Patching Support and Hecke Packets
Conditional automorphic completion
Paper XII · Komorebi P. · Operation Komorebi
Accepted reading release 1.0.0, 10 October 2026, checkpoint P12-PUB-B01.
October 11 delivery preserved; distribution frozen 21 October 2026.
| Read | Pages |
|---|---|
| Traditional monograph | 40 |
| Visual guide | 28 |
| Lean and evidence guide | 31 |
| Total | 99 |
Open START_HERE.html. Keep the three PDF filenames together for local companion links. The 28-page visual guide contains its cover and 27 complete worked lessons. Examples are not additional theorem claims.
Exact accepted contract
The 49 revised internal claims map to 291 distinct production targets. The original wording retains its separate census: 41 complete, seven partial and one unchecked. The eight amended identifiers are 6.12, 9.4, 9.5, 9.6, 10.5, 12.2, 12.4 and 12.6. These amendments are not retrospective proofs of stronger original formulations. This freeze adds no mathematical amendment.
An arithmetic application supplies the actual residual/deformation problem, an applicable patching package and full patched support. Descending support alone does not supply a compatible Hecke point over the original coefficient field. The same-field point and its compatibility remain inputs. Classicality must hold for the selected eigensystem, with the occurring object, attached representation and matching Frobenius polynomials supplied by the applicable realization input. Continuity, Hausdorff coefficient topology, density, semisimplification and Brauer–Nesbitt hypotheses remain explicit.
Theorem 10.5 constructs from nonempty admissible finite conjugacy classes under its coefficient completeness, separatedness, finite-quotient, continuity, integral-spine, reduction-stability, retained-residual-class and every-frame polynomial-relation assumptions. It does not create missing finite classes or prove that arbitrary arithmetic local conditions are polynomial ideals. Propagation compares two already existing compatible families for the same automorphic object and common algebraic spine; it does not create missing companions. Augmentation at coefficient prime two does not remove residual-image, local-geometry or classicality assumptions. No proof of Paper XI's general Conjecture 66 is assumed.
Formal and written evidence
The inherited formal record has 96 registered production modules, 1,229 public named declarations, 748 Paper XII theorem declarations and 81 reused Paper X theorem declarations. These are lexical/historical units, not independent discovery counts or a fresh full owning-module census. The 24 exact teaching modules and 96 production modules retain their accepted bytes. September 2026 compiler, object, log, axiom and negative-control records are authenticated historical evidence. This freeze does not execute Lean/Lake or the auditor. The exact runtime and dependency cache remain external replay prerequisites.
All 52 main proof bodies and 82 statement-environment bodies remain unchanged. The accepted publication redrew four of eighteen main figures; fourteen retained exact bytes. The current sources, figure assets, raw catalogues and rendered claim links are preserved. No new figure regeneration occurs in this freeze.
Bounded checks, references and readers
The accepted October 10 publication passed seven named gates: source/object integrity; the original 92,892-check finite suite; 31 exact appendix checks; 46 exact visual checks; 3,216 primitive-benchmark assertions; native historical- record authentication; and 26 publication regression methods. These overlapping counts are not summed into a theorem total. Hash/log authentication is not compiler execution. This freeze authenticates those records without rerunning the finite/scientific suites or their controls.
The 27 bibliography keys resolve, with selected primary metadata checks and explicit access limits. This is not a new theorem/application audit of all 27 works. The accepted isolated source rebuild matched all three PDFs and four redrawn figure PDFs byte for byte in its checked environment, with text and 100-dpi pixel comparisons recorded separately. That dated result is not a guarantee across TeX, fonts, Python/PyMuPDF versions or operating systems. This freeze preserves the accepted PDF bytes and performs no PDF build.
Existing build diagnostics remain explicit: nine underfull-spacing messages for the monograph, two for the visual guide and one for the Lean guide; two pdfLaTeX runs warn that epstopdf shell escape is disabled. The accepted final build found no overfull boxes, missing characters or unresolved references. It was not warning-free. Fresh freeze reader QA is a separate bounded review.
Complete package layout
- core/ is the exact expanded 3,796-file source-and-evidence release. Its original manifest, scripts, sources, readers and research ledgers are unchanged.
- preserved_delivery/ retains all five October 11 delivery members byte for byte: its original entry page, manifest and three ZIPs for readers, source/evidence and delivery receipts. Their container hashes remain exact.
- verification/freeze_2026-10-21/ contains fresh identity, saved-evidence, reader and licensing audits plus a baseline map.
- FREEZE_RECORD.json and FREEZE_PROGRESS_LEDGER_v1.0.0.md record this freeze.
- Original research ledger, machine ledger and continuation contracts retain their dated scopes.
The original October 11 entry page describes a wider retrieval snapshot and is historical. This root guide is the entry point for the current single Paper XII distribution. Five delivery members and 3,796 expanded core files are separate, overlapping preservation units, not a count of independent scientific results.
Nine standalone font binaries were deliberately omitted from the recovered predecessor copy. Retained payloads and exclusions are documented; scientific source/proofs were not removed. Its old historical distribution manifest is not a current sanitized-tree manifest. Fonts are external build dependencies.
Verify and reproduce
Extract this single ZIP and run the standard-library outer strict checker:
python3 -B scripts/verify_integrity.py --strict
It verifies exact regular-file membership, safe canonical paths, sizes and SHA-256. Its byte-identical portable code and own accepted 21-control receipt are reused from the saved Paper X freeze, with exact provenance in the audit. Controls are not rerun. The unchanged Paper XII core checker is separate:
cd core
python3 -B tools/verify_package.py
The inner checker was checked on Linux and uses platform-specific path rendering; use the outer portable checker as the primary integrity route on Windows. No native Windows execution is claimed. The original core manifest authenticates the unchanged inner tree. The outer manifest additionally authenticates that manifest, all preserved delivery ZIPs and every freeze addition. The checksum list excludes itself and the outer manifest; the outer manifest additionally covers the list.
Use core/BUILD.md for scoped reproduction commands in a separate writable copy, keeping outputs outside the sealed tree. Some historical formal runners mutate their build/log directories and must not run in this distribution. A fresh pinned Lean replay or a new arithmetic application is a separate task.
Open use and third-party terms
Original software, machine-readable material and code listings use MIT. Original writing, figures and editable writing sources use CC BY 4.0. The author's open- license authorization supersedes the old unassigned manuscript status retained inside the historical formal release, for original project material only. Third-party work and fonts retain their own terms; the retained Mathlib Apache terms and authenticated font notices accompany the grants.
See LICENSE.md, LICENSE_STATUS.json and LICENSES/. Current PDF notices are under LICENSES/PDF_NOTICES/; the smaller reader ZIP also places those notices adjacent to its three PDFs. Neither PDF bytes nor original core license files were changed.
The twelve core distributions I–XII have now completed the sequential freeze pass within their accepted scopes. Open research, inherited-evidence limits and disclosed archival gaps remain. The wider Komorebi Space, Realization Calculus companions, Proof-Path Theory and software projects have separate closeouts. No new compiler, scientific/control suite, TeX/PDF build, figure regeneration, external source-theorem audit or whole-paper proof audit is claimed. No public repository or website was published by this task.