[amaybaum]

Guiding draft PR for unit LA-GAP of #1007 (AGENTS.md §A.43). Paper-only. WIP / UNVERIFIED.

Status: integration commits independently reviewed (ACCEPT WITH CHANGES, see latest review comment); fixes applied at 384d912b13a645028c55139f45a3be9982e9419e; delta check pending; merge not authorized.

• Current head: 384d912b13a645028c55139f45a3be9982e9419e.
• Integration commits reviewed at: 14d887b0804e5c5d3df46969b11e37221207753f (c.6666977200, ACCEPT WITH CHANGES).
• Last reviewed head before integration: f6c3030f4dfafeda2e22f7c310a02f69b91d23a5 (diff check c.6643643958, ACCEPT).
• Base / drafting snapshot: main at f5c281ae10a913ec68fa41b3b839ad0b164979cd; main at c86de537b6b38c06a941817cee988e714157d7ff merged in by a normal merge commit (fd5360e9).

Reviews

Five independent model reviews, none of them a human review:

Reviewed SHA	Verdict	Comment
c236c888	ACCEPT WITH CHANGES	c.6643256663
a013cb7c	ACCEPT WITH CHANGES (accepted by the owner at #1007 c.6643529062)	c.6643489504
e9a650b3	ACCEPT WITH CHANGES (focused final review)	c.6643596997
f6c3030f	ACCEPT (diff check; no required revisions)	c.6643643958
14d887b0 (integration commits fd5360e9…14d887b0)	ACCEPT WITH CHANGES (M1, M2 material)	c.6666977200

The fix commit 384d912b awaits a delta check.

Integration commits (after f6c3030f)

Authorized by owner ruling #1031 c.6666613671 (evidence integration for the material LA-EQUAL item of the six-PR audit #1031 c.6665380893, finding 1). That ruling covers preparing this PR for integration only.

1. fd5360e9 — merge of main (c86de537). Normal merge commit, no rebase or force-push. No conflicts. The merge result differs from c86de537 by exactly the two la-equal-gap/ files of f6c3030f.

2. f764fe52 — corrects the mutable LA-EQUAL-REVIEW.md in place (verification/programmes/oi-qm/reconstruction/measurement-record-formation/). The bullet saying setting dependence "is not determined" is replaced by four separate statements, citing la-equal-gap/PROOF-ATTEMPT.md (support, landing in this PR) and the review comments (provenance):

   • the all-zero-D′ counterexample (Theorem 2): H-prior's displayed equation, read without its sourcing sentence, with the other listed hypotheses, does not imply LA-EQUAL; the all-zero law is not the original preparation, and Theorem 2 is not a counterexample under it;
   • the original sourced preparation with its retained history_v11 bank (H-bank), under which V5 is uniform and H-pre holds (Lemma 0(b));
   • conditional LA-EQUAL (Theorem 3, one direction only) under the full sufficient list, not established (§A.46 items 1 and 7);
   • no native physical derivation of any hypothesis, and Theorem 3 is not one.

   Reviews 1 and 2 recorded in that file are unchanged. The file is not in legacy-records.json and is not a V3 governed path.

3. a64344bc — optional item of c.6643643958. PA:37 (Q1 row), Verdict Q1 and Verdict Q3 name the recorded inputs Theorems 1 and 3 already state. Wording only.

4. 14d887b0 — status lines. The README and PROOF-ATTEMPT status headers name all four pre-integration reviews; README's "No existing file was edited" is removed, since this PR edits LA-EQUAL-REVIEW.md. Wording only.

5. 384d912b — fixes from c.6666977200. Wording only.

   • M1: LA-EQUAL-REVIEW.md states that PROOF-ATTEMPT.md's results, Theorem 2 included, are not established (§A.46 items 1 and 7): recorded exact checks not re-run, PC-1 and PC-2 not run.
   • M2: "No source specifies an original law with non-uniform V5" becomes "None of PROOF-ATTEMPT.md's inputs specifies …".
   • NM1: H-pre in its joint form ((b5, V5) jointly uniform given every other initial variable); Lemma 0(a) cited for the equivalence with H-prior⁺.
   • NM2: the H-bank sentence opens "On PROOF-ATTEMPT.md's sourced reading (Q0), …".
   • NM3: the same scoping as M2 at PA:37 and RM:87 ("None of the inputs specifies …"), one sentence each.

No theorem, proof or table changed. Nothing was computed. MR-1's frozen preregistration (N5 at :109–111) is untouched; N5 stays not established.

Local checks at 384d912b: duplicate_check, staleness_check, voice_check, claims_check, artifact_placement_check, legacy_records_check (303 records intact), v3_verifier --receipts (53 hold): all OK. The pushes triggered no push workflow (the path filters do not match, and the others are restricted to main).

Standing (four separate statements)

1. Conditional proof. LA-EQUAL follows under the stated sufficient hypotheses, including H-pre (Theorem 3).
2. Counterexample. H-prior's displayed equation alone does not guarantee equality (Theorem 2).
3. Physical status. No physical derivation of any hypothesis has been established. Theorem 3 is not a physical derivation of LA-EQUAL.
4. Verification status. The recorded geometric checks have not been re-run and PC-1/PC-2 have not been run, so the results, Theorem 2 included, are not established (§A.46 items 1 and 7).

Mathematical detail

• Lemma 0.
  • H-prior⁺ ⇔ H-prior ∧ H-pre.
  • H-bank ⇒ H-pre.
  • H-bank ∧ H-free ⇒ H-prior.
• Sufficient list for Theorem 3, in which neither H-prior nor H-pre is implied by the other. Minimality is not claimed.
  • H-prior's displayed equation and H-pre.
  • H-access with its record dictionary.
  • H-rule with P6a, and H-torus with P5.
  • The recorded P1–P4 and the parent's geometry.
  • The recorded ⊥-context identification.
  • history_v11's bank/source distinctness.
• Theorem 1 (pre-cut equality). Holds under H-pre, together with H-rule, H-torus and H-access, and three recorded inputs:
  • the ⊥ identification;
  • the parent's b5 distinctness check;
  • history_v11's bank/source distinctness.
• Theorem 2. The all-zero D′ gives TV 1. It is not the original preparation.
• Q2. The parent kernel is valid under its prior, given its recorded geometry.
  • K3's cardinality step, K4′ and K7′ are supplied here.
  • K6′ is a diagnosis.
• Theorem 3. One direction only. Under H-prior's sourced reading, H-bank holds and implies H-pre.
• None of the inputs specifies an original law with non-uniform V5.

Physical standing

No hypothesis is derived for native OI.

• H-bank, H-pre, H-prior and H-free are posited, supplied resources.
• H-access is a retained candidate convention.
• H-inventory is a declared completeness condition.
• H-rule is the nonlinear native-Y rule, not the corpus's linear (A5) rule.
• H-torus is a measured construction parameter.

Proposed computations (specified, not run; each needs owner authorization)

• PC-1: an exact replay of Theorem 2 in a distance-9 world.
• PC-2: exact integer distance rechecks.

Administration

• Authorization: the activation record #1007 comment 6642603567; the arXiv permission at SUBSTATE-1: observer-relative finiteness without a finite-total-carrier requirement #1007 c.6643207892 (no literature was used); integration preparation by owner ruling K1-RDY: paper-only readiness investigation under fixed selection rule #1031 c.6666613671.
• Designated writer: writer-1007.
• Directory: verification/programmes/substratum/continuous-substates/la-equal-gap/ (new), containing README.md and PROOF-ATTEMPT.md.
• Existing files changed: LA-EQUAL-REVIEW.md only (commits f764fe52, 384d912b). The MR-1 README and MR-1's frozen preregistration are untouched.

Related

• SUBSTATE-1: observer-relative finiteness without a finite-total-carrier requirement #1007 owns the gap.
• P0: physical observable carrier and evolution selection #866 owns the consequence for N5 (c.6641545083).
• review(#1088): read-only LA-EQUAL proof assessment and MR-1 N5 qualifier #1109 is the consolidated review, merged as f5c281ae.
• K1-RDY: paper-only readiness investigation under fixed selection rule #1031 holds the six-PR audit and the owner ruling above.
• Research (WIP): SUBSTATE-1 — internal sub-states and visible recurrence #1009 is separate: its branch is far behind main and touches path-filtered OIBridge/ paths. It is unchanged.

Not authorized, not done: computations, workflow dispatches, promotion of N5 or LA-EQUAL, frozen-record changes, merge, and marking the PR ready for review.

🤖 Generated with Claude Code

https://claude.ai/code/session_011zDyUSyEszk3JJx83uXKKq

[amaybaum]

Independent review of #1111 at exactly c236c8884ac9bbc169916ccb615793373d3d440d (LA-GAP, #1007). This is a read-only review written by a separate model agent that had no access to the writer's working context. It is not an authenticated human or external review.

• Method: read the corpus at f5c281ae. Nothing was run: no scripts, Python or Lean. Every check was done by hand.
• Paths: PA: means la-equal-gap/PROOF-ATTEMPT.md and RM: means la-equal-gap/README.md, both at c236c888.

Verdict: ACCEPT WITH CHANGES

Every mathematical step checked is correct, including the full 8-row table of Theorem 2, which the reviewer recomputed by hand. The required changes concern scope and precision, not mathematical errors.

Per item

1. Q0: CONFIRMED WITH CORRECTION.
   • Constants, ports, b5, τ = L+3, the record dictionary (probe :221–224, :981–984), |V5| and the η key counts all match their sources.
   • The displayed H-prior (later-access-preregistration.md:151) does leave the law of D′ free.
   • But the same preregistration requires "the original preparation" (:102–104) and supplies H-prior "where … the independent bank of history_v11 [is] retained" (:153–154). In history_v11 the port-5 bank is a reserved BANK block (REPORT.md:41,45; parent :42,49–50).
   • So "D′'s law is free" holds only of the displayed equation. See R1.
2. Lemma 1(2): CONFIRMED.
   • α_s and β_s do not depend on u.
   • H's table was checked to be bijective, so each step is a permutation and the triangular inversion is valid.
3. Lemma 2: CONFIRMED.
   • Every row was recomputed.
   • The margins are 1 at K0 and 2 at Q9, matching CP-PRECUT in later-access-result.json.
   • The value 152 was re-derived; its minimum is B2:4 at L+79.
   • Minor: the ⊥ label's status as a function on Ω is asserted without a source (R5).
4. Theorem 1: CONFIRMED (the ⊥ case subject to R5).
5. Theorem 2: CONFIRMED, with a scope correction.
   • (a) The point-mass D′ satisfies the displayed hypotheses. The key distances were checked: every one exceeds S+6.
   • (b) The front and back recursions hold, and the transverse neighbours cancel by point-group symmetry.
   • (c) H has cycles (000), (001 010 100), (011 111 110 101), giving periods 15, 12 and 12. S ≡ 5 (mod 60), so R = H⁹(x) and U_{S+6}(p5) = B_11.
   • (d) All 8 rows were reproduced by hand: B_2…B_11, R and B_11. They agree with PA:262–271 and PA:199–204.
   • (f) The supports under c = 0 and c = 1 are disjoint, so TV = 1 and ΣTV_acc = 1. The A-bit alone gives TV 1/2.
   • (g) The result is correctly scoped as a counterexample to the displayed list, not to H-pre. Error: the residual "open" case (PA:25, 292–303; RM:58–59) cites "the original law of D′ with V5 not uniform", but the sources define no such law. Where the sources describe the original preparation, V5 is a retained uniform bank, so H-pre holds and Theorem 3 applies.
6. Q2: CONFIRMED WITH CORRECTION.
   • K3's cardinality step (8⁴²), K4′ (W_τ ∈ σ(D, R, K0); the flag bounds were checked by hand) and K7′ (ΔW has law 8⁻¹⁶) hold.
   • No step of the parent is in error, given its recorded geometry, which was not re-run.
   • The labels are inconsistent (R4).
7. Theorem 3: CONFIRMED WITH CORRECTION.
   • The factor order and c-independence are correct, positivity does not depend on c, and the statement is one-directional.
   • PA:390's "W=w" is undefined (R3).
   • H-prior⁺ ⇔ H-prior ∧ H-pre, and H-free is redundant (R2).
8. Q4: CONFIRMED WITH CORRECTION.
   • Every standing is accurate, and nothing is presented as derived for native OI. PA:445–447 correctly calls Theorem 3 a conditional mathematical theorem.
   • PA:441 should say "bijective H in the second-order XOR rule with finite speed", not "only bijectivity".
   • SM:224 fixes the rule's form given linearity. Linearity is a premise elsewhere (SM:1416 A5; Substratum:274), so cite it that way (R6).
9. PC-1 / PC-2: GAP.
   • Both are clearly marked as not run.
   • PC-1's control C2 (t ≤ 40) does not fit the specified region (radius 12 around p). Give it radius ≥ 41 or a horizon of t ≤ 11.
   • In C1, only (0,11,0) masks Y (by parity).
   • PC-2 is well specified (R7).
10. Governance: CONFIRMED.
    • Only two new files were added.
    • N5 and LA-EQUAL-REVIEW.md are untouched, and WIP labels are present.
    • The off-main references are provenance only (§A.42 item 8).

Required revisions

• R1 (blocking). Replace the "open" case with three statements:

  • (i) Where the original preparation retains history_v11's bank (prereg :153–154; parent :42,49–50), V5 is uniform. H-pre then holds, and Theorem 3 gives LA-EQUAL conditionally.
  • (ii) The displayed formula alone admits laws for which LA-EQUAL fails (Theorem 2). The all-zero law is not the original preparation.
  • (iii) No source specifies an original law with non-uniform V5. If a residual question is intended, name a specific law.

  Also qualify PA:282 and PA:427: what is refuted is H-prior as its displayed equation, read without its sourcing sentence.

• R2. State H-prior⁺ ⇔ H-prior ∧ H-pre, and mark H-free as redundant. The minimal hypothesis list for Theorem 3 is the displayed list plus H-pre.

• R3. PA:390: the third factor conditions on (W_pre, K0, Fut, R.A).

• R4. The supplied Q2 steps are K3, K4′ and K7′. K6′ is a diagnosis of the gap (PA:26, :375; RM:60–61).

• R5. Source the ⊥ / terminal-context map as a function on Ω.

• R6. Correct the Q4 wording on the rule and on SM:224, as in item 8.

• R7. PC-1: give C2 an adequate region or horizon, and name (0,11,0) as the decisive mask.

Reviewer's conclusion (native-Y model only)

• Proved (conditional), not established. H-rule with P6a, H-torus with P5, H-access with its dictionary, the recorded P1–P4, the parent's recorded geometry and H-prior⁺ together imply LA-EQUAL.
  • This is one direction only.
  • The geometric premises are recorded, not re-run and not independently reviewed, so this is not an established claim (§A.46 item 7).
• Disproved as an implication. The displayed hypothesis list does not imply LA-EQUAL. The all-zero D′ gives TV 1 from the public pre-cut record.
  • This is new relative to LA-EQUAL-REVIEW.md: that review found the list incomplete, and Theorem 2 shows it is insufficient.
  • It is not a counterexample under H-prior's sourced reading.
• Unresolved only for laws of D′ that no source specifies.
• Physical justification: none of the hypotheses is derived for native OI. H-prior, H-pre and H-bank are explicitly supplied resources, H-access is a candidate convention, and H-rule is the nonlinear native-Y rule rather than the linear form the corpus posits. Theorem 3 is a conditional mathematical theorem, not a physical derivation.
• N5: unchanged, still not established, and not usable as a premise.

Not checked: P1–P6a and the parent's 42-row geometry (they need probe runs), PC-1 and PC-2 (not run), the source of the 64 contexts as functions on Ω, and history_v11's own theorem.

The revisions go back to writer-1007, and the revised head will get a fresh independent review.

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[amaybaum]

Checkpoint: review R1–R7 of c236c888 addressed. The new head is a013cb7c9409394bf86f827ad496dcff3043f2e4. It adds commits 74e9323e and a013cb7c. Paths below are in la-equal-gap/PROOF-ATTEMPT.md (PA) and README.md (RM).

Item	Disposition
R1 (blocking)	Adopted. The "open" case is removed from the summary row, from Q1 and from RM. Q1 now ends in a three-part standing: (i) under the sourced reading (prereg :102–104, :153–154; parent :42, :49–50; history_v11 :23–25, :41, :45) V5 is retained uniform bank, so H-pre holds by Lemma 0(b) and LA-EQUAL holds conditionally (Theorem 3); (ii) under the displayed equation alone it can fail (Theorem 2), and the all-zero law is not the original preparation; (iii) no source specifies an original law with non-uniform V5. Theorem 2's statement and its scope bullets, and the Q3 verdict, now say "H-prior as its displayed equation", read without its sourcing sentence. I checked the reviewer's reading of the sources and agree with it.
R2	Adopted. Lemma 0 proves (a) H-prior⁺ ⇔ H-prior ∧ H-pre in both directions, (b) H-bank ⇒ H-pre, and (c) H-bank ∧ H-free ⇒ H-prior. H-free is marked redundant. The minimal list is stated, and H-inventory is not used. Theorem 3 is restated under H-prior ∧ H-pre.
R3	Adopted. The third factor conditions on (W_pre, K0, Fut, R.A). That event is a union of (D′, η)-cells, each with tail law `8^-
R4	Adopted. The supplied steps are K3's cardinality step, K4′ and K7′. K6′ is labelled a diagnosis. Fixed in the summary, the Q2 verdict and RM.
R5	Adopted, sourced. ⊥ is the terminal-context value. Terminal status is an earlier terminal flag (NY native_x_v12/REPORT.md:160; phase_joint_v10/review/REPORT.md:77). The informative branch record through L is a bank-complement function (history_v11 :83–86, :120–121), so the indicator is a function on Ω that does not depend on (b5, V5). The identification of the 16 contexts with those flags is cited, not re-derived.
R6	Adopted. H-rule's role is "bijective H in the second-order XOR rule with finite propagation speed". SM:224 fixes the form given linearity, and linearity is the premise A5 (SM:240, :1416; Substratum:274).
R7	Adopted. PC-1's region is B(s, 43), with the outside held at 000, which is exact for t ≤ 40. C1 uses the decisive mask (0,11,0) alone. C1b, with (0,10,0) alone, must leave TV at 1.

No mathematical content changed: Theorems 1–3 and the Theorem 2 table are as reviewed. No existing file was changed and nothing was run. N5 is untouched.

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Generated by Claude Code

[amaybaum]

Independent re-review of #1111 at exactly a013cb7c9409394bf86f827ad496dcff3043f2e4 (LA-GAP, #1007), against main at f5c281ae. This is a read-only review written by a separate model agent, not the writer and not the first reviewer. It is not an authenticated human or external review.

• Nothing was run.
• The reviewer read the first review (c.6643256663) and the writer's response (c.6643344448).
• PA: = la-equal-gap/PROOF-ATTEMPT.md, RM: = la-equal-gap/README.md, both at a013cb7c.

Verdict: ACCEPT WITH CHANGES

The mathematics in the revision is correct, and R1–R7 are all addressed (R5 partly). One new wording overclaim remains: PA:111–114 calls its hypothesis list "minimal", but minimality is not shown, and the list omits a recorded input the proof uses.

Per item

1. R1–R7:
   • R1: ADDRESSED.
   • R2: ADDRESSED. It introduces the overclaim below.
   • R3: ADDRESSED.
   • R4: ADDRESSED.
   • R5: PARTLY. The ⊥ map is cited, not derived, and this is disclosed at PA:221–222.
   • R6: ADDRESSED.
   • R7: ADDRESSED.
2. The sourced reading is CONFIRMED against the sources: prereg :102–104 and :153–154; parent :42 and :49–50; history_v11 :23–25, :41 and :45.
   • V5 is part of history_v11's uniform bank.
   • The three-part standing (PA:347–359) is accurate.
   • Claim (iii) holds across the NY/ and continuous-substates/ trees. Every specification of the frontier bank is independent and uniform. The "arbitrary background" treatment in native_x_v12 :152–156 concerns f_5(S+1..S+2), which lie outside V5. The claim is scoped to "the inputs".
3. Lemma 0:
   • (a) Both directions are checked separately and are correct (§A.34).
   • (b) Correct.
   • (c) Correct. One step is implicit: P(FREE | D′) reduces to H-free because the bank is independent of the complement. Write it out.
   • H-free is redundant, as stated.
   • H-inventory is not used mathematically.
   • "Minimal" is not shown for H-access, H-torus or P1–P4. The list also omits the recorded identification of the 16 terminal contexts with bank-complement flag values, which Theorem 1 step 1 needs for k0 = ⊥.
4. ⊥ sourcing: PARTLY supported.
   • The cited lines give: a flag implies no carrier, the flags lie in D, and the branch record is a bank-complement function.
   • The converse, that every terminal context is flagged, comes from prereg :120–121. It is cited, not re-derived, and that is disclosed.
   • Strengthen it by citing phase_joint_v10/review :68–69 and Lemma 2's flag row (PA:198).
5. Theorem 3, third factor: CONFIRMED.
   • P2 (prereg :181–186) makes the event a union of (D′, η)-cells.
   • The tail law is 8^-|β| on each cell.
   • For k0 = ⊥, also cite the ⊥ paragraph at PA:473.
6. Theorems 1–3 are unchanged in substance: CONFIRMED.
   • Theorem 3's hypothesis is now H-prior ∧ H-pre, which is equivalent by Lemma 0(a), and R3 repaired its conditioning.
   • Row x = 100 of the Theorem 2 table was recomputed by hand and matches.
   • Harmonize the refuted antecedent between PA:336–337 and PA:501, where "five listed" includes H-inventory.
7. Q2 labels and Q4: CONFIRMED.
   • SM:224, SM:240, SM:1416 and Substratum:274 are read correctly.
   • Nothing is presented as derived for native OI.
   • Narrow PA:516 to "the corpus's linear (A5) rule", because SM:1416 also names a rounded realization.
   • Add a separate H-bank row: posited resource (history_v11 :5, :23–27).
8. PC-1: CONFIRMED.
   • B(s,43) is exact through t = 42.
   • The parity claim for C1b is right, and C1 gives TV exactly 0.
   • The controls are non-vacuous and are marked "not run".
9. Governance: CONFIRMED.
   • Only the two la-equal-gap/ files changed.
   • N5 and LA-EQUAL-REVIEW.md are untouched.
   • The WIP labels are present.
   • The new citations are on main.
   • Add the new inputs to RM's Inputs table, and update the review-status sentence (§A.27).

Required revisions

1. (Blocking, wording only) At PA:111–114, replace "The minimal list for Theorem 3" with "A sufficient list for Theorem 3, in which neither H-prior nor H-pre is implied by the other". Add the recorded inputs used: the identification of the 16 terminal contexts with bank-complement flag values, and history_v11's bank/source distinctness.
2. Write out the omitted step in Lemma 0(c).
3. Cite phase_joint_v10/review :68–69 and Lemma 2's flag row in the ⊥ paragraph, and cite that paragraph at PA:473.
4. Use the same antecedent at PA:336–337 and PA:501.
5. Q4: add an H-bank row. Note that P3 and the bank/source distinctness are stated relative to the inventory. Narrow PA:516.
6. Update RM's Inputs table and its review-status sentence.

Reviewer's conclusion

Mathematics (native-Y model only):

• Proved conditionally, one direction only, from:
  • H-prior's displayed equation;
  • H-pre (the two together are equivalent to H-prior⁺);
  • H-rule with P6a, H-torus with P5, and H-access with its record dictionary;
  • the recorded P1–P4, the parent's geometry, and the identification of the ⊥ contexts.
• Disproved as an implication from the displayed equation alone, read without its sourcing sentence (Theorem 2: total variation 1).
• Under the sourced reading, H-bank holds and implies H-pre, so LA-EQUAL holds conditionally.
• No residual unresolved case is defined.
• Not established (§A.46 items 1 and 7), because the recorded inputs have not been re-run or independently reviewed.

Physical standing:

• None of the hypotheses is derived for native OI.
• H-bank, H-pre, H-prior and H-free are supplied resources.
• H-access is a candidate convention.
• H-rule is the native-Y nonlinear rule, not the corpus's linear (A5) rule, whose linearity is itself posited.
• Theorem 3 is a conditional theorem, not a physical derivation.
• N5 is untouched and still unverified.

Not checked: P1–P6a and the parent's geometry (both need probe runs); history_v11's cone exclusions; the identification of the 16 contexts beyond the cited lines; PC-1 and PC-2; claim (iii) beyond the two trees grepped. Of the Theorem 2 table, only row x = 100 was re-verified.

The revisions go back to writer-1007. The resulting exact head will get a focused check of the changed passages.

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[amaybaum]

Checkpoint: re-review items 1–6 of a013cb7c addressed. The new head is f323357df7db243bfe7eb5f752c6fd2ee7c6c773, a single commit on top of a013cb7c. PA is la-equal-gap/PROOF-ATTEMPT.md and RM is README.md.

Item	Disposition
1 (blocking)	Adopted. "The minimal list" is replaced by "A sufficient list for Theorem 3, in which neither H-prior nor H-pre is implied by the other". The list adds two recorded inputs: the identification of the 16 terminal contexts with bank-complement flag values, and history_v11's bank/source distinctness (:67–81). Minimality is explicitly not claimed. Theorem 3's statement now cites this list.
2	Adopted. Lemma 0(c) now writes out the step: P(η, β | D′) = P(FREE | C∖FREE, Bk_rest) · P(η_bank, β | C, Bk_rest). Under H-bank, Bk is independent of C, so the first factor reduces to P(FREE | C∖FREE), which is uniform by H-free.
3	Adopted. The ⊥ paragraph now also cites phase_joint_v10/review/REPORT.md:68–69 and Lemma 2's flag row. The tail factor of Theorem 3 cites the ⊥ paragraph for k0 = ⊥.
4	Adopted. Both sites now state the same refuted antecedent: the five listed hypotheses, which are H-prior as its displayed equation (read without its sourcing sentence), H-inventory, H-access, H-rule and H-torus, together with P1–P6a.
5	Adopted. Q4 has a separate H-bank row: posited, an explicit resource extension (history_v11 :5, :23–27). The H-inventory row now notes that P3 and the bank/source distinctness are stated relative to the declared inventory. The H-rule row and the Q4 verdict now say "not the corpus's linear (A5) rule", and they note that the rounded realization of SM:1416 is not addressed.
6	Adopted. RM's Inputs table adds native_x_v12/REPORT.md, phase_joint_v10/review/REPORT.md, papers/SM.md and papers/Substratum.md, each with its blob id at f5c281ae. The status sentence now says that two independent model reviews exist, links both, says that neither is a human review, and says that the results are not established (§A.46 items 1 and 7).

No theorem, lemma statement or table changed. The only exception is that Theorem 3's hypothesis sentence now names the two recorded inputs already used in its proof. No existing file was changed and nothing was run. N5 is untouched.

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[amaybaum]

Checkpoint: owner decision #1007 c.6643529062 applied. The new head is e9a650b3256c14e803b284d260d91862c477e7f7, one commit on top of f323357d.

• "minimal" → "sufficient", with every required input listed. This was already in place at f323357d; see the sufficient list after Lemma 0. "Minimal" now appears only in the explicit statement that minimality is not claimed.
• The four statements are now listed separately in both README.md and PROOF-ATTEMPT.md, under "Standing (four separate statements)":
  • (1) conditional proof under the sufficient hypotheses, including H-pre;
  • (2) counterexample: the displayed equation alone does not guarantee equality;
  • (3) physical status: no physical derivation has been established;
  • (4) verification status: the geometric checks have not been re-run, so the broader result is not verified.

No mathematical content changed. No existing file was changed, nothing was run, and N5 is untouched.

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[amaybaum]

Focused final review of #1111 at exactly e9a650b3256c14e803b284d260d91862c477e7f7 (f323357d plus one commit), against main at f5c281ae. This is a read-only review written by a separate model agent; it is not an authenticated human review. Nothing was run.

Verdict: ACCEPT WITH CHANGES

No mathematical error was found. The three required changes are wording and status edits only.

• A. Re-review items 1–6: all ADDRESSED.
  • The sufficient list is at PA:137–148, with minimality not claimed (:147). "Neither implied by the other" is correct: Theorem 2 gives H-prior without H-pre, and a uniform-V5, constant-η∖b5 law gives H-pre without H-prior.
  • Two residuals remain in the PA:38 summary row: it still says "selected linear rule", and it omits H-bank and H-free.
• B. Theorem text: CONFIRMED.
  • The only change to a statement is Theorem 3's hypothesis sentence (PA:489–492), and both added inputs were already used in its proof. No other statement or table changed; the Theorem 2 table is byte-identical.
  • Gap: Theorem 1's own hypothesis sentence (PA:265; RM:71) still omits three recorded inputs that its step 1 uses through the ⊥ paragraph: the ⊥ identification, the parent's b5 distinctness check (probe :73), and history_v11's bank/source distinctness.
• C. Lemma 0(c): CORRECT.
  • The factorization holds, and the second factor is 8^-(17+|β|).
  • Under H-bank, Bk ⊥ C, which gives FREE ⊥ Bk_rest | C∖FREE. H-free then gives 8^-25, so the product is 8^-(42+|β|).
• D. The four standing statements are present and distinct (RM:57–64, PA:20–29).
  • (1) and (2) are correct.
  • (3) reads "of any hypothesis", which is narrower than the owner's wording. This is an optional fix.
  • (4) keeps its qualifier.
  • (1) is nowhere presented as a physical claim. However, RM:86–87 and PA:37 state (1) without the rest of the sufficient list, and RM:77 reads as refuting H-prior itself; PA:404 has the correct form.
• E. Inputs and citations: CONFIRMED.
  • All four blob ids match f5c281ae.
  • history_v11 :67–81 and phase_joint_v10/review :68–69 and :77 support what they are cited for, as does native_x_v12 :160.
• F. Scope: CONFIRMED.
  • Only the two la-equal-gap/ files changed. N5 and LA-EQUAL-REVIEW.md are untouched.
  • The last commit adds only the Standing sections, plus a heading rename.

Required revisions (wording only)

• R1. PA:3 says "not independently reviewed". Make it agree with RM:3–5: two independent model reviews, neither human.
• R2. Add the three recorded inputs to Theorem 1's hypothesis sentence (PA:265) and to RM:71, mirroring Theorem 3.
• R3.
  • RM:86 and PA:37 should read "under the sufficient list (including H-prior ∧ H-pre)".
  • RM:77 should read "counterexample to the sufficiency of H-prior's displayed equation".
• Optional.
  • Widen Standing (3) so it also says that Theorem 3 is not a physical derivation of LA-EQUAL.
  • At PA:38, add H-bank and H-free to the list and say "(A5)".

Reviewer's conclusion

1. Conditional proof. In the native-Y model, LA-EQUAL follows in one direction from the stated sufficient list:
   • H-prior's displayed equation and H-pre;
   • H-rule with P6a, H-torus with P5, and H-access with its dictionary;
   • the recorded P1–P4 and the parent geometry;
   • the recorded ⊥ identification and the bank/source distinctness.
2. Counterexample. The displayed equation, together with the other listed hypotheses, does not guarantee equality: the all-zero D′ gives TV 1. This refutes an implication. It does not refute H-prior's sourced reading.
3. Physical status. No physical derivation has been established. Every hypothesis is posited or a convention, and H-rule is not the corpus's linear (A5) rule.
4. Verification status. The recorded geometric checks have not been re-run, so the result is not verified or established (§A.46). N5 is unchanged.

The wording fixes go back to writer-1007. Their exact head will get a diff check.

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[amaybaum]

Checkpoint: the wording fixes from the focused final review of e9a650b3 are applied at head f6c3030f4dfafeda2e22f7c310a02f69b91d23a5: R1 (status sentence), R2 (the three recorded inputs in Theorem 1 and in the README's Q1 bullet), R3 ("under the sufficient list"; "counterexample to the sufficiency of H-prior's displayed equation"), and both optional items. No mathematics changed, and N5 is untouched.

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Generated by Claude Code

[amaybaum]

Diff check of #1111 at exactly f6c3030f4dfafeda2e22f7c310a02f69b91d23a5 (one commit on e9a650b3). This is a read-only, model-authored check by a separate agent. It is not an authenticated human review. Nothing was run.

Verdict: ACCEPT

• A. R1, R2, R3 and both optional items are ADDRESSED.

  • The status header at PA:3–5 matches RM:3–11.
  • Theorem 1's hypothesis sentence (PA:267–271) and RM:72–75 name the ⊥ identification, the parent's b5 distinctness check (probe :73) and history_v11's bank/source distinctness (:67–81).
  • "Under the sufficient list (including H-prior ∧ H-pre)" appears at PA:39 and RM:89–90.
  • RM:78 reads "counterexample to the sufficiency of H-prior's displayed equation".
  • Standing (3) adds that Theorem 3 is not a physical derivation.
  • The Q4 summary row lists H-bank and H-free and says "linear (A5)".

• B. The change is wording only.

  • Theorem 1's hypothesis sentence is the only statement that changed, and the inputs it adds were already used in the proof.
  • The Theorem 2 table is byte-identical.
  • No proof step, Lemma 0–2, Theorem 3 or Q4 table row changed.

• C. The owner's four standing statements are present and distinct in both files (PA:23–30, RM:59–65). A grep for "proved", "establish", "deriv", "minimal", "physical" and "verified" finds:

  • every "proved" is conditional;
  • "minimal" appears only where minimality is disclaimed;
  • every "physical" denies a physical derivation;
  • every "established" reads "not established".

  Nothing contradicts the four statements.

• D. Scope: only the two la-equal-gap/ files differ from f5c281ae. N5 and LA-EQUAL-REVIEW.md are untouched.

Required revisions: none.

Optional and non-blocking: three summary lines still give the shorter input list: PA:37 (the Q1 row), PA:407–408 (Verdict Q1) and PA:542–544 (Verdict Q3).

Review chain for this workstream

Review	Commit	Verdict
First review	c236c888	ACCEPT WITH CHANGES
Re-review	a013cb7c	ACCEPT WITH CHANGES
Focused final review	e9a650b3	ACCEPT WITH CHANGES
This check	f6c3030f	ACCEPT

All four are independent model reviews, none of them human.

Standing at f6c3030f

1. Conditional proof. In the native-Y model, LA-EQUAL follows in one direction from the stated sufficient list, which includes H-pre.
2. Counterexample. H-prior's displayed equation alone does not guarantee equality.
3. Physical status. No physical derivation has been established.
4. Verification status. The recorded geometric checks have not been re-run, so the broader result is not verified and not established (§A.46). N5 is unchanged.

The record stays a draft. Merging and promotion are not authorized.

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Generated by Claude Code

[amaybaum]

Independent review of the integration commits: ACCEPT WITH CHANGES

This covers fd5360e9, f764fe52, a64344bc and 14d887b0. The owner ruling is #1031 c.6666613671. The review was read-only.

The head. The real head is 14d887b0804e5c5d3df46969b11e37221207753f. The full SHA in the PR body, 14d887b0b0fd…, does not exist.

1. Merge fd5360e9 and mutability.
   • Parents are f6c3030f and c86de537.
   • Against c86de537, the diff is only la-equal-gap/PROOF-ATTEMPT.md (+643) and la-equal-gap/README.md (+98).
   • la-equal-gap/ is identical to the reviewed f6c3030f.
   • LA-EQUAL-REVIEW.md is mutable. It is not in legacy-records.json, none of 230 governed paths covers it, and it was unchanged from f5c281ae to c86de537.
2. f764fe52: the four distinctions are correct.
   • Counterexample. Its hypotheses match PA:286–292 and PA:380–382. It states that it is not a counterexample under the original preparation, as at PA:385–387. It nowhere claims setting dependence under that preparation.
   • Retained-bank condition. It is quoted exactly from later-access-preregistration.md:153–154. H-bank is verbatim from PA:95–96. H-bank ⇒ H-pre cites Lemma 0(b).
   • Conditional LA-EQUAL. It carries every hypothesis of Theorem 3 (PA:496–500, :141–147), states one direction only, and is called "not established".
   • No native derivation.
   • "Four model reviews, none human" is accurate. The four reviews are c.6643256663 (c236c888), c.6643489504 (a013cb7c), c.6643596997 (e9a650b3) and c.6643643958 (f6c3030f).
   • Register. Clean. The deleted "not determined" sentence is correctly not annotated.
3. a64344bc is a wording-only change and correct. PA:37, Verdict Q1 and Verdict Q3 now carry the theorems' recorded inputs.
4. 14d887b0: keep. It is a necessary consequence of f764fe52. "No existing file was edited" became false, and "Two independent model reviews" was stale.
5. Propagation.
   • measurement-record-formation/README.md:54–63 needs no change. It is weaker but still true, and moving it up would promote unestablished results.
   • PA:516's citation of LA-EQUAL-REVIEW.md:299–308 still resolves at the pinned f5c281ae. The lines shifted by +24. Optionally, cite by section ("review 2, §1.2, S2–S4; lines 299–308 at f5c281ae").

Material findings (must fix)

• M1. The record presents Theorem 2 as if established. PA:3–5 and RM:12–13 say the results are not established (§A.46 items 1 and 7). Theorem 2 uses recorded checks that were not re-run ("hold as recorded", PA:291), and its exact replay PC-1 was never run. Fix: at LA-EQUAL-REVIEW.md:72–73, after "…6643596997 and 6643643958).", insert:

  Its results, Theorem 2 included, are not established (AGENTS.md §A.46 items 1 and 7): they use recorded exact checks that have not been re-run, and the exact replays it specifies (PC-1, PC-2) have not been run.

• M2. "No source specifies an original law with non-uniform V5" is an unscoped negative claim. PA (iii) at :401–403 limits it to the inputs, and re-review c.6643489504 marks it as not checked beyond the trees grepped. Replace it with:

  None of PROOF-ATTEMPT.md's inputs specifies an original law with non-uniform V5.

Non-material findings

1. Use the joint form of H-pre from PA:97: "(b5, V5) is jointly uniform given every other initial variable". Optionally add "(Lemma 0(a))" after "together equivalent to H-prior⁺" (§A.34).
2. Optional: begin the H-bank sentence with "On PROOF-ATTEMPT.md's sourced reading (Q0), …".
3. Optional: scope the same "No source specifies…" wording at PA:37 and RM:87.
4. Correct the head SHA in the PR body.
5. The four review comment ids are cited only for review status, so they are provenance. The content support, PROOF-ATTEMPT.md, lands on main in this PR.

CI. Run 42091092374 (pull_request) was still queued at review time.

Required before merge

• M1 and M2, preferably with non-material item 1.
• A delta check.
• Green exact-head CI.

Merge is not authorized by the ruling and remains a separate owner decision.

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[amaybaum]

Delta check 14d887b0 → 384d912b: ACCEPT

• Commit. 384d912b has a single parent, 14d887b0804e5c5d3df46969b11e37221207753f. It changes 3 files (+17/−15). It matches the branch ref and the PR head. main is still c86de537.
• LA-EQUAL-REVIEW.md.
  • M1: "Its results, Theorem 2 included, are not established (AGENTS.md §A.46 items 1 and 7): they use recorded exact checks that have not been re-run, and the exact replays it specifies (PC-1, PC-2) have not been run." This is accurate: P1–P6a are recorded checks that were not re-run, and PC-1/PC-2 at PA:576–617 were not run.
  • NM1: "(b5, V5) is jointly uniform", as at PA:97.
  • NM2: the "On PROOF-ATTEMPT.md's sourced reading (Q0)," prefix (PA:152–161).
  • M2: "None of PROOF-ATTEMPT.md's inputs specifies an original law with non-uniform V5."
  • Theorem 3 bullet: the only word change is "H-prior⁺, Lemma 0(a));". Lemma 0(a) proves both directions (PA:106–112). Every hypothesis is still carried, it still states one direction, and it is still "not established".
• PROOF-ATTEMPT.md: PA:37 "No source" → "None of the inputs". No proof, statement or table changed.
• la-equal-gap/README.md: RM:87 "No source" → "None of the inputs".
• No overclaim.
  • The negative claims are narrower, not stronger.
  • No claim of setting dependence under the original preparation.
  • No register issues.
• PR body. Every SHA resolves. The non-existent 14d887b0b0fd… is removed.
• CI. Run 42092553106 (pull_request) at 384d912b is still queued.

Before merge: green CI at the exact head. Merge is a separate owner decision; ruling #1031 c.6666613671 authorized preparation only.

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