Shared-edge covariance and nontrivial matching holonomy are established internally; the response shell preserves the immutable scientific core. Governed release package · 0.1Facet-Frame Transport and Yale Response ShellShared-edge covariance and nontrivial matching holonomy are established internally; the response shell preserves the immutable scientific core.StatusEXACT TRANSPORT / RESPONSE PENDINGPhysical promotion0Package files13Hash manifestVerified · 12 filesDownload immutable release ZIP ↓Package compositionpackage root13Show all 13 preserved pathsUD_DELTA4_FACET_FRAME_AND_YALE_RESPONSE_SHELL_v0.1_HASH_MANIFEST.jsonUD_DELTA4_FACET_FRAME_EDGE_GATE_TRANSITION_AND_GLOBAL_FACE_VIABILITY_VERIFICATION_v0.1.jsonUD_DELTA4_FACET_FRAME_EDGE_GATE_TRANSITION_AND_GLOBAL_FACE_VIABILITY_v0.1.mdUD_E2_APPARATUS_SPECIFIC_PREREG_CORE_v0.1.jsonUD_HARRIS_YALE_E2_PI_RESPONSE_SCHEMA_v0.1.jsonUD_HARRIS_YALE_E2_RESPONSE_READY_INSTANCE_SHELL_v0.1.jsonUD_HARRIS_YALE_E2_RESPONSE_READY_INSTANCE_SHELL_v0.1.mdUD_HARRIS_YALE_E2_RESPONSE_SHELL_METHOD_TEST_v0.1.jsonUD_HARRIS_YALE_PROVISIONAL_E2_APPARATUS_BINDING_v0.1.jsonUD_MANUSCRIPT_MILESTONE_ADDENDUM_FACET_FRAME_YALE_RESPONSE_v0.12.mdUD_PROVENANCE_LEDGER_ADDENDUM_FACET_FRAME_YALE_RESPONSE_v0.11.mdingest_harris_yale_e2_pi_response_v0_1.pyverify_delta4_facet_frame_gate_v0_1.pyUD_DELTA4_FACET_FRAME_EDGE_GATE_TRANSITION_AND_GLOBAL_FACE_VIABILITY_v0.1.mdUD Delta4 Facet-Frame Edge-Gate Transition and Global Face Viability v0.1 Date: 2026-09-14 Status: PARTIAL_PASS / FACET TRANSITION CLOSED / GLOBAL AND DESCENT CONDITIONAL / NONFLAT MATCHING FRAME Physical promotion: 0 1. Source-bound starting point Current UD already contains an exact tetrahedral relative-frame theorem. For an exact S4S_4 vertex frame receipt rr, the visible opposite-edge matching-frame receipt is σ=πℳ(r)∈S3. \sigma=\pi_{\mathcal M}(r)\in S_3. Frame receipts compose in order and transform covariantly under relabeling. That machinery can be reused as representation grammar for adjacent tetrahedral facets of Δ4\Delta^4, while preserving provenance: rj←igeom≠rntransport. r^{\mathrm geom}_{j\leftarrow i} \neq r_n^{\mathrm transport}. The first is a simplicial adjacency map. The second is a source-derived dynamical transport receipt. Equal group elements would not make them the same object. 2. Canonical local facet frames Let Fi={0,1,2,3,4}\{i} F_i = \{0,1,2,3,4\}\setminus\{i\} be the tetrahedral facet opposite vertex ii. Choose the increasing vertex order on each FiF_i as its local K4K_4 chart ℓi:{0,1,2,3}→Fi. \ell_i:\{0,1,2,3\}\to F_i. Within each chart use the canonical three perfect matchings A=(01)(23),B=(02)(13),C=(03)(12). A=(01)(23), \qquad B=(02)(13), \qquad C=(03)(12). These are local matching labels only. 3. Exact adjacent-facet transition Two distinct facets Fi,FjF_i,F_j share one triangular face. There is a unique simplicial vertex map sij s_{ij} that: maps FiF_i to FjF_j; fixes all three shared vertices; maps the unique nonshared vertex j∈Fij\in F_i to i∈Fji\in F_j. As a global five-vertex permutation this is simply the transposition sij=(ij). s_{ij}=(ij). The local tetrahedral frame transition is therefore rj←igeom=ℓj−1sijℓi∈S4. \boxed{ r^{\mathrm geom}_{j\leftarrow i} = \ell_j^{-1}s_{ij}\ell_i \in S_4. } Its visible matching-frame transition is σj←i=πℳ(rj←igeom)∈S3. \boxed{ \sigma_{j\leftarrow i} = \pi_{\mathcal M} \left( r^{\mathrm geom}_{j\leftarrow i} \right) \in S_3. } No fitted coefficient appears. AUTO_LOCK DELTA4_ADJACENT_TETRAHEDRAL_FACETS_HAVE_A_UNIQUE_SHARED_TRIANGLE_FIXING_S4_FRAME_TRANSITION_THEOREM_v0.1 AUTO_LOCK DELTA4_FACET_MATCHING_FRAME_TRANSITION_IS_THE_S3_PROJECTION_OF_THE_GEOMETRIC_S4_TRANSITION_THEOREM_v0.1 4. Shared-edge covariance For every adjacent facet pair and every edge ee of their shared triangle, pj(e)=σj←i(pi(e)). \boxed{ p_j(e) = \sigma_{j\leftarrow i}\bigl(p_i(e)\bigr). } Exact audit: 10×3=30 10\times3=30 shared-edge label checks, 30/30PASS. \boxed{30/30\ \mathrm{PASS}.} Thus the apparent conflict between local pair labels is exactly a frame transition, not an inconsistent edge identity. 5. Pair-state transition Let θi=(θi,A,θi,B,θi,C) \theta_i = (\theta_{i,A},\theta_{i,B},\theta_{i,C}) be the closure state expressed in facet frame FiF_i. Under the matching-frame transition, define θj=σj←i⋅θi \boxed{ \theta_j = \sigma_{j\leftarrow i}\cdot\theta_i } by permuting the three coordinates. Then on every shared edge, 1−θi,pi(e)=1−θj,pj(e). \boxed{ 1-\theta_{i,p_i(e)} = 1-\theta_{j,p_j(e)}. } Exact audit: 10×8×3=240 10\times8\times3=240 edge-gate comparisons, 240/240PASS. \boxed{240/240\ \mathrm{PASS}.} This is a frame-covariance statement, not a claim that arbitrary independently sourced facet states must obey the transition. 6. Matching-frame holonomy The five facets form the adjacency graph K5. K_5. There are (53)=10 \binom53=10 three-facet loops. Composing the canonical matching-frame transitions around every such loop gives a nonidentity transposition in S3S_3. Thus: 10/10facet triangles carry transposition matching-frame holonomy. \boxed{ 10/10\ \text{facet triangles carry transposition matching-frame holonomy}. } The three named transpositions occur with chart-dependent multiplicities 4,3,3, 4,\ 3,\ 3, but every holonomy lies in the single S3S_3 transposition conjugacy class. AUTO_LOCK CANONICAL_DELTA4_FACET_MATCHING_FRAME_CONNECTION_HAS_NONTRIVIAL_TRANSPOSITION_HOLONOMY_ON_EVERY_FACET_TRIANGLE_THEOREM_v0.1 This is finite matching-frame geometry only. It is not physical gauge curvature. 7. No global parallel nontrivial pair address The ten loop holonomies generate the full permutation action on the three pair coordinates. The binary vectors fixed by every loop holonomy are exactly 000,111. \boxed{ 000,\qquad111. } Therefore a globally parallel nontrivial pair address such as 100,010,001,110,101,011 100,\ 010,\ 001,\ 110,\ 101,\ 011 does not exist for this canonical facet connection. AUTO_LOCK / NO-GO NONFLAT_DELTA4_FACET_MATCHING_CONNECTION_FORBIDS_A_GLOBAL_PARALLEL_NONTRIVIAL_THETA_ADDRESS_THEOREM_v0.1 This sharpens the previous no-global-three-class-frame result. 8. Global AND face closure nevertheless descends For a shared triangular face ff, each local K4K_4 chart assigns its three edges one each of the labels A,B,C. A,B,C. Under complete-boundary viability, the local closure contribution is Cf,i∧=∏e⊂f(1−θi,pi(e)). C_{f,i}^{\wedge} = \prod_{e\subset f} \left( 1-\theta_{i,p_i(e)} \right). Because every label occurs exactly once, Cf,i∧=∏p∈{A,B,C}(1−θi,p). \boxed{ C_{f,i}^{\wedge} = \prod_{p\in\{A,B,C\}} (1-\theta_{i,p}). } This scalar is invariant under every S3S_3 matching-frame permutation. If adjacent facet states are transition-compatible, θj=σj←iθi, \theta_j = \sigma_{j\leftarrow i}\theta_i, then Cf,i∧=Cf,j∧. \boxed{ C_{f,i}^{\wedge} = C_{f,j}^{\wedge}. } Exact audit: 10×8=80 10\times8=80 shared-face closure products, 80/80PASS. \boxed{80/80\ \mathrm{PASS}.} The scalar is also invariant under all ten nontrivial loop holonomies. AUTO_LOCK — CONDITIONAL GLOBAL DESCENT S3_INVARIANT_COMPLETE_BOUNDARY_AND_CLOSURE_SCALAR_DESCENDS_ACROSS_DELTA4_FACET_FRAMES_THEOREM_v0.1 9. Transport-integrity factor The transport-integrity bit on a global edge is Tint,ehard=𝟏[Ue†Ue=I]. T_{{\mathrm int},e}^{\mathrm hard} = \mathbf1[U_e^\dagger U_e=I]. Under an orthogonal/unitary change of edge frame, Ue↦RUeR−1, U_e\mapsto R U_e R^{-1}, the predicate Ue†Ue=I U_e^\dagger U_e=I is invariant. Therefore the face integrity product Tf∧=∏e⊂fTint,ehard \boxed{ T_f^\wedge = \prod_{e\subset f} T_{{\mathrm int},e}^{\mathrm hard} } is frame-independent. The complete candidate global face gate is consequently hf∧=Cf∧Tf∧. \boxed{ h_f^\wedge = C_f^\wedge T_f^\wedge. } No new continuous parameter is introduced. 10. Conditional versus unconditional consistency PASS The global AND face gate is well-defined when the two incident facet receipts are frame-compatible, or more weakly when they agree on the S3S_3-invariant reference/nonreference closure scalar. NO-GO Arbitrary independently assigned local facet states can disagree: θi=000,θj≠000 \theta_i=000,\qquad \theta_j\neq000 would make one incident facet call the shared face closure-open and the other closure-closed. Therefore: frame transition law+complete-boundary viability \boxed{ \text{frame transition law} + \text{complete-boundary viability} } does not by itself derive the dynamical compatibility of independently sourced facet states. That remains a source/transport constraint. 11. Ruling EXACT / AUTO_LOCK canonical adjacent-facet S4S_4 transition; induced S3S_3 matching-frame transition; 30/30 shared-edge pair-label covariance; 240/240 transition-compatible edge-gate covariance; nontrivial transposition holonomy on all ten facet triangles; only 000000 and 111111 are globally parallel binary pair states; AND closure scalar is S3S_3-invariant; 80/80 shared-face AND descent checks pass; transport-integrity AND is frame invariant. CANDIDATE SOURCE SEMANTICS COMPLETE_BOUNDARY_FACE_VIABILITY_SOURCE_ADDENDUM_v0.1 OPEN source law enforcing compatible facet-state receipts across shared faces; empirical/dynamical validation of facet-transition use; physical correspondence. Physical promotion remains 0. UD_HARRIS_YALE_E2_RESPONSE_READY_INSTANCE_SHELL_v0.1.mdHarris/Yale E2 Response-Ready Instance Shell v0.1 Status: AWAITING_PI_RESPONSE Purpose: ingest the eight technical follow-up answers without altering the frozen E2 scientific core. Physical promotion: 0 Immutable The following remain inherited from UD_E2_APPARATUS_SPECIFIC_PREREG_CORE_v0.1 and are not PI-answer fields: event definitions; qualification and primary counts; 3σ3\sigma state-separation threshold; 3σ3\sigma phase gate; clock gate; pχ2p_{\chi^2} gate; |ΔAICc||\Delta{\mathrm AICc}| gate; no-intercept rule; no empirical extra-scatter rule; burden/leakage separation; no posttarget relabeling; no outcome-dependent invalidation; raw-data freeze before scoring; physical promotion 0. Any requested change is captured as a deviation and returns: NEW_VERSION_REQUIRED_BEFORE_DATA_EXPOSURE. Mutable PI capability answers Only: HY1 current carrier platform; HY2 absolute n=2/n=3n=2/n=3 qualification; HY3 single-slip certification; HY4 common acquisition timing; HY5 frozen controls; HY6 single-event thermometry/calorimetry; HY7 independent environment/leakage; HY8 raw-data custody. Each answer is: YES / NO / CONDITIONAL plus note and evidence receipts. Decision logic The minimum core is {HY1,HY2,HY3,HY8}. \{HY1,HY2,HY3,HY8\}. any NO in the core → BLOCKED_CORE_CAPABILITY_NO; any CONDITIONAL in the core → CONDITIONAL_CORE_CAPABILITY_REVIEW; all core YES, but timing/controls unresolved → preregistration draft may be built but qualification remains open; HY1,HY2,HY3,HY4,HY5,HY8=YESHY1,HY2,HY3,HY4,HY5,HY8=\text{YES} → READY_FOR_QUALIFICATION_BINDING; HY6 and HY7 remain independently typed optional/scoring lanes. The shell does not infer missing answers. UD_MANUSCRIPT_MILESTONE_ADDENDUM_FACET_FRAME_YALE_RESPONSE_v0.12.mdUnified Dynamics — Manuscript Milestone Addendum: Delta4 Facet-Frame Gate Descent and Yale Response Shell v0.12 Date: 2026-09-14 Status: INSERT_READY_MILESTONE_ADDENDUM Physical promotion: 0 1. Delta4 facet-frame transition Let Fi={0,1,2,3,4}\{i} F_i=\{0,1,2,3,4\}\setminus\{i\} be a tetrahedral facet and let ℓi\ell_i be its increasing local K4 chart. For adjacent Fi,FjF_i,F_j, the unique simplicial map fixing their shared triangle is the global transposition (ij)(ij). The local geometric frame transition is rj←igeom=ℓj−1(ij)ℓi∈S4. r^{\mathrm geom}_{j\leftarrow i} = \ell_j^{-1}(ij)\ell_i \in S_4. Using the already-held matching-frame projection, σj←i=πℳ(rj←igeom)∈S3. \sigma_{j\leftarrow i} = \pi_{\mathcal M}(r^{\mathrm geom}_{j\leftarrow i}) \in S_3. This is geometric facet provenance and is distinct from the transport-derived relative frame rnr_n. 2. Shared-edge covariance For every shared triangular edge, pj(e)=σj←i(pi(e)). p_j(e) = \sigma_{j\leftarrow i}(p_i(e)). Exact checks: 30/30 30/30 shared-edge pair-label identities pass. When θj=σj←iθi, \theta_j = \sigma_{j\leftarrow i}\theta_i, the local closure edge bits also agree: 240/240 240/240 transition-compatible edge-gate checks pass. 3. Nonflat matching-frame connection The facet adjacency graph is K5K_5. There are 10=2⋅5 10=2\cdot5 three-facet loops. Every loop carries a nonidentity S3S_3 transposition holonomy. Thus the matching-frame connection is non-flat. Only 000,111 000,\qquad111 are fixed by every loop holonomy, so no globally parallel nontrivial pair address exists. This is internal matching-frame geometry, not physical gauge curvature. 4. Global complete-boundary AND descent Under complete-boundary viability, Cf∧=∏e⊂f(1−θp(e)). C_f^\wedge = \prod_{e\subset f} (1-\theta_{p(e)}). Each triangular face contains one local edge from each matching class A,B,CA,B,C. Therefore Cf∧=∏p=A,B,C(1−θp), C_f^\wedge = \prod_{p=A,B,C}(1-\theta_p), which is S3S_3-invariant. Exact checks: 80/80 80/80 shared-face closure products agree under transition-compatible facet states, and the scalar is invariant under all ten loop holonomies. The transport-integrity factor Tf∧=∏e⊂f𝟏[Ue†Ue=I] T_f^\wedge = \prod_{e\subset f} \mathbf1[U_e^\dagger U_e=I] is also frame-invariant under orthogonal/unitary edge-frame changes. Hence hf∧=Cf∧Tf∧ \boxed{ h_f^\wedge = C_f^\wedge T_f^\wedge } is a parameter-free globally descending scalar conditional on compatible adjacent facet receipts. Arbitrary independently sourced local facet states can still disagree on shared-face reference status; therefore global source compatibility remains open. 5. Yale response-ready binding shell The Harris/Yale apparatus packet now has a machine-ingestible eight-field response shell. Mutable fields are only: HY1,…,HY8. HY1,\ldots,HY8. The immutable E2 core is copied by hash and is not writable through the PI-response schema. Decision logic: core capability NO → blocked; core capability CONDITIONAL → conditional review; all core YES but timing/controls open → preregistration draft only; HY1,HY2,HY3,HY4,HY5,HY8=YESHY1,HY2,HY3,HY4,HY5,HY8=\text{YES} → ready for qualification binding; any requested immutable scientific change → new preregistration version required before data exposure. Synthetic method tests passed all five branches. 6. Current status AUTO_LOCK adjacent-facet geometric S4S_4 transition; induced S3S_3 matching transition; shared-edge and transition-compatible closure covariance; nontrivial transposition holonomy on all facet triangles; no globally parallel nontrivial theta address; S3S_3-invariant AND face-gate descent under compatible facet receipts; immutable-core Yale response ingestion. OPEN dynamical/source law guaranteeing compatible neighboring facet states; admission of complete-boundary face viability as primitive source semantics; actual Yale PI response; real E2 apparatus binding and acquisition; physical bridge. Physical promotion remains 0. UD_PROVENANCE_LEDGER_ADDENDUM_FACET_FRAME_YALE_RESPONSE_v0.11.mdUD Provenance Ledger Addendum — Facet Frame + Yale Response Shell 2026-09-14 v0.11 Physical promotion: 0 ID Object Exact form Claim bin Status Next gate FF01 Delta4 facet Fi=V\{i}F_i=V\setminus\{i\} EXACT_INTERNAL AUTO_LOCK none FF02 adjacent geometric frame rj←igeom=ℓj−1(ij)ℓi∈S4r^{geom}_{j\leftarrow i}=\ell_j^{-1}(ij)\ell_i\in S_4 EXACT_INTERNAL AUTO_LOCK none FF03 matching transition σj←i=πℳ(rj←igeom)∈S3\sigma_{j\leftarrow i}=\pi_{\mathcal M}(r^{geom}_{j\leftarrow i})\in S_3 EXACT_INTERNAL AUTO_LOCK none FF04 shared-edge pair covariance pj(e)=σj←ipi(e)p_j(e)=\sigma_{j\leftarrow i}p_i(e) EXACT_INTERNAL 30/30 PASS none FF05 transition-compatible closure-edge covariance local bits agree EXACT_INTERNAL 240/240 PASS source compatible theta FF06 facet-loop matching holonomy transposition on all 10 three-facet loops LOCKED_MATHEMATICAL_GEOMETRY AUTO_LOCK none FF07 globally parallel binary theta only 000,111000,111 LOCKED_NO_GO AUTO_LOCK local/source field if nontrivial address needed FF08 AND closure scalar ∏p(1−θp)\prod_p(1-\theta_p) EXACT_CONDITIONAL S3-INVARIANT / 80/80 PASS complete-boundary semantics FF09 transport-integrity face scalar ∏e⊂f1[Ue†Ue=I]\prod_{e\subset f}1[U_e^\dagger U_e=I] EXACT_CONDITIONAL frame-invariant source actual UeU_e FF10 global AND face gate hf∧=Cf∧Tf∧h_f^\wedge=C_f^\wedge T_f^\wedge EXACT_CONDITIONAL DESCENDS if facet receipts compatible source compatibility law FF11 unconditional descent from arbitrary local theta false LOCKED_NO_GO AUTO_LOCK adjacent-state compatibility YR01 Yale response shell HY1-HY8 only PROTOCOL_CONTROL FROZEN / AWAITING PI PI reply YR02 PI response schema YES/NO/CONDITIONAL + note/evidence PROTOCOL_CONTROL IMPLEMENTED real response YR03 response ingestor immutable core not writable PROTOCOL_CONTROL METHOD PASS real response YR04 immutable deviation handling new version required before data exposure PROTOCOL_CONTROL METHOD PASS none