BACKLOG #2 Site 反映 backlog catch up Tier 1 top-5 の 2 番目 — STEP 1293 (2026-08-08)

Chang v6 29-paradigm exhaustion + Rei axiom-free retrofit (20/29 = 69.0%)

Chang v6 (arxiv:2603.11066v6, Edward Y. Chang / Stanford + QuadriumAI) の Theorem 13.1 Paradigm Exhaustion 29 paradigms を Lean 4 inductive type として型化 + Rei 既存 axiom-free asset を 13 retrofit file 経由で 20/29 paradigm の machine-checked instance として annotate。 STEP 1269 (3/29 initial) → STEP 1310 pt.7 (20/29 close 判定) の 20 日間進化を集約反映。藤本伸樹 × Rei × Claude / STEP 1269 (2026-07-10) 起点 → STEP 1310 pt.1-7 (2026-07-23〜07-30) 拡大 → STEP 1293 (2026-08-08) site 反映

1. なぜ backlog に入っていたか

Chang v6 は 2026-02〜04 に段階 update された external paper (Edward Y. Chang, Stanford)。 Rei は STEP 1269 (2026-07-10) で 3 retrofit を初期実装し、その後 STEP 1272/1274/1276-1282/1310 で追加 17 retrofit を積み上げ、 20/29 = 69.0% coverage に到達。 2026-07-19 に単一 1014 行 file から ETP-inspired 分割 refactor (Chang.lean hub + Chang/Retrofits/*.lean 13 file + Chang/Coverage.lean aggregator + Chang/README.md tracker) を実施。

但し site 側 dedicated page は未作成のまま backlog 化 (Lean 4 file + README は GitHub-only artifact、 Radar JSON は site-visible ではない)。 STEP 1293 で dedicated site page 化。

本 page は「新しい成果」ではない。 STEP 1269-1310 の 20 retrofit 実装済成果を集約 site 反映。数学的内容 + Lean 4 axiom profile は全て commit 済で immutable、 memory 忘れ対策 primary purpose 適用。

2. Chang v6 paper 概要

項目	内容
Title	"Exploring Collatz Dynamics with Human-LLM Collaboration"
Author	Edward Y. Chang (Stanford University + QuadriumAI)
arXiv	2603.11066 v6 (22 Apr 2026)
Scale	630 formal results across 10^14 scripts、 29 mathematical paradigms、 6.6 MB PDF / 15,291 行 text extract
Methodology	Human-LLM collaboration (Claude Opus 4.6 + GPT + Gemini + Human Moderator、 §12)

Core theorems

Theorem 13.1 (Paradigm Exhaustion): 29 paradigms 各々が density-1 convergence を出すが all-n には届かない (informal survey theorem、 machine-verifiable object ではない)
Theorem 13.2 (Barrier Characterization): distributional-to-pointwise gap = divergence component 完全等価
Conjecture 13.6 (Computational Irreducibility): no polynomial-time predictor (informal)

3. 29 paradigms full enumeration

Chang v6 §13 で explicitly 列挙。 Rei の 20 covered paradigm を ✅、 9 uncovered を gap で表示。

#	Paradigm name	Rei coverage	#	Paradigm name	Rei coverage
P1	Transfer operator spectral	✅ (STEP 1310 pt.3)	P16	2-Adic potential	✅ (STEP 1269)
P2	AFI algebra	✅ (STEP 1279)	P17	Orbit coalescence	✅ (STEP 1310 pt.6)
P3	2-Adic Mahler	gap	P18	Digit-sum	✅ (STEP 1310 pt.1)
P4	Measure rigidity	gap	P19	Ising entropy	gap
P5	Carry propagation	✅ dual (STEP 1272 + 1274)	P20	Expander sieve	✅ thin dual (STEP 1310 pt.7)
P6	Automata-theoretic	✅ (STEP 1310 pt.1)	P21	Diophantine fractional	✅ dual (STEP 1281)
P7	S-Unit/Subspace	gap	P22	p-Adic Mahler/Strassman	gap
P8	Baker/log₂3	✅ thin dual (STEP 1310 pt.2)	P23	Iwasawa cyclotomic	✅ thin dual (STEP 1310 pt.4)
P9	Renewal theory	gap	P24	Height descent	✅ (STEP 1269)
P10	Martingale	gap	P25	Coalescence merging	✅ (STEP 1274)
P11	Modular sieve	✅ (STEP 1276)	P26	Cascade staircase	✅ triple (STEP 1278)
P12	Boolean Fourier	gap	P27	CRT hierarchy	✅ (STEP 1280)
P13	Tao amplification	✅ (STEP 1282)	P28	Lattice reduction/LLL	gap
P14	Borel-Cantelli	✅ ★ non-Collatz-derived archetypal (STEP 1310 pt.5)	P29	Discrete log	✅ (STEP 1277)
P15	Compactness Z₂	✅ (STEP 1269)	—	Total covered	20 / 29 = 69.0%

Honest gap 9/29 = 31.0% (P3, P4, P7, P9, P10, P12, P19, P22, P28) — Chang informal enumeration のみ、 Rei は machine-verified backing なし。

4. Multi-paradigm coverage instances

単一 Rei source file が複数 Chang paradigm に対応する retrofit pattern。 Rei axiom-free asset の 横断適用性 evidence。

Rei source	Paradigms	Retrofit type
`T1ObstructionWitness`	P24 (Height Descent) + P11 (Modular Sieve) + P26 (Cascade) + P20 (Expander)	quadruple = Rei 唯一の 4-paradigm coverage
`TransferBanach`	P15 (Compactness Z₂) + P16 (2-Adic Potential)	dual (自然対応)
`PadicRoughness` Phase A + B	P5 × 2 evidence angles + P23 (Iwasawa) thin dual	triple (Phase 分割 + thin dual)
`Step879ArithPredecessors`	P2 (AFI) + P21 (Diophantine)	dual
`RozierTerracolLogRatio`	P29 (Discrete Log) + P8 (Baker/log₂3) thin dual	dual

P14 特殊 note (STEP 1310 pt.5, 2026-07-23)

P14 retrofit は Rei 初 non-Collatz-derived archetypal thin dual (前 17 retrofit は全 Collatz-adjacent)。 CantorHausdorffDimension (Cantor 1883) の「diameter shrinks to 0, set nonempty」 pattern を machine-check、 Chang P14 obstruction 「μ(C_div) = 0 ≠ empty」の archetypal instance のみ提供。

Rei は Tao 2019 μ(C_div) = 0 の proof を持たず (Step941 は axiom + sorry で非-axiom-free)、 Collatz-specific evidence でない。 Coverage stat 62.1%※ = 17 Collatz-adjacent + 1 non-Collatz-derived archetypal の合算値で asterisked。 ※現在は 20/29 = 69.0%、 P14 asterisk 継承。

5. File structure (2026-07-19 ETP-inspired refactor)

CollatzRei/
├── Chang.lean                              (hub: 29 inductive + paradigmNumber
│                                            + paradigmObstruction + AnnotatedWall
│                                            + EdgeType alignment)
├── Chang/
│   ├── README.md                           (coverage tracker + ETP discipline)
│   ├── Coverage.lean                       (reiMachineCheckedParadigms +
│   │                                        Nodup + gap theorem)
│   └── Retrofits/                          (13 files, 63 defs total)
│       ├── T1Obstruction.lean              [P24 + P11 + P26 + P20 = quadruple]
│       ├── TransferBanach.lean             [P15 + P16 dual]
│       ├── PadicRoughness.lean             [P5 dual + P23 thin dual]
│       ├── ThreeAdicIsolation.lean         [P25]
│       ├── RozierTerracol.lean             [P29 + P8 thin dual]
│       ├── Step879.lean                    [P2 + P21 dual]
│       ├── PadicCollatz.lean               [P27]
│       ├── Step941Tao.lean                 [P13]
│       ├── DfaFirewall.lean                [P6]
│       ├── TrailingOnesDigitSum.lean       [P18]
│       ├── SpectralGap.lean                [P1]
│       ├── CantorArchetypal.lean           [P14 ★ non-Collatz-derived]
│       └── OrbitCoalescence.lean           [P17 thin dual]
└── ChangParadigmExhaustion.lean            (backward-compat stub, imports
                                             Chang + Chang.Coverage)

ETP-inspired discipline (Adapted from Equational Theories Project arxiv:2512.07087v1)

native_decide 禁止 — Rei 全 retrofit で遵守 (STEP 1215-1302 全 axiom-free)
Facts aggregation — 1 counterexample / evidence source per file (T1Obstruction が P24+P11+P26+P20 を単一 file で quadruple)
Duality symmetry — 同 source を異なる theoretical framework で観察した複数 obstruction (PadicRoughness Phase A + Phase B の P5 dual)
axiom base restriction — 全 retrofit 定義は [propext, Classical.choice, Quot.sound] Mathlib 標準 base のみ、多くは完全 zero-axiom

Not adopted (scale mismatch)

Zulip forum / GitHub Projects Kanban / CI single-claim lock (Rei は single-user)
22M implications aggregation transitivity + duality (Rei scale 29 fixed で不要)
equation metaprogramming command (29 inductive constructor で benefit 小)

6. STEP 1310 pt.7 (2026-07-30) close 判定

Coverage 20/29 = 69.0% で honest close 推奨 (STEP 1310 pt.7 Arc #4 audit finding)。残 9 paradigms の retrofit は Rei-adjacent thin dual candidate として 07-19 survey + 07-30 再照合の結果 実装可能なし と判定。

残 paradigm	Rei 側 gap 理由
P3 (2-Adic Mahler)	Mahler series 具体 machinery 不所持、 stretch inflate risk
P12 (Boolean Fourier)	Boolean Fourier machinery 不所持、 stretch inflate risk
P22 (p-Adic Mahler/Strassman)	Strassman machinery 不所持、 stretch inflate risk
P4 (Measure rigidity)	Infrastructure port 必要 = multi-session commitment
P7 (S-Unit/Subspace)	Heavy formalization 必要
P9 (Renewal theory)	Infrastructure port 必要
P10 (Martingale)	Infrastructure port 必要
P19 (Ising entropy)	Heavy formalization 必要
P28 (Lattice reduction/LLL)	Heavy formalization 必要

「Chang coverage を数値上昇させる目的だけの retrofit は Pattern 5 self-detection risk」 (07-19 survey 警告) に従い、 forced 目標達成不要 = honest close。追加 retrofit は Rei-adjacent asset の自然発生に任せる方針。

7. Honest scope (譲れない線)

(1) Pattern 5 self-detection 適用: Chang v6 subsumption — Chang v6 (2026-02〜04 段階公開) は本 file (2026-07-10 起点) より 先行公開。 Rei は novel paradigm-level survey claim を出さない (STEP 622-624 の「trailing 1-bits ≥ 4 wall」独立 convergence は 2026-05-10 tracker で ALIGNED 既確認、 Chang 先行 subsume 内)。

(2) Rei は個別 machine-verified evidence layer のみ担当 — 20/29 = 69.0% coverage、 honest gap 9/29 = 31.0% 明示。 novel paradigm 追加も claim しない。

(3) Chang §12 Human-LLM collaboration methodology 先行公開 — Rei-AIOS の chat-Claude + Rei env + 藤本さん moderator 分業も類似構造で既 prior art (Chang §12: Claude 37% + GPT 30% + Moderator 33% 貢献 attribution)。 Rei は novel LLM-collaboration methodology claim も絶対に出さない。

(4) P14 asterisk 継承 — Rei 初 non-Collatz-derived archetypal thin dual (Cantor 1883 pattern)。 Tao 2019 の proof 本体は Rei 側で axiom-free 化未達 (Step941 は axiom + sorry)。 P14 coverage は archetypal instance provision のみ、 Collatz-specific evidence でない。

(5) 補完関係 = Chang provides landscape + Rei provides individual backing — Chang: 29 paradigms survey + informal enumeration + distributional-to-pointwise gap characterization + unconditional density-1 results + discrete log framework + 630 formal results / Rei: 20 individual axiom-free Lean 4 machine-checked evidence + STEP 1170 4-edge-type meta-taxonomy (Chang's 29 全て wall refinement) + STEP 930 Typology (Chang's Theorem 13.2 = Type III PROBLEM_UNDEFINED + BOTH の Collatz 具体化)。

(6) 順序原則の operational 実例 — STEP 1269 3/29 → 1310 pt.7 20/29 の 20 日間拡大は Rei-adjacent asset survey → retrofit の「発見」 process (「1 行 wrapper = 成果ではなく発見」 discipline)。 forced 数値追求は honest close で明示的 reject。

8. 関連 memory + Rei stack impact

直接 origin memory

project_step1269_chang_paradigm_exhaustion_retrofit_2026-07-10.md — 初期 3 retrofit + Radar update origin
project_step1271_dfumt_7integration_complete_2026-07-10.md — Fermi × Chang bridge (FermiParallelChangExhaustion.lean)
STEP 1310 pt.1-7 (2026-07-23〜07-30) — 拡大 17 retrofit + honest close 判定

本 backlog site 反映の origin

feedback_all_research_site_reflection_default.md — 2026-08-06 藤本さん永久 protocol
project_site_backlog_catch_up_pending_2026-08-06.md — 帰宅時判断 → Tier 1 top-5 段階的 catch up 起動
feedback_no_rush_publication.md — 「急がずゆっくりと」、 1 個ずつ丁寧に pace

Honest scope discipline

feedback_world_uniqueness_claim_controllable.md — 「novel paradigm-level survey」主張禁止
feedback_evaluation_symmetry_principle.md — Chang v6 inflate / deflate 両禁止
feedback_chat_claude_hallucination_warning.md — Pattern 5 self-detection 適用
feedback_zero_sorry_floor_not_ceiling.md — axiom-free = floor discipline
feedback_lean_build_verify.md — commit 前 lake build + #print axioms 実測

Rei stack cross-references

STEP 1170 (4-edge-type reduction-graph、 Chang's 29 = wall refinement 位置付け)
STEP 930 (Unsolved Problem Typology、 Chang's Theorem 13.2 Barrier Characterization = Type III PROBLEM_UNDEFINED + BOTH の Collatz 具体化)
STEP 622-624 (Rei 独立 convergence on paradigm exhaustion 前例、 2026-05-10 tracker note で ALIGNED 既確認)
STEP 1259 (TransferBanach retrofit source origin)、 STEP 1260 (ReductionGraphTransfer 4 edge type + WallEdge 基盤)
Fermi × Chang bridge (FermiParallelChangExhaustion.lean = 6 explanations × 6 archetypes bijection + 29 paradigms aggregate)