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Book B.7: D-gauge classification from GR §3.3; GR §3.3 brought into agreement - #921
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Appendix B.7 (book/appendix-b-derivations.md, mirrored byte-identically in
FULL.md, §A.14) gains, after Lemma B.7.5, the material its proof defers to
[GR §3.3], written from GR, not from the Explainer:
- Theorem B.7.5a, Bohr-frequency completeness, with GR's proof (GR.md:172-174);
- the dimensional obstruction (GR.md:176, with the generator formula of
GR.md:298 and the diagonal-rephasing item of GR.md:296);
- Lemma B.7.5b, the real-to-integer transfer, stated from the kernel lemma
`real_to_integer_surrogate` (TurnpikeScopeTransfer.lean:536): no
classification assumed, discharges no hypothesis (BG-3 non-inference rule);
- Theorem B.7.5c, D-gauge completeness in two-branch form, with H-BG stated in
full, and its conditional proof (GR.md:178-180);
- the scope paragraph (GR.md:182): Bekir-Golomb comparison open;
`BGIntegerClassification` false, with the explicit rulers;
`twoBranch_of_BGClassification` not establishing reconstruction;
- Corollary B.7.5d, operational antiunitary invariance, with its kernel
citation (GR.md:184-186).
Departures from GR's wording, each deliberate:
- the conditional proof's expansion uses e^{-i(E_a-E_b)t}, as in the theorem
and GR.md:174; GR.md:180's e^{-i(E_b-E_a)t} with the same tensor evaluates
to |U_ji(t)|^2 (numerical check), so GR.md:180 carries a sign slip;
- the C4-ring sentence states the supported scope: the ring (distinct
eigenvalues, uniform overlaps, degenerate gaps) has conj(H) matching every
|U_ij(t)|^2 with conjugated loop product, and conj(H) = -D_s conj(H) D_s
lies in the reflection branch, as bohr_frequency_probe.py F5 records. GR's
"Omitting the gap condition fails on the C4 ring" is not carried, since the
ring does not fail the two-branch disjunction;
- the transfer is added to the list of results kernel-proved independently
of the refuted premise (GR.md:182 lists three; ROADMAP P2 lists four).
Pointers: Lemma B.7.5's proof cites Theorem B.7.5c; the B.1 entry for B.7
names the new results; ch03 Level G1 (and FULL.md:944) cites Appendix B.7.
Census (§A.35): no kernel theorem is strengthened. The "Hamiltonian
reconstruction" family gains anchors in book/appendix-b-derivations.md and
FULL.md on "Thus the two Hamiltonian branches follow conditional on H-BG", so
the census guards the book's conditional statement.
Artifacts: book/The-Incompleteness-of-Observation-FULL.tex regenerated with
the build.sh recipe and source stamp (pandoc 3.1.3, which reproduces main's
.tex byte for byte). STALE: book/The-Incompleteness-of-Observation-FULL.pdf
is not rebuilt (no xelatex in this environment); rebuild with
`sh ./build.sh --book` before release.
papers/ is unchanged.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
Review nits N1-N3 on 5c4f641, applied in appendix-b and mirrored in FULL.md: - N1/N2: the C4-ring sentence names conj(H) as what lies in the reflection branch and adds the connective "The ring therefore does not exhibit a failure of the two-branch form without the gap condition". The connective is scoped to the exhibited partner conj(H), which the exact identity conj(H) = -D_s conj(H) D_s settles; it does not assert that no same-data partner of the ring lies outside both branches, which only numerics support. - N3: the "Hamiltonian reconstruction" census family gains a second book anchor, "*Conditional proof.* Equality of the probability families", in book/appendix-b-derivations.md and FULL.md. Deleting either anchor phrase from either file fails the census (checked on copied roots). Artifacts: book/The-Incompleteness-of-Observation-FULL.tex regenerated with the build.sh recipe and source stamp (pandoc 3.1.3). STALE: book/The-Incompleteness-of-Observation-FULL.pdf is not rebuilt (no xelatex in this environment); rebuild with `sh ./build.sh --book` before release. papers/ is unchanged. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
…ality lint
GR.md §3.3 is brought into agreement with the reviewed book Appendix B.7 at
exactly three points, and nothing else in papers/ changes:
- GR.md:180, conditional proof: the expansion's exponent is e^{-i(E_a-E_b)t},
as in GR.md:174, Main.md:228 and the book. With e^{-i(E_b-E_a)t} the
displayed sum with that coefficient tensor is |U_ji(t)|^2.
- GR.md:182, the C4-ring sentence: replaced by the book's wording, which
settles only the exhibited partner conj(H) exactly: the gap condition is
where coefficient matching induces a bijection of mode pairs; the ring has
distinct eigenvalues, uniform overlaps and degenerate gaps; conj(H)
reproduces the data, conjugates the loop product and lies in the reflection
branch, conj(H) = -D_s conj(H) D_s; the ring does not exhibit a failure,
without the gap condition, of the two-branch form conditional on H-BG.
The sentence is byte-identical in GR.md and the book.
- GR.md:182, the list of results kernel-proved independently of the refuted
premise: the real-to-integer transfer is added, with its kernel citation
(`real_to_integer_surrogate`, OIBridge/TurnpikeScopeTransfer.lean:536), as
the book states it; no hypothesis is said to be discharged.
Repair, book (appendix-b and FULL.md, mirrored): bohr_frequency_probe.py's F8
lint requires every "two-branch form/classification" to have H-BG or
"classification hypothesis" within 250 characters. Two phrasings from the
two previous commits failed it: the B.1 entry's "conditional two-branch
classification" (5c4f641) and the C4 connective's "two-branch form"
(839534c). Both now name H-BG. F8 was checked with a replica that executes
the probe's own F8 source; the probe itself needs scipy, which is absent here.
Coverage: no statement fingerprint moved (coverage_check OK); nothing
re-affirmed. Census: no registry change; the family note names no anchors.
Artifacts: papers/GR.tex and book/The-Incompleteness-of-Observation-FULL.tex
regenerated with the build.sh recipe and source stamps (pandoc 3.1.3, which
reproduces main's GR.tex byte for byte). STALE: papers/GR.pdf and
book/The-Incompleteness-of-Observation-FULL.pdf are not rebuilt (no xelatex
in this environment); rebuild with `sh ./build.sh GR` and
`sh ./build.sh --book` before release.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
papers/GR.pdf and book/The-Incompleteness-of-Observation-FULL.pdf are rebuilt with `sh ./build.sh GR` and `sh ./build.sh --book` from the source at 41844e9 (XeTeX, TeX Live 2023; pandoc 3.1.3). Both builds report no missing glyphs and leave the committed .tex byte-identical. GR.pdf: 85 pages, sha256 b60060a945c576da65d2cb42e9c14928159be3532807ca3d03b651cfde4b777a. FULL.pdf: 550 pages, sha256 51b6897b7fac1b66fa0d0277ab7452ab9ac98222a311f93d165c8379b8a99ec8. No source, .tex or other file changes. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
Brings the Chapter 7 / GR correction (#920) into #921. The Markdown sources merge without conflict: #920 edits GR §7, §7.3 and App. A and book ch07, ch09, ch18, ch19, glossary and bibliography; #921 edits GR lines 180/182, book App. B (B.1, B.7) and ch03. For GR.md and FULL.md the merged file differs from main by exactly #921's diff and from 0707ddb by exactly #920's diff. The generated GR.tex and FULL.tex conflicted and are regenerated from the merged sources with build.sh (pandoc 3.1.3, unicode-fix header, source-sha256 stamps match). GR.pdf and the book PDF are taken from main and are stale relative to the merged sources; the next commit rebuilds them. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
papers/GR.pdf and book/The-Incompleteness-of-Observation-FULL.pdf are rebuilt with `sh ./build.sh GR` and `sh ./build.sh --book` from the sources at 65a8b40 (XeTeX, TeX Live 2023; pandoc 3.1.3). No missing glyphs. GR.pdf 86 pages, sha256 fde4a0e21dbfcaab7d9b6793441a83588911ad41d199195a425492dfdb36f339. Book 552 pages (547 at c91bf5d, +2 from #920, +3 from #921), sha256 997b23da06ee486cdbf0e8532f86f4f30564c9dd406804261e6940bb4d372b7f. Both builds leave the committed .tex files byte-identical. No source, .tex or other file changes. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
amaybaum
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October 25, 2026 16:43
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Head:
7a12fdbda50a73b6e48e93db9d4e4bcc32c545b4, based onmainc37700ad(after #920). Six commits:5c4f6417: migration;839534c9: review nits;41844e9b: GR §3.3 brought into agreement, lint repair;0707ddb7: PDFs rebuilt, PDF files only;65a8b409: merge ofmainc37700ad;7a12fdbd: PDFs rebuilt from the merge, PDF files only.Changes:
book/appendix-b-derivations.md: B.7 and the B.1 entry.book/ch03-structural-realism.md: one cross-reference.The-Incompleteness-of-Observation-FULL.md.papers/GR.md§3.3, lines 180 and 182.verification/lean-manuscript-census.json: two book anchors per family entry..texfiles and rebuilt PDFs.What it does
Book Appendix B.7 now carries the D-gauge material that only GR §3.3 and the Explainer had. The source is GR §3.3, not the Explainer. It adds:
real_to_integer_surrogate(TurnpikeScopeTransfer.lean:536). No discharge is claimed.BGIntegerClassificationis false, with the rulers;twoBranch_of_BGClassificationdoes not establish reconstruction.GR §3.3 now agrees with the book at three points:
Census. Book anchors on "conditional on H-BG" and on "Conditional proof. Equality of the probability families". The census fails if the book drops the conditional wording.
Verification
Review of the D-gauge change: accept at
41844e9b. This was an independent mathematical-fidelity review, with a focused review of the final candidate. The reviewer:One conflict remains outside this PR:
papers/Explainer.md:492still says that dropping the gap condition fails on the C₄ ring.Correction of an earlier verdict. The reviewer withdrew its earlier acceptances of
5c4f6417and839534c9.verification/lean/bohr_frequency_probe.pyfails its F8 lint: a "two-branch" phrase without H-BG within 250 characters, at the B.1 entry and at the C₄ connective.41844e9brepairs both phrasings. The probe passes atc91bf5ddand41844e9b, and fails at839534c9.Reconciliation with #920: independent review accept at
7a12fdbd.mainby exactly this PR's diff;0707ddb7by exactly Chapter 7 and GR: Page-time scope, island correspondence, generalized second law #920's diff..texfiles rebuild byte-identically. The PDFs reproduce their text exactly on an independent rebuild: GR 86 pages, book 552 (547 atc91bf5dd, plus 2 from Chapter 7 and GR: Page-time scope, island correspondence, generalized second law #920 and 3 from this PR). No glyphs are missing, and the rendered changed pages are correct.Checks at
7a12fdbd, all passing:legacy_records_check(303 intact);v3_verifier --self-testand--corpus;bohr_frequency_probe.py.65a8b409on its own carries stale PDFs, as its message says. Land it together with7a12fdbd.Merge: not authorized.
Related: #918, #920.
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