{
  "edition": "0.4",
  "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.",
  "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": "e4468363b04295ce1c56e346b5cb8d1535b93cce",
  "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": []
    }
  ],
  "edges": [
    {
      "from": "P-DEF",
      "to": "P-ADM",
      "kind": "proof_premise",
      "reason": "Defines the masks in the inequalities.",
      "citations": [
        {
          "source_id": "E04",
          "section": "§2",
          "anchor_text": "admissible",
          "snapshot_sha256": "0243b70b3077ad58303ffad4f13d73fdc32bbe55fd204e52d2877c36318f4553"
        }
      ]
    },
    {
      "from": "P-ADM",
      "to": "P-IDLE",
      "kind": "proof_premise",
      "reason": "The inequalities make h an admissible residual mask.",
      "citations": [
        {
          "source_id": "C0963",
          "section": "declared_source_variables / exact_response_form",
          "anchor_text": "q = omega OR h",
          "snapshot_sha256": "6da081eec3922f361d4e616673b0f994eed9471c050e818e8b98b80b46e9d2bc"
        }
      ]
    },
    {
      "from": "P-RANK",
      "to": "P-INDEX",
      "kind": "proof_premise",
      "reason": "Finite domain and codomain dimensions determine the index.",
      "citations": [
        {
          "source_id": "C0884",
          "section": "§2",
          "anchor_text": "Rank-nullity",
          "snapshot_sha256": "027b1d033ef17e7d9946b18cd577b5e370e7c9319bf439a6ba689249f71971b5"
        }
      ]
    },
    {
      "from": "P-DEF",
      "to": "P-BUDGET",
      "kind": "proof_premise",
      "reason": "Uses Theta=1−q on both three-seat states.",
      "citations": [
        {
          "source_id": "C0957",
          "section": "Theorem",
          "anchor_text": "Hamming event budget",
          "snapshot_sha256": "6ea514e6f5af3cbce082605d2575259748aa22e976be5a4d8dfec5855824fae1"
        }
      ]
    },
    {
      "from": "P-IDLE",
      "to": "P-CORRECT",
      "kind": "proof_premise",
      "reason": "Separates viable and idle counts.",
      "citations": [
        {
          "source_id": "C0957",
          "section": "Theorem",
          "anchor_text": "residual idle-response index",
          "snapshot_sha256": "6ea514e6f5af3cbce082605d2575259748aa22e976be5a4d8dfec5855824fae1"
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      "reason": "Uses the admitted binary response inequalities.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§1",
          "anchor_text": "I is the intact-null potential mask",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
        }
      ]
    },
    {
      "from": "R-I",
      "to": "R-FIBER",
      "kind": "proof_premise",
      "reason": "Defines the intact-null positions.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§2",
          "anchor_text": "response fiber has exactly 2^i",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
        }
      ]
    },
    {
      "from": "P-IDLE",
      "to": "R-FIBER",
      "kind": "proof_premise",
      "reason": "Supplies the unique disjoint mask decomposition.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§2",
          "anchor_text": "response fiber has exactly 2^i",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
        }
      ]
    },
    {
      "from": "R-FIBER",
      "to": "R-COUNT",
      "kind": "proof_premise",
      "reason": "Counts the size-j subsets of the idle domain.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§§2–3",
          "anchor_text": "binomial(i,j)",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
        }
      ]
    },
    {
      "from": "P-CORRECT",
      "to": "R-COUNT",
      "kind": "proof_premise",
      "reason": "Relates idle count to full Hamming budget.",
      "citations": [
        {
          "source_id": "RESPONSE01",
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          "anchor_text": "binomial(i,j)",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
        }
      ]
    },
    {
      "from": "R-I",
      "to": "R-REDUCED",
      "kind": "proof_premise",
      "reason": "Identifies equivalent intact-null addresses.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§4",
          "anchor_text": "using only (T,L)",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
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      ]
    },
    {
      "from": "R-FIBER",
      "to": "R-DETERMINISTIC",
      "kind": "proof_premise",
      "reason": "Provides the allowed response masks.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§4",
          "anchor_text": "must be constant",
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      ]
    },
    {
      "from": "R-REDUCED",
      "to": "R-DETERMINISTIC",
      "kind": "proof_premise",
      "reason": "Fixes the symmetry and limited information domain.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§4",
          "anchor_text": "must be constant",
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      ]
    },
    {
      "from": "R-FIBER",
      "to": "R-KERNEL",
      "kind": "proof_premise",
      "reason": "Provides the response support and cardinality orbits.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§4",
          "anchor_text": "one probability p_j",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
        }
      ]
    },
    {
      "from": "R-REDUCED",
      "to": "R-KERNEL",
      "kind": "proof_premise",
      "reason": "Requires invariance on equivalent idle addresses.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§4",
          "anchor_text": "one probability p_j",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
        }
      ]
    },
    {
      "from": "R-FIBER",
      "to": "R-UNIQUE-NOGO",
      "kind": "proof_premise",
      "reason": "Provides both masks and their distinct responses.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§3",
          "anchor_text": "both h=000 and h=I",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
        }
      ]
    },
    {
      "from": "P-CORRECT",
      "to": "R-UNIQUE-NOGO",
      "kind": "proof_premise",
      "reason": "Their budgets differ by the idle-count difference.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§3",
          "anchor_text": "both h=000 and h=I",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
        }
      ]
    },
    {
      "from": "R-COUNT",
      "to": "R-PACKET",
      "kind": "proof_premise",
      "reason": "Distinguishes the count and address routes.",
      "citations": [
        {
          "source_id": "RESPONSE01",
          "section": "§5",
          "anchor_text": "complete prospective packet",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
        }
      ]
    },
    {
      "from": "P-SOURCE",
      "to": "R-PACKET",
      "kind": "evaluation_requirement",
      "reason": "Prospective viability must have an independently frozen source.",
      "citations": [
        {
          "source_id": "RESPONSE01",
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          "anchor_text": "complete prospective packet",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
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      ]
    },
    {
      "from": "P-HSOURCE",
      "to": "R-PACKET",
      "kind": "evaluation_requirement",
      "reason": "An actual idle law or receipt must be acquired before endpoint exposure.",
      "citations": [
        {
          "source_id": "RESPONSE01",
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          "anchor_text": "complete prospective packet",
          "snapshot_sha256": "5337a05b7ead54cada83df5e51adf6cb9ff7213cc5aaf3c844988adf39f946e4"
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    {
      "from": "P-FRAME",
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      "kind": "evaluation_requirement",
      "reason": "Directed addresses require the frame receipt.",
      "citations": [
        {
          "source_id": "RESPONSE01",
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          "anchor_text": "complete prospective packet",
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      ]
    }
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    {
      "id": "E04",
      "title": "UD polarity pipeline synthetic consistency audit v0.1",
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      "id": "C0963",
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    {
      "id": "C0884",
      "title": "Constitutive Receipt-Index Event Operator",
      "path": "/sources/dependency-snapshots-v0.3/C0884.txt",
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    {
      "id": "C0957",
      "title": "Viable-Lane Plus Idle-Response Index",
      "path": "/sources/dependency-snapshots-v0.3/C0957.txt",
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    {
      "id": "R35",
      "title": "POC-1 frozen sidecar recovery and scoring gate v0.1",
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    {
      "id": "E11",
      "title": "UD_SUBSTRATE_PHYSICAL_CLOCK_SCALE_GAUGE_THEOREM_v0.1",
      "path": "/sources/dependency-snapshots-v0.3/E11.txt",
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    {
      "id": "C0579",
      "title": "Xi-Hbar and Hodge–Dirac Action Recovery",
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      "id": "C0906",
      "title": "Native Hodge Action–Phase Specific Scale Theorem",
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      "id": "L65",
      "title": "UD_COEFFICIENT_PROVENANCE_LEDGER_v0.65_C3_7_CLOSURE_N1_N2.json",
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      "id": "REC02",
      "title": "Presentation reconciliation and versioned dispositions v0.2",
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      "id": "C0883",
      "title": "QPB-1 Independent Action-Ratio Test",
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      "id": "E13",
      "title": "UD_GENESIS_HODGE_CANONICAL_ACTION_CLOCK_INTERTWINER_v0.1",
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      "id": "RESPONSE01",
      "title": "Minimal pre-event response source theorem and contract v0.1",
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      "id": "idle-law",
      "title": "Withdraw binding POC-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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    {
      "id": "prior",
      "title": "Remove the saturated prior premise",
      "changes": [
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      "must_preserve": [
        "P-BUDGET",
        "P-CORRECT",
        "P-INDEX"
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      "note": "Permutation-invariant cardinality identities survive; address predictions require rechecking."
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      "id": "g05",
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      "changes": [
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      "must_preserve": [
        "A-ALG",
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      "note": "No proof edge from a retired universal alias to conditional supplied-scalar algebra is licensed."
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      "id": "metric",
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        "A-SCALE",
        "A-REC",
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      "must_preserve": [
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      "id": "action-anchor",
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      "changes": [
        "A-ANCHOR"
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      "must_preserve": [
        "A-ACTION",
        "A-SCALE",
        "A-GAUGE",
        "A-CLOCK"
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    {
      "id": "clock-anchor",
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      "changes": [
        "A-CLOCK-ANCHOR"
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      "must_preserve": [
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        "A-GAUGE",
        "A-SCALE"
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      "id": "same-history",
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      "changes": [
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      "must_preserve": [
        "A-ACTION",
        "A-GAUGE",
        "G-GLOBAL-NOGO"
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      "id": "reduced-carrier",
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        "R-KERNEL"
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      "must_preserve": [
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        "R-COUNT",
        "P-CORRECT"
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      "note": "Changing the information carrier requires rederiving the restricted symmetry result; finite response algebra survives."
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  "excluded_inferences": [
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      "from": "P-INDEX",
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      "from": "P-INDEX",
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      "reason": "Rank-nullity does not generate target-hidden obligation spaces."
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      "reason": "Signed support is a diagnostic; universal flux-index equality has a counterexample."
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      "from": "A-G05",
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      "reason": "Retiring a universal native alias does not retract supplied-scalar conditional algebra."
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      "from": "A-SCALE",
      "to": "A-ETA",
      "reason": "An exact internal factor 1/2 does not supply a measured physical action correspondence."
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    {
      "from": "A-ANCHOR",
      "to": "A-CLOCK",
      "reason": "A0 is invariant under lambda. A separate scale-sensitive anchor is needed."
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    {
      "from": "G-LOCAL",
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      "reason": "A local ratio of historically typed units gives no absolute seconds."
    },
    {
      "from": "A-REC",
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      "reason": "A normalized recurrence does not prove support quantization."
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    {
      "from": "R-FIBER",
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      "reason": "Counting admissible responses does not select the no-idle law."
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    {
      "from": "R-PACKET",
      "to": "P-SCORE",
      "reason": "Structural receipt validation does not establish native truth, chronology authentication or empirical score eligibility."
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  ],
  "target_closure": [
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      "target": "P-IDLE",
      "direct_premises": [
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      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
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    {
      "target": "P-INDEX",
      "direct_premises": [
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      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "P-BUDGET",
      "direct_premises": [
        "P-DEF"
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      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "P-CORRECT",
      "direct_premises": [
        "P-IDLE",
        "P-INDEX",
        "P-BUDGET"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "P-EQUAL",
      "direct_premises": [
        "P-CORRECT"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "P-SAT",
      "direct_premises": [
        "P-CORRECT",
        "P-PRIOR"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "P-ADDRESS",
      "direct_premises": [
        "P-DEF",
        "P-NOIDLE"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "P-SHELL",
      "direct_premises": [
        "P-BURDEN"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "P-CONFLICT",
      "direct_premises": [
        "P-ADM",
        "P-ADDRESS",
        "P-SHELL"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "P-FLUX-NOGO",
      "direct_premises": [
        "P-FLUX"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "A-J",
      "direct_premises": [
        "A-CARRIER"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "A-ACTION",
      "direct_premises": [
        "A-J",
        "A-PHASE",
        "A-UNIT"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "A-SCALE",
      "direct_premises": [
        "A-ACTION"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "A-REC",
      "direct_premises": [
        "A-ACTION",
        "A-NORM",
        "A-CARRIER"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "A-END-NOGO",
      "direct_premises": [
        "A-END",
        "A-ACTION"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "A-SPEED",
      "direct_premises": [
        "A-UNIT"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "A-GAUGE",
      "direct_premises": [
        "A-SPEED"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "A-ANCHOR-NOGO",
      "direct_premises": [
        "A-GAUGE"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "G-LOCAL",
      "direct_premises": [
        "G-HISTORY",
        "G-STATIONARY",
        "G-EVENT",
        "A-J",
        "A-UNIT"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "G-GLOBAL-NOGO",
      "direct_premises": [
        "G-VARY",
        "G-CONST"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "R-FIBER",
      "direct_premises": [
        "R-I",
        "P-IDLE"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "R-COUNT",
      "direct_premises": [
        "R-FIBER",
        "P-CORRECT"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "R-DETERMINISTIC",
      "direct_premises": [
        "R-FIBER",
        "R-REDUCED"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "R-KERNEL",
      "direct_premises": [
        "R-FIBER",
        "R-REDUCED"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    },
    {
      "target": "R-UNIQUE-NOGO",
      "direct_premises": [
        "R-FIBER",
        "P-CORRECT"
      ],
      "completeness": "Declared finite target only; source identities remain premises; new refinement is development with no registry entry."
    }
  ]
}
