE",
        "SP-BANK",
        "SP-STOP"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "SP-H-LATCH",
      "direct_premises": [
        "SP-HOLD",
        "SP-DRIVE",
        "SP-BANK",
        "SP-STOP"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "SP-PROJECTION",
      "direct_premises": [
        "SP-STATE",
        "SP-DRIVE",
        "SP-CLOSE"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "HR-FINITE-NOGO",
      "direct_premises": [
        "HR-EXACT",
        "HR-SURJ",
        "HR-FINITE",
        "SP-TERM"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "HR-UNIFORM-NOGO",
      "direct_premises": [
        "HR-EXACT",
        "HR-SURJ",
        "HR-UNIFORM"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "HR-PERIOD-NOGO",
      "direct_premises": [
        "HR-EXACT",
        "HR-PERIOD",
        "SP-TERM"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "HR-RECURRENCE",
      "direct_premises": [
        "HR-SKEW"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "HR-ROBUST-NOGO",
      "direct_premises": [
        "HR-EXACT",
        "HR-RECURRENCE",
        "HR-STABLE",
        "SP-TERM"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "HR-NORM-NOGO",
      "direct_premises": [
        "HR-NORM-ID",
        "HR-SKEW",
        "SP-STOCK",
        "HR-EXACT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "HR-WRAP",
      "direct_premises": [
        "HR-WINDOW",
        "HR-SKEW",
        "A-CARRIER",
        "SP-DRIVE",
        "SP-TERM"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "HR-LATENT-MISMATCH",
      "direct_premises": [
        "HR-LATENT",
        "HR-WINDOW",
        "A-CARRIER"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "JC-GATE",
      "direct_premises": [
        "JC-MAP"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "JC-U",
      "direct_premises": [
        "JC-GATE",
        "JC-SCHEDULE"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "JC-WINDOW",
      "direct_premises": [
        "JC-U",
        "JC-TAPS",
        "JC-BANK",
        "JC-SCHEDULE"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "JC-EXPORT",
      "direct_premises": [
        "JC-PIV-EXPORT",
        "JC-BANK",
        "JC-SCHEDULE"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "JC-CAPACITY",
      "direct_premises": [
        "JC-MAP",
        "JC-BANK",
        "JC-SCHEDULE"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "JC-COLLISION",
      "direct_premises": [
        "JC-MAP"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "JC-TOKENS",
      "direct_premises": [
        "SP-STOCK",
        "JC-WINDOW",
        "JC-EXPORT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "JC-WRAP",
      "direct_premises": [
        "JC-GATE",
        "JC-SCHEDULE",
        "JC-MAP"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "JC-ERROR",
      "direct_premises": [
        "JC-BANK",
        "JC-U"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "PC-END",
      "direct_premises": [
        "PC-H",
        "PC-SPIN"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "PC-PATH",
      "direct_premises": [
        "PC-METRIC",
        "PC-H",
        "PC-WORD"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "PC-ODD",
      "direct_premises": [
        "PC-END"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "PC-PAD",
      "direct_premises": [
        "PC-WORD",
        "PC-ODD",
        "PC-PATH"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "PC-TET-NOGO",
      "direct_premises": [
        "PC-END",
        "A-CARRIER"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "PC-RESOURCES",
      "direct_premises": [
        "JC-CAPACITY",
        "PC-H",
        "PC-PAD"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "PC-DIST",
      "direct_premises": [
        "PC-END"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "PC-ERROR",
      "direct_premises": [
        "PC-DIST",
        "PC-H"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "PC-ADMISSION",
      "direct_premises": [
        "PC-ENCODE",
        "PC-H"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "NA-DIM",
      "direct_premises": [
        "PC-RESOURCES",
        "NA-CLASSES"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "NA-SPECTRAL",
      "direct_premises": [
        "PC-ENCODE",
        "PC-END",
        "NA-CLASSES"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "NA-MULT",
      "direct_premises": [
        "NA-SPECTRAL",
        "PC-END"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "NA-MIN",
      "direct_premises": [
        "NA-SPECTRAL",
        "NA-SCALE",
        "NA-CLASSES"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "NA-UNION",
      "direct_premises": [
        "NA-MIN",
        "PC-END"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "NA-SHARP",
      "direct_premises": [
        "NA-MIN",
        "NA-CLASSES",
        "NA-SCALE"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "NA-NOGO",
      "direct_premises": [
        "PC-END",
        "NA-CLASSES"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "NA-TIME",
      "direct_premises": [
        "NA-MIN",
        "PC-END",
        "PC-ADMISSION"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "NA-ALIAS",
      "direct_premises": [
        "NA-CLASSES",
        "PC-END",
        "PC-ENCODE"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "NA-ERROR-TYPE",
      "direct_premises": [
        "NA-TIME",
        "NA-ALIAS"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "MF-CONVENTIONS",
      "direct_premises": [],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "MF-S4",
      "direct_premises": [
        "MF-S4-SOURCE"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "MF-DEGREE",
      "direct_premises": [
        "MF-CONVENTIONS",
        "MF-S4"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "MF-NOGO",
      "direct_premises": [
        "MF-S4",
        "MF-CONTRACT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "MF-RESIDUAL",
      "direct_premises": [
        "MF-S4",
        "MF-CONTRACT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "MF-GRAM-ID",
      "direct_premises": [
        "MF-GRAM",
        "MF-CONVENTIONS"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "MF-GRAM-NOGO",
      "direct_premises": [
        "MF-GRAM-ID",
        "MF-CONTRACT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "MF-GLUED-NOGO",
      "direct_premises": [
        "MF-GLUED",
        "MF-CONTRACT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "SG-GRAM",
      "direct_premises": [
        "SG-SOURCE"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "SG-EUCLIDEAN",
      "direct_premises": [
        "SG-GRAM"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "SG-NORMALIZATIONS",
      "direct_premises": [
        "SG-GRAM",
        "MF-CONVENTIONS"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "SG-RETRACT",
      "direct_premises": [
        "SG-GRAM",
        "SG-R"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "SG-SPD",
      "direct_premises": [
        "SG-RETRACT",
        "SG-H"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "SG-DYNAMICS",
      "direct_premises": [
        "SG-SPD",
        "SG-RETRACT",
        "MF-CONVENTIONS"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "SG-COMPLEMENT",
      "direct_premises": [
        "SG-RETRACT",
        "SG-DYNAMICS"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "SG-SQRT2",
      "direct_premises": [
        "SG-GRAM"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "MS-FIDELITY",
      "direct_premises": [],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "MS-CLASSIFY",
      "direct_premises": [
        "MS-CONTRACT",
        "MF-CONVENTIONS"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "MS-METRIC-NONUNIQUE",
      "direct_premises": [
        "MS-CLASSIFY",
        "SG-RETRACT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "MS-OBS-NONUNIQUE",
      "direct_premises": [
        "SG-RETRACT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "MS-DIAGONAL",
      "direct_premises": [
        "SG-GRAM",
        "MF-CONVENTIONS"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "MS-SELECT-H",
      "direct_premises": [
        "MS-AXIOMS",
        "MS-CLASSIFY"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "MS-SELECT-K",
      "direct_premises": [
        "MS-AXIOMS",
        "SG-RETRACT",
        "MS-FIDELITY"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "MS-RECEIPTS",
      "direct_premises": [
        "MS-SELECT-H",
        "MS-SELECT-K"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "MS-CURRENT",
      "direct_premises": [
        "MS-SELECT-H",
        "MS-SELECT-K",
        "SG-DYNAMICS"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "RT-SPLIT",
      "direct_premises": [
        "SG-GRAM",
        "SG-RETRACT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "RT-STEPWISE",
      "direct_premises": [
        "MS-SELECT-H",
        "RT-SPLIT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "RT-MISMATCH",
      "direct_premises": [
        "RT-STEPWISE",
        "RT-FRESH",
        "RT-CONTRACT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "RT-W20",
      "direct_premises": [
        "RT-SPLIT",
        "RT-STEPWISE"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "RT-ASSOCIATIVE",
      "direct_premises": [
        "RT-W20",
        "RT-HISTORY",
        "RT-CONTRACT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "RT-OBS",
      "direct_premises": [
        "RT-SPLIT",
        "MS-SELECT-K"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "RT-EFFECTS",
      "direct_premises": [
        "RT-STEPWISE",
        "RT-OBS"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "RT-COUNTS",
      "direct_premises": [
        "SG-SOURCE"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "RT-RESOURCES",
      "direct_premises": [
        "RT-COUNTS",
        "RT-SPLIT",
        "JC-RESET"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "HC-STAR",
      "direct_premises": [
        "HC-CONTRACT",
        "MS-SELECT-H"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "HC-CAPACITY",
      "direct_premises": [
        "HC-STAR",
        "HC-CONTRACT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "HC-S4",
      "direct_premises": [
        "HC-CAPACITY",
        "HC-CONTRACT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "HC-LOSS",
      "direct_premises": [
        "HC-CONTRACT",
        "SG-RETRACT"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "HC-RECORD",
      "direct_premises": [
        "HC-LOSS",
        "JC-RESET"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "HC-NOSEED",
      "direct_premises": [],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    },
    {
      "target": "HC-COUPLING",
      "direct_premises": [
        "HC-NOSEED"
      ],
      "completeness": "Scoped conditional target only; native history/excitation and physical/global closure remain OPEN."
    }
  ]
}
