Removal of the spatial cutoff for weakly coupled P(phi)_2

Provenance

How the manuscript was built, what it was built from, what was found wrong along the way, and how to check any of it yourself.

Frozen sources

part_i/main.tex is an assembly of earlier documents, each frozen at the moment it was consumed. Every transcribed display carries a % src: comment naming its origin, and part_i/README.md maps each section back to the draft it came from.

file	role
m6/main.tex (v2, audited repair)	predecessor manuscript; statements and compressed proofs
audit_2026/critical_proof_audit.tex	independent audit, frozen against the v1 SHA-256
audit_2026/lamport_euclidean_to_gap.tex	fully explicit proof, GJS ⟹ (M₂) + (G)
audit_2026/lamport_gap_to_main.tex	fully explicit proof, (M₂) + (G) ⟹ main theorem
audit_2026/citation_screenshot_dossier.tex + evidence/	page images for every import
m4/r1-check.tex	gate R1: h-uniformity of the Euclidean inputs
m4/r2-check.tex	gate R2: printed norms and exact constants, from the page image of p. 594
m0/m0.tex, m2/m2.tex, m3/m3.tex	spectral passage; quadratic-model rate; dichotomy
m4/m2-audit.tex, m4/g-side.tex	superseded derivations, kept with update notices
strategy.md	the programme record: every phase, gate and adversarial round

The two structured reconstructions follow Lamport’s hierarchical proof format.

Corrections history

The point of publishing this is that the errors are part of the record.

• v0 → v1 merge (9 Aug 2026): filter-transform sign corrected to +1/E; a spurious factor ½ removed from the one-path bound; an unnecessary g″ detour eliminated; the averaging identity of the canonical-vacuum corollary repaired.
• Gate R2 (9 Aug 2026, page-image inspection of GJS p. 594): prefactor K₁ to the first power; local weight K₂^{2N(Δ)}; an earlier “correction” in m4/m2-audit.tex Rem. 5.3(i) was itself an OCR artifact and is withdrawn; a half-degree slip in the v0 assembly was found and fixed. The cell-pair count for (M₂) is 9, not 32.
• Independent audit (9 Aug 2026): severity register P1 (the two-phase corollary was missing premise (B4) — repaired by conditioning on Hypothesis 13.1); S1–S3 (citation pinpoints for FKN, hypercontractivity, domain smoothing); L1–L6 (cell count, negative- time norm ratio, nonnegative FKN inputs, signed and clipped truncations, exponential- moment prefactor, spectral-parameter range); C1 (dimensionless scaling made explicit); C2 (all imports enumerated as A1–A8); H1–H2 (literature claims narrowed). No P0 defect was found.
• Scope amendment (5 Sep 2026): the status of U_GJS re-based — see imports. No proof changed; all 125 labels unmoved.

Withdrawn routes, kept in the record and not used: m4/h6-attack.tex Thm. 2.3 (UV-divergent double commutator); the gap-based (H6) proofs; wavelet-MRA-as-Polchinski decomposition, which moved to the Part II documents.

The citation dossiers

Every load-bearing citation is matched to an image of the page it is taken from, at the theorem actually used. The dossier sources are in the repository; the page images are not — they are third-party copyrighted material, and the JSTOR scans additionally carry a watermark naming the downloading institution. Building a dossier without the corpus gives a framed placeholder naming each missing file, with every claim, page reference and finding intact.

To regenerate the corpus from your own copies of the sources:

sh fresh_audit_2026_08_16/render_evidence.sh

Each call is pinned to a one-based page number, so the images are reproducible for anyone with legal access to the papers. The render lines name the file expected for each source under refs/.

Checking the inventory

The result inventory is generated, and can be re-derived:

cd part_i && pdflatex main.tex && pdflatex main.tex && pdflatex main.tex
cd .. && python3 docs/extract.py

python3 docs/extract.py --check exits non-zero if the committed inventory has drifted from the manuscript. The numbers come from part_i/main.aux, never from hand-editing.

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