[amaybaum]

This PR is correction unit S1 of the Main proof-independence work on #1029. It is a re-cut of #1042, changing commit metadata only, as the owner decided in #1042 comment 6579764705 (option (b)). Merge is not authorized.

Re-cut

• Head: 290cdce3af40cd91d51ba49d5911dca4d33486b3, one commit on main a65fe8a8.
• Tree: bec590a78403385187759c156ff13191cc1d367a, identical to Main posit ledger: second-order posit, A5 scope, external results, Substratum hypotheses (#1029 S1) #1042's reviewed head bac7999f. git diff bac7999f 290cdce3 is empty.
• Commit message: the sentence that overstated scope is replaced with the owner's wording:

  In the passages corrected by S1, the claimed equivalence between amplitude-scale gauge invariance and linearity is withdrawn. Linearity (A5) is retained as an imposed restriction of the selected model. Remaining assertions that center freedom yields linearity are assigned to P1 and are not corrected by this commit.

• Main posit ledger: second-order posit, A5 scope, external results, Substratum hypotheses (#1029 S1) #1042 is left unmerged. Its commit, review record (comment 6579686254) and CI (run 41460684154) are preserved.

Content (unchanged from #1042)

1. Posit (xiii). The second-order form of the update, x(t+1) = F(x(t)) − x(t−1), in the kernel's ruleDynamics form. It is stated as a posit of the selected lattice model, not derived and not an axiom of OI. The ledger count changes from twelve to thirteen and the range from (iv)–(xii) to (iv)–(xiii).
2. A5 (linearity) at Main item (vii) and in the passages restating it: Structure:219/:259, Substratum:100/:104/:220/:272/:274, ch02:84 and FULL:727.
   • Amplitude-scale gauge invariance yields an affine restriction. Linearity is an imposed restriction of the selected model.
   • Assigned to P1, not corrected here:
     • SM:240 and Explainer:767 still assert that centre freedom yields linearity;
     • SM:96 and Structure:301 describe SM's gauge-based linearity argument.
3. External results at Main:72, :630 and :658. Besides the textbook results [15, 16], the load-bearing imports are Barandes [11, 12], [55] and canonical typicality [31].
4. Substratum hypotheses: those of the cited Substratum results are stated in Main item (ii).

No Lean, LEDGER, census-registry or grade change, and no new citation of a downstream paper. Main, Structure, Substratum and the book are rebuilt (pages 100, 99, 54, 560). The SC-42 integration result is regenerated: 642 checks, PASS.

#1036 and #1037 stay paused, and the five standing holds (#1009, #1023, #1011, #1003, #918) are unchanged.

🤖 Generated with Claude Code

https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

[amaybaum]

Exact-head review record: 290cdce3

Verdict: READY-WITH-NITS (N2 fixed). The review was independent. The head is 290cdce3af40cd91d51ba49d5911dca4d33486b3, a single parent a65fe8a8, and main is unchanged at a65fe8a8.

Same tree, metadata-only re-cut.

• The tree is bec590a78403385187759c156ff13191cc1d367a, identical to Main posit ledger: second-order posit, A5 scope, external results, Substratum hypotheses (#1029 S1) #1042's reviewed head bac7999f.
• git diff bac7999f 290cdce3 is empty.
• Every tree-level finding of the Main posit ledger: second-order posit, A5 scope, external results, Substratum hypotheses (#1029 S1) #1042 review (comment 6579686254) carries over unchanged.

Commit message (N1 resolved).

• Each of the owner's three sentences (Main posit ledger: second-order posit, A5 scope, external results, Substratum hypotheses (#1029 S1) #1042 comment 6579764705) appears exactly once, verbatim.
• The overstated sentence is gone.
• The new sentences are accurate: SM:240 and Explainer:767 still carry the centre-free step, and this commit does not touch them.
• The counterexample basis is stated within its verified scope.
• The page counts (100/99/54/560), "642 checks, PASS", "no Lean/LEDGER/registry/grade change" and "same tree as bac7999" are all correct.
• The only model identifier is the required trailer.

PR body (N2, fixed). The body had called SM:96 and Structure:301 "centre-freedom-to-linearity assertions". They describe SM's gauge-based linearity argument; only SM:240 and Explainer:767 assert the centre-free step. The body now distinguishes the two. All four sites stay with P1.

Mergeability. git merge-tree --write-tree origin/main 290cdce3 is clean, and its result tree equals the head's tree.

CI at 290cdce3. Run 41463134737 is green: 25 jobs passed, and 1 (A42 exclusion (${{ matrix.part }})) was skipped by its condition.

No merge is authorized. Merging needs separate exact-SHA approval from the owner.

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Generated by Claude Code

[amaybaum]

Exact-head owner decision and confirmed merge — 2026-11-02

APPROVED and merged #1043 at the reviewed exact head 290cdce3af40cd91d51ba49d5911dca4d33486b3.

• Independent review: READY-WITH-NITS (N2 fixed), comment 6579961749. This was a metadata-only re-cut of the independently accepted S1 tree from Main posit ledger: second-order posit, A5 scope, external results, Substratum hypotheses (#1029 S1) #1042; commit-message N1 and PR-body N2 were resolved.
• Ordinary PR CI: 41463134737, completed/success at the exact reviewed head.
• Pre-merge main a65fe8a844e774a5737d47b1cb49db9ab0751077; head unchanged, clean merge. Marked the draft ready, then GitHub normal merge with expected-head SHA returned merged=true.
• Merge SHA and verified new main: b87733a400c563592774dad2a61425c7663b69d1.
• S1 establishes selected-model second-order posit (xiii), explicit A5 assumption, corrected external dependency accounting and precise Substratum hypotheses, propagated to its approved mirrors. All theorem grades remain unchanged. P1 still owns SM:96/240, Explainer:767 and Structure:301; S2 is the next queued MI-1 correction.
• Ordinary post-merge main CI is a separate gate; this record does not claim its result.

No authorization of further scientific execution, claim promotion, or the paused #1036/#1037. Five standing holds unchanged.

[amaybaum]

Post-merge verification: b87733a4

This record supplements the owner's exact-SHA merge record (comment 6580448303).

• Merge commit: b87733a400c563592774dad2a61425c7663b69d1, with parents a65fe8a8 (previous main) and 290cdce3 (the approved head).
• Tree: bec590a78403385187759c156ff13191cc1d367a, identical to the reviewed head's tree.
• main CI on b87733a4: verify, push event, run 41467454828, is green. 25 jobs passed and 1 (A42 exclusion (${{ matrix.part }})) was skipped by its condition. This includes the SC-42 cmp, the Lean kernel check and Mathlib bridge, and every numerical probe shard.

S1 is complete. P1 keeps SM:96, SM:240, Explainer:767 and Structure:301. The other open S1 follow-ups go to C1, S2 and L1, as recorded on #1029. #1042, the superseded original with the same tree, stays unmerged.

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