[amaybaum]

This PR is correction unit S2 of the Main proof-independence work on #1029. It replaces #1045 and implements the owner's decision of #1029 comment 6582374258: relocate U10 to Substratum, and re-cut with a corrected commit message. Merge is not authorized. #1045 stays unmerged, with its review and CI preserved.

Base: main 1482b90e, the #1044 merge, which adds the proof-placement rule. Head: 5850059c, one commit.

Differences from #1045

• U10 relocated.
  • Main:726 (xi) states A4 as two clauses, with no claim that they are logically independent.
  • The independence result moves to A4's definition at Substratum:98. It keeps both countermodels and their scope: second-order rules over Z_q on a periodic cubic lattice of side ≥ 3, with site-wise gauge on each site's (previous, current) pair.
  • The paper argument is general: a gauge preserves which sites each update reads.
  • Under AGENTS.md §A.42, the sentence that cited off-main exhaustive-check scripts was dropped. No result or scope depends on it.
• Commit message corrected for Main conditional and physical claims: relocate downstream content, correct unsupported estimates (#1029 S2) #1045's review nits 2–4:
  • Main's (E/M_Pl)² sentence is removed. SM holds only the Lorentz-violation scaling, at its own status.
  • The 10^183 figure is called a "count of distinguishable positions", not a configuration count.
  • The overbroad "only use of the cosmological realization" wording is gone.
• Rebuilt: Substratum is now rebuilt as well as Main and GR.

Changes (unchanged from #1045 apart from U10)

Site	Outcome	What changes
Main:670, O1	relocate	The condensate / rotational-protection clause leaves Main. It is held at full strength in SM:136 and SM §4.1 (ohInvariant_eq_scalar).
Main:354 → GR:134, O2	relocate	The common-mode sentence moves to the end of the GR:134 paragraph, with its conditions. The first-order drift derivation stays with P1.
H-Bell (Main:22, :414, :416, :772), O5	relocate	Main keeps the finite Bell result, and no-signaling is posed as open. The continuum clause stays at Substratum:133/:171 and SM:150.
Main:224, G06/O6	correct / relocate	~10^183 is stated for an assumed Planck-order ε. The e^{S_dS} bound and the 1/√dim H estimate are removed. Main's (E/M_Pl)² sentence is removed.
Main:702, G28/C05	relocate / correct	The calibration report leaves Main (GR §3–§5). Hidden-sector finiteness is stated through posit (ii).
Main:72	correct	The input inventory names the conditional results' hypotheses.
Main:726 (xi) → Substratum:98, U10	relocate	See above.
Main:648	correct	The structure count matches the items listed.

LEDGER: two fingerprints move (bell-lattice-obstruction, boost-rotation). No assumption or grade change.

Not changed

• No book file. O3 and O4 are deferred. The stale pointers at Explainer:58/:709 and Substratum:467 are recorded for a later unit.
• No downstream citation is added to Main.
• No census-registry change.
• Sites owned by S3, P1, C1, Correction planning: scientific overclaims and status corrections (from the 2026-11-01 disposition) #1028 and Main:356 are untouched.

Checks

• Rebuilt with sh ./build.sh Main GR Substratum. Main is 100 → 99 pages, GR 90 → 91 and Substratum 54 → 55.
  • No dropped glyphs and no U+FFFD.
  • PDF word changes track the source edits.
  • The stamps match.
• Local checks: lean_manuscript_census, coverage_check, voice_check, claims_check, duplicate_check, mirror_check, citation_check, dependency_label_check --strict and staleness_check all pass. The R7-CTN/R7-PTR guards are true.
• SC-42: the --verbose output is byte-identical to the checked-in result.
• Proof census: only the two reviewed fingerprints move.

10 files. #1036 and #1037 stay paused, and the five standing holds are unchanged.

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Generated by Claude Code

[amaybaum]

Exact-head review record: 5850059c

Verdict: READY. The review was independent. The head is 5850059c3ad840b46b94d9842432b00889ca2eef, single parent 1482b90e, and main is 1482b90e, the #1044 merge, which changes only AGENTS.md relative to b87733a4.

Fidelity. edits_S2e applied to 1482b90e reproduces the head's Main, GR, Substratum and LEDGER byte for byte, with all 17 tuples applying cleanly. Relative to the reviewed #1045 edit set, only M11 changes and the Substratum:98 tuple is new.

Condition 1, U10 domain. The reviewer re-derived the paper proof independently.

• Scope. It holds for every q ≥ 2, every side ≥ 3 and any dimension. At side ≥ 3 every coefficient in both rules is exactly 1, so no q makes a coefficient vanish.
• Gauge. The site-wise gauge argument also covers time-dependent site-wise gauges.
• Controls, all passing:
  • 45 cases (d = 1–3, side 3–5, q = 2–6) with no failures;
  • site-wise conjugation preserves the read relation;
  • a non-site-wise bijection breaks it, so the site-wise restriction is needed;
  • side 2 with q = 2 degenerates, so side ≥ 3 is needed;
  • none of the 13,824 gauge images of the first countermodel drops its own present value.
• Restrictions. They are exact as written. q ≥ 2 is implicit in "Z_q", since independence fails at q = 1; writing it out is an optional nit. Nothing depends on the dropped off-main checker sentence.

Condition 2, proof placement.

• Main:726 (xi) drops exactly "logically independent" and keeps both clauses verbatim. Main carries no U10 proof and no downstream dependency.
• Substratum:98 holds the theorem and its self-contained proof at A4's definition.

Condition 3, scientific preservation.

• GR.md, GR.tex and LEDGER.json are the same blobs as in the reviewed Main conditional and physical claims: relocate downstream content, correct unsupported estimates (#1029 S2) #1045 tree (0aaab912). Main.md differs from it only at line 726. All O1–O6 corrections are unchanged.
• proof_census: only the two fingerprints move. No grade or assumption changes.
• The commit message fixes all three earlier nits, and its other claims are accurate, including the page counts 99/91/55.

Generated files.

• All stamps match, and pandoc regenerates all three .tex files byte for byte.
• Pages: Main 100 → 99, GR 90 → 91, Substratum 54 → 55.
• No U+FFFD characters, and the word diffs track the edits.

Checks at the head.

• All battery checks match 1482b90e, and the R7-CTN/R7-PTR guards are true.
• SC-42 --verbose is byte-equal to the checked-in result.
• No probe-guard pin is lost.
• git merge-tree is clean, and the result tree equals the head's tree.

CI at 5850059c. Run 41482987563 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]

S2 #1046 exact-SHA owner approval and verified normal merge — 2026-11-02

APPROVED AND MERGED PR #1046 at exact independent-reviewed head 5850059c3ad840b46b94d9842432b00889ca2eef.

• Exact-head independent READY review: science and U10 scope/proof placement accepted, no blockers.
• PR Actions 41482987563: completed/success at that exact head (25 jobs passed, 1 expected skip).
• Verified base and main at 1482b90eb5b6de2f08296daf4606b7ecfe9cdfa7 prior to merge; head unchanged and mergeable. Marked draft ready, then GitHub normal merge with expected-head protection returned merged=true, commit 06df90c963a452d43bb1eef927b8a62c8bbed5e0.
• Re-fetched: main = 06df90c963a452d43bb1eef927b8a62c8bbed5e0, parents exactly base 1482b90e and reviewed head 5850059c. Files changed are Main/GR/Substratum Markdown and regenerated PDF/TeX, plus verification/coverage/LEDGER.json; no book file.
• S2 preserves all approved O1–O6 corrections, moves U10's independently justified two-countermodel proof to Substratum:98 while retaining A4 clauses in Main; two ledger fingerprints moved, grades unchanged, no unsupported numerical bound retained in Main.
• Post-merge main CI 41484472079 was queued when checked; its result is not implied by the successful PR CI.

No broader scientific authorization: GR common-mode relocation does not supply Main's missing first-order drift proof, which stays P1. Other deferred book corrections, downstream reference fixes, #1036/#1037 and five holds remain unchanged. S3 can receive a separate proposal-only scope, without immediate manuscript execution or merge.

[amaybaum]

Post-merge verification: 06df90c9

• Merge commit: 06df90c963a452d43bb1eef927b8a62c8bbed5e0, with parents 1482b90e (previous main) and 5850059c (the reviewed head).
• Tree: 03acc890d482d109c5641548f4efb8cdcbdb934e, identical to the reviewed head's tree.
• main CI on 06df90c9: verify, push event, run 41484472079, 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, Mathlib bridge and every numerical probe shard.

S2 is complete. #1045, the superseded original, stays unmerged. Items carried forward:

• P1: the Main:354 first-order drift derivation.
• Later unit: the stale pointers at Explainer:58/:709 and Substratum:467.
• Separately scoped book units: O3 and O4.

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Generated by Claude Code