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#1004 correction: remove the θ = 0 claim from ch02 and align Structure Q12 with SM §8.7 - #1027

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fix/strong-cp-1004-20261101
Nov 2, 2026
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fix/strong-cp-1004-20261101

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@amaybaum amaybaum commented Nov 1, 2026

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Draft. Correction for #1004: Edits 1 and 2 only.

What changes

  • Edit 1. Book ch02 (book/ch02-substratum.md:106) and its FULL mirror (book/The-Incompleteness-of-Observation-FULL.md:749). The sentence saying the QCD θ-angle "is exactly zero as a consequence of the substratum's structural T-symmetry" is deleted. The preceding sentence stays unchanged: T-invariance with detailed balance narrows θ to {0, π} and does not fix θ̄, which is open (SM §5). This matches SM Theorem 18 (θ ∈ {0, π}, with selecting 0 needing H-top), Proposition 20, Theorem 21 (θ̄ is not determined by the construction) and §5.5 (H-top and H-det are not discharged). The measured bound |θ̄| < 10⁻¹⁰ is still stated at ch06:52 and ch19:78 and their FULL mirrors.
  • Edit 2. Structure Q12 (papers/Structure.md:1081). "(T-invariance → θ = 0;" becomes "(T-invariance → θ ∈ {0,π}, θ̄ not fixed;", matching the SM §8.7 table it cites (SM:1510).

Not changed

Regenerated

  • sh ./build.sh Structure and sh ./build.sh --book: build OK, no dropped glyphs. Page counts unchanged (Structure 99, FULL 559). Each .tex differs only in the edited paragraph and its source-sha256 stamp.
  • SC-42 integration result replayed, following the 41aa01c precedent. The only change is one added passing mirror row (617 → 618 predicates). The controls file is unchanged.

Checks (local)

  • Exit 0: mirror, coverage, architecture (0 violations), voice, voice-scope, staleness, claims, citation, census, SC-42 (normal, -O, --self-test).
  • Undecidable in a shallow clone, left for CI: legacy-records, v3-receipts, citation-roles and three v3-corpus history vectors. Their output is identical on unchanged main.
  • Re-grep: "exactly zero as a consequence" has 0 hits in book/ and papers/ .md/.tex. One historical audit report quotes it and is kept as provenance.
  • Independent review: accept with nits.

Links

No merge without exact-SHA owner approval.


Generated by Claude Code

…§8.7 (#1004)

The book's Chapter 2 asserted that the QCD theta-angle "is exactly zero as a
consequence of the substratum's structural T-symmetry", directly after the
sentence stating that T-invariance narrows theta to {0, pi} and does not fix
theta-bar. The anchor is SM §5: Theorem 18 gives theta in {0, pi} at a
T-invariant point and leaves the branch choice to the separate condition
H-top; Proposition 20 and Theorem 21 show the construction fixes neither theta
nor arg det(Y_u Y_d), so theta-bar is not determined; §5.5 leaves strong CP
open under H-top and H-det. All three are paper derivations.

- book/ch02-substratum.md:106 and its mirror FULL.md:749: delete the
  theta = 0 sentence. The preceding sentence, which states the status, is
  unchanged; the paragraph now ends "(SM §5).". The 10^-10 bound remains at
  ch06:52 / FULL:1574 and ch19:78 / FULL:5232 (and the ch06 and ch19 tables).
- papers/Structure.md:1081 (Q12): "T-invariance -> theta = 0" becomes
  "T-invariance -> theta in {0, pi}, theta-bar not fixed", the wording of the
  SM §8.7 table row it cites.

No proof, claim grade, count or G-row changes. The SM §8.8 "dissolves all
three" / "three instances" sites (Edit 3 of the #1004 assessment) are
deferred to a separate follow-up and are not touched here.

Regenerated with sh ./build.sh Structure and sh ./build.sh --book
(pandoc 3.1.3, xelatex, lmodern present; no shim). No dropped glyphs.
The .tex diffs are confined to the edited paragraphs and the source-sha256
stamp. Structure.pdf: 99 pages, median 2931 chars/page, before and after.
FULL.pdf: 559 pages, median 3068 chars/page, before and after.

Re-grep: "exactly zero as a consequence" has 0 hits in book/ and papers/
.md/.tex (one historical audit report under verification/audits quotes the
old sentence and is left as provenance); "T-invariance → $\theta = 0$" has
0 hits in .md; '\(\theta = 0\); topology' has 0 hits in Structure.tex;
theta in {0, pi} sites in book/ and papers/ are unchanged (27) plus the new
Q12 site.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
The SC-42 integration check adds a mirror-parity predicate for each changed
chapter line. The ch02:106 edit adds one passing row ("chapter line mirrored
in FULL: T-invariance of the bijection $\varphi$ combined with detail...").
PASS (618 predicates, 280 mirror); -O output identical; added-text scan 0
hits; controls unchanged.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

amaybaum commented Nov 1, 2026

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Exact-head review: #1027 at e523fcefa1a0f28213aa250484410b6aa0520e30

Verdict: READY-FOR-OWNER-MERGE-DECISION. This review is read-only. It does not approve a merge. Merging requires the owner's explicit approval of the exact SHA e523fcefa1a0f28213aa250484410b6aa0520e30.

Head

  • The PR head is e523fcef… and branch fix/strong-cp-1004-20261101 points to the same commit. This is the expected head, and the branch has not moved since the pre-push review.
  • The base is 07d94f2c, and main is still 07d94f2c618c17237bea5b8bbf914417e598940b, so there is no base drift.
  • There are two commits, each single-parent and linear: 43432128 (Edits 1–2) on 07d94f2c, then e523fcef (the SC-42 replay).

Scope (diff 07d94f2c..e523fcef, 8 files, +21 −19)

  • book/ch02-substratum.md:106 and book/The-Incompleteness-of-Observation-FULL.md:749: the sentence "The QCD theta-angle … is exactly zero as a consequence of the substratum's structural T-symmetry." is deleted, identically in both files. The preceding sentence (θ ∈ {0,π}; θ̄ not fixed, open, SM §5) is unchanged.
  • papers/Structure.md:1081 (Q12): "T-invariance → $\theta = 0$" becomes "T-invariance → $\theta \in {0,\pi}$, $\bar\theta$ not fixed".
  • Structure.tex and FULL.tex change only in the edited text and the source-sha256 stamp. Each stamp equals the sha256 of its .md.
  • Both PDFs were regenerated. Extracted text: Structure Q12 has the new wording, and FULL has 0 occurrences of the deleted sentence. Page counts are unchanged: 99 and 559.
  • sc42-integration-result.json gains one row: the passing mirror predicate for the edited ch02 line.
  • Nothing else changes. No SM file changes; Edit 3, SM §8.8, is deferred as stated. No LEDGER, proof or grade changes.

CI at the exact head (structured results)

There is one workflow run, verify (run 41331022784, event pull_request, attempt 1, conclusion success). It reported 26 check-runs on head_sha e523fcef, all completed:

  • 25 concluded success. These are Lean kernel check, Mathlib bridge, Numerical probes and its 22 matrix jobs.
  • 1 concluded skipped: Numerical probes / A42 exclusion (${{ matrix.part }}), the matrix template entry.
  • Mathlib bridge checks out with fetch-depth: 0. Its Release gate step concluded success.
    • That step runs tools/release_gate.py, which exits 0 only if every gate step exits 0.
    • The gate steps include legacy-records, v3-corpus (every vector as expected, including the three s8-landed-* history vectors), v3-receipts and citation-roles.
    • All four were undecidable in the local shallow clone and are decided here on full history.
    • The only skipped step in that job is the KTRANS-SEP-2 negative marker. Skipped is its passing state.
  • Numerical probes / core B step SC-42 integration source scope and must-fail controls concluded success. That step compares the checker's output with the committed sc42-integration-result.json, so the replay is confirmed in CI.

The run tests the synthetic merge 94b35d20 (parents 07d94f2c, e523fcef). Its tree 38ae88e8 is identical to the head's tree, so the result applies to the head's content. This is PR verification only; no V3 round is involved.

Mergeability and other open PRs

Scientific and editorial check

  • Edit 1 is correct.
    • SM Theorem 18 (SM:633): a T-invariant point satisfies θ ∈ {0,π}. SM:637: choosing θ = 0 is the separate condition H-top, which T symmetry does not supply.
    • SM Theorem 21 (SM:651): T-invariance with reciprocity fixes neither θ nor arg det(Y_uY_d), so θ̄ is not determined.
    • The deleted sentence asserted the opposite and contradicted the sentence before it. Deleting it, without adding a replacement, is the minimal correction (§A.30).
    • The measured bound of 10⁻¹⁰ is still stated at ch06:52 and ch19:78 and their FULL mirrors.
  • Edit 2 is correct. Q12 now matches the SM §8.7 table row it cites (SM:1510: "$\theta \in {0,\pi}$ in QCD; $\bar\theta$ not fixed"). It adds no new claim.
  • Re-grep. "exactly zero as a consequence" has 0 hits in papers/ and book/ .md/.tex. Structure has no remaining "theta = 0" in Q12.
  • Register. The added text is one parenthetical. It has no self-narration, history voice, caps emphasis or overclaim (§A.32, §A.33).
  • Local checks re-run at this head, all exit 0: staleness, voice, coverage (134 statements), mirror (0 chapter lines absent from FULL), and citation (112 citations, 0 broken). The SC-42 checker's output is byte-equal to the committed result. The tree was clean afterwards.

Verdict

READY-FOR-OWNER-MERGE-DECISION. The scope matches Edits 1–2 plus the SC-42 replay, with SM deferred. CI is fully green at the exact head, including the full-history gate steps and the SC-42 comparison. The PR is cleanly mergeable on unchanged main, and both edits are accurate against SM Theorems 18 and 21 and §8.7. Merging requires the owner's exact-SHA approval of e523fcefa1a0f28213aa250484410b6aa0520e30. If the branch or main moves first, this review must be repeated.


Generated by Claude Code

@amaybaum
amaybaum marked this pull request as ready for review November 2, 2026 01:37
@amaybaum
amaybaum merged commit 0200969 into main Nov 2, 2026
26 checks passed
@amaybaum
amaybaum deleted the fix/strong-cp-1004-20261101 branch November 2, 2026 01:37
amaybaum added a commit that referenced this pull request Nov 2, 2026
Reconcile with main through #1026 and #1027; retain reviewed audit files byte-for-byte and preserve original commits. No scientific or manuscript changes.

amaybaum commented Nov 2, 2026

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Merge record (verification). The merge commit is 02009693c7b92f511e0d1c9435d2c5043d8670c8, with parents 15162605 (main after #1026) and e523fcefa1a0f28213aa250484410b6aa0520e30 (the owner-approved exact head). The merge adds exactly the PR's own diff against its base 07d94f2c: the diff from 15162605 to 02009693 is byte-identical to the diff from 07d94f2c to e523fcef. Push CI on the merge commit, run 41373426359, passed: 25 jobs succeeded and 1 was skipped as expected. Nothing else is open on this PR.


Generated by Claude Code

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