Edition README
Paper XII: Patching Support, Hecke Packets, and Conditional Automorphic Completion
README.md
1 # Patching Support and Hecke Packets
2
3 **Conditional automorphic completion**
4 Paper XII · Komorebi P. · Operation Komorebi
5
6 Accepted reading release **1.0.0, 10 October 2026**, checkpoint P12-PUB-B01.
7 October 11 delivery preserved; distribution frozen **21 October 2026**.
8
9 | Read | Pages |
10 |---|---:|
11 | [Traditional monograph](core/publication/pdfs/Paper_XII_Traditional_v1.0.0.pdf) | 40 |
12 | [Visual guide](core/publication/pdfs/Paper_XII_Visual_Guide_v1.0.0.pdf) | 28 |
13 | [Lean and evidence guide](core/publication/pdfs/Paper_XII_Lean_Guide_v1.0.0.pdf) | 31 |
14 | Total | 99 |
15
16 Open [START_HERE.html](START_HERE.html). Keep the three PDF filenames together
17 for local companion links. The 28-page visual guide contains its cover and
18 27 complete worked lessons. Examples are not additional theorem claims.
19
20 ## Exact accepted contract
21
22 The 49 revised internal claims map to 291 distinct production targets. The
23 original wording retains its separate census: 41 complete, seven partial and
24 one unchecked. The eight amended identifiers are 6.12, 9.4, 9.5, 9.6, 10.5,
25 12.2, 12.4 and 12.6. These amendments are not retrospective proofs of stronger
26 original formulations. This freeze adds no mathematical amendment.
27
28 An arithmetic application supplies the actual residual/deformation problem,
29 an applicable patching package and full patched support. Descending support
30 alone does not supply a compatible Hecke point over the original coefficient
31 field. The same-field point and its compatibility remain inputs. Classicality
32 must hold for the selected eigensystem, with the occurring object, attached
33 representation and matching Frobenius polynomials supplied by the applicable
34 realization input. Continuity, Hausdorff coefficient topology, density,
35 semisimplification and Brauer–Nesbitt hypotheses remain explicit.
36
37 Theorem 10.5 constructs from nonempty admissible finite conjugacy classes under
38 its coefficient completeness, separatedness, finite-quotient, continuity,
39 integral-spine, reduction-stability, retained-residual-class and every-frame
40 polynomial-relation assumptions. It does not
41 create missing finite classes or prove that arbitrary arithmetic local
42 conditions are polynomial ideals. Propagation compares two already existing
43 compatible families for the same automorphic object and common algebraic spine;
44 it does not create missing companions. Augmentation at coefficient prime two
45 does not remove residual-image, local-geometry or classicality assumptions.
46 No proof of Paper XI's general Conjecture 66 is assumed.
47
48 ## Formal and written evidence
49
50 The inherited formal record has 96 registered production modules, 1,229 public
51 named declarations, 748 Paper XII theorem declarations and 81 reused Paper X
52 theorem declarations. These are lexical/historical units, not independent
53 discovery counts or a fresh full owning-module census. The 24 exact teaching
54 modules and 96 production modules retain their accepted bytes. September 2026
55 compiler, object, log, axiom and negative-control records are authenticated
56 historical evidence. This freeze does not execute Lean/Lake or the auditor.
57 The exact runtime and dependency cache remain external replay prerequisites.
58
59 All 52 main proof bodies and 82 statement-environment bodies remain unchanged.
60 The accepted publication redrew four of eighteen main figures; fourteen retained
61 exact bytes. The current sources, figure assets, raw catalogues and rendered
62 claim links are preserved. No new figure regeneration occurs in this freeze.
63
64 ## Bounded checks, references and readers
65
66 The accepted October 10 publication passed seven named gates: source/object
67 integrity; the original 92,892-check finite suite; 31 exact appendix checks;
68 46 exact visual checks; 3,216 primitive-benchmark assertions; native historical-
69 record authentication; and 26 publication regression methods. These overlapping
70 counts are not summed into a theorem total. Hash/log authentication is not
71 compiler execution. This freeze authenticates those records without rerunning
72 the finite/scientific suites or their controls.
73
74 The 27 bibliography keys resolve, with selected primary metadata checks and
75 explicit access limits. This is not a new theorem/application audit of all
76 27 works. The accepted isolated source rebuild matched all three PDFs and four
77 redrawn figure PDFs byte for byte in its checked environment, with text and
78 100-dpi pixel comparisons recorded separately. That dated result is not a guarantee
79 across TeX, fonts, Python/PyMuPDF versions or operating systems. This freeze
80 preserves the accepted PDF bytes and performs no PDF build.
81
82 Existing build diagnostics remain explicit: nine underfull-spacing messages
83 for the monograph, two for the visual guide and one for the Lean guide; two
84 pdfLaTeX runs warn that epstopdf shell escape is disabled. The accepted final
85 build found no overfull boxes, missing characters or unresolved references.
86 It was not warning-free. Fresh freeze reader QA is a separate bounded review.
87
88 ## Complete package layout
89
90 - [core/](core/) is the exact expanded 3,796-file source-and-evidence release.
91 Its original manifest, scripts, sources, readers and research ledgers are unchanged.
92 - [preserved_delivery/](preserved_delivery/) retains all five October 11 delivery
93 members byte for byte: its original entry page, manifest and three ZIPs for
94 readers, source/evidence and delivery receipts. Their container hashes remain exact.
95 - [verification/freeze_2026-10-21/](verification/freeze_2026-10-21/) contains fresh
96 identity, saved-evidence, reader and licensing audits plus a baseline map.
97 - [FREEZE_RECORD.json](FREEZE_RECORD.json) and
98 [FREEZE_PROGRESS_LEDGER_v1.0.0.md](FREEZE_PROGRESS_LEDGER_v1.0.0.md) record this freeze.
99 - [Original research ledger](core/PROGRESS_LEDGER.md),
100 [machine ledger](core/PROGRESS_LEDGER.json) and
101 [continuation contracts](core/CONTINUE_HERE.md) retain their dated scopes.
102
103 The original October 11 entry page describes a wider retrieval snapshot and is
104 historical. This root guide is the entry point for the current single Paper XII
105 distribution. Five delivery members and 3,796 expanded core files are separate,
106 overlapping preservation units, not a count of independent scientific results.
107
108 Nine standalone font binaries were deliberately omitted from the recovered
109 predecessor copy. Retained payloads and exclusions are documented; scientific
110 source/proofs were not removed. Its old historical distribution manifest is not
111 a current sanitized-tree manifest. Fonts are external build dependencies.
112
113 ## Verify and reproduce
114
115 Extract this single ZIP and run the standard-library outer strict checker:
116
117 ```sh
118 python3 -B scripts/verify_integrity.py --strict
119 ```
120
121 It verifies exact regular-file membership, safe canonical paths, sizes and
122 SHA-256. Its byte-identical portable code and own accepted 21-control receipt
123 are reused from the saved Paper X freeze, with exact provenance in the audit.
124 Controls are not rerun. The unchanged Paper XII core checker is separate:
125
126 ```sh
127 cd core
128 python3 -B tools/verify_package.py
129 ```
130
131 The inner checker was checked on Linux and uses platform-specific path
132 rendering; use the outer portable checker as the primary integrity route on
133 Windows. No native Windows execution is claimed. The original core manifest
134 authenticates the unchanged inner tree. The outer
135 manifest additionally authenticates that manifest, all preserved delivery ZIPs
136 and every freeze addition. The checksum list excludes itself and the outer
137 manifest; the outer manifest additionally covers the list.
138
139 Use [core/BUILD.md](core/BUILD.md) for scoped reproduction commands in a separate
140 writable copy, keeping outputs outside the sealed tree. Some historical formal
141 runners mutate their build/log directories and must not run in this distribution.
142 A fresh pinned Lean replay or a new arithmetic application is a separate task.
143
144 ## Open use and third-party terms
145
146 Original software, machine-readable material and code listings use MIT. Original
147 writing, figures and editable writing sources use CC BY 4.0. The author's open-
148 license authorization supersedes the old unassigned manuscript status retained
149 inside the historical formal release, for original project material only.
150 Third-party work and fonts retain their own terms; the retained Mathlib Apache
151 terms and authenticated font notices accompany the grants.
152
153 See [LICENSE.md](LICENSE.md), [LICENSE_STATUS.json](LICENSE_STATUS.json) and
154 [LICENSES/](LICENSES/). Current PDF notices are under LICENSES/PDF_NOTICES/;
155 the smaller reader ZIP also places those notices adjacent to its three PDFs.
156 Neither PDF bytes nor original core license files were changed.
157
158 The twelve core distributions I–XII have now completed the sequential freeze
159 pass within their accepted scopes. Open research, inherited-evidence limits
160 and disclosed archival gaps remain. The wider Komorebi Space, Realization
161 Calculus companions, Proof-Path Theory and software projects have separate
162 closeouts. No new compiler, scientific/control suite, TeX/PDF build, figure
163 regeneration, external source-theorem audit or whole-paper proof audit is claimed.
164 No public repository or website was published by this task.