---
name: project-step1178-dossier-update-2026-06-29
description: "STEP 1178 Collatz Frontier dossier 2026-06-29 update with 3 Research Radar arXiv papers (Chang 2026 paradigm exhaustion superset / Reyes 2026 Fibonacci mod-6 Lean candidate / Niu 2026 withdrawn redirect to Rozier-Terracol 2025), v0.1 publish gate strengthened, Janik 教訓 reframe operational"
metadata: 
  node_type: memory
  type: project
  originSessionId: 85e02543-9e2e-46fe-8773-71384f33768f
---

## STEP 1178 Collatz Frontier dossier — 2026-06-29 update

3 paper integrated into `papers/collatz-frontier-dossier-DRAFT.md` §6 new section + status header update.

### Paper 1: Chang 2026 (★ direct superset of §3 frontier map)
- **arxiv:2603.11066v6** (2026-03-10) "Exploring Collatz Dynamics with Human-LLM Collaboration"
- Author: Edward Y. Chang
- Core: **29 distinct mathematical paradigms** + ~10¹⁴ computational experiments + 630 formal results → **Paradigm Exhaustion Theorem** (every framework for distributional → pointwise convergence encounters irreducible structural obstruction)
- **Direct superset of our §3 7-route table** (2-adic ⊂ p-adic interpolation, Ergodic ⊂ martingale methods, Baker ⊂ S-unit equations, etc.)
- **Implication**: dossier §3 is **not novel in coverage**; v0.1 publish gate now **stricter** (must articulate contribution beyond Chang's 29-paradigm exhaustion; currently nothing identified)
- Honest scope: full chapter-level reading **required** before any §3 update is published (abstract only at 2026-06-29)

### Paper 2: Reyes 2026 (★ Lean 4 formalization candidate)
- **arxiv:2606.02621v2** (2026-05-28) "A Fibonacci theorem for Collatz trajectories via modular graph structure"
- Author: Manuel-Alejandro Reyes Jiménez
- Core: ∀m≥1, **F(m+1) odd integers in {1,…,2^m}** avoid 4 mod 6 during steps 2,…,m, decay rate (φ/2)^m; directed graph G mod 6 + absorbing component G[{1,2,4,5}] spectral radius 2 → φ (vertex 4 removal spectral gap) + explicit bijection Ψ_m
- **Overlap with Rei STEP 685-689 (Mod-6 Theorem) + STEP 697 (Fibonacci × π(64)=96)** area
- **Lean 4 formalizability: high (L5=0.60)** — graph G has 6 vertices, spectral computation elementary
- **STEP 1246 candidate**: ReyesFibonacciMod6.lean (subject to controllable "first Lean 4" claim verification per `[[feedback-world-uniqueness-claim-controllable]]` — Mathlib4 grep + github-state.json prior-art audit 必須)
- Honest scope: Lean 4 formalization of an existing result = **modest contribution** (per §0 non-claim 3)

### Paper 3: Niu 2026 (★ withdrawn 2026-05-20, redirect)
- **arxiv:2605.13886v2** (2026-05-11) "Parity vectors and paradoxical sequences in the accelerated Collatz map"
- Author: Tong Niu
- **Status: WITHDRAWN 2026-05-20** due to anticipated duplication with Rozier-Terracol (arXiv:2502.00948, 2025)
- 3 theorems (sharp finitary Terras density / closed-form Ω_k(n) count / density-zero bounded paradoxical sequences) build on Rozier-Terracol 2025 + Terras 1976 + Lagarias 1985 + Tao 2019
- **Action**: do NOT cite Niu 2026 as primary literature. Cite Rozier-Terracol 2025 instead
- Withdrawal itself informative — parity-vector area is competitively active, overlap risk high

## ★ STEP 690-696 Janik 教訓 reframe (operational)

Janik syracuse-confinement (2026-02 公開) を知らずに 21 連続 STEP 走った incident (CLAUDE.md):
> 「Janik's syracuse-confinement (2026-02 公開) を知らずに 21 連続 STEP を走った。 最新研究無視は **研究労力の大幅浪費を招く**。 絶対にこの過ちを繰り返さない。」

本日 2026-06-28 Research Radar = 3 paper 全 dossier touch area:
- Chang 2026 = §3 frontier map superset
- Reyes 2026 = §2 mod-6 / Fibonacci area
- Niu 2026 = §2 inverse tree / parity vector area (withdrawn)

**Audit log applied**:
- Chang 2026: abstract reading 完了 (2026-06-29), full chapter pending (publish gate requirement)
- Reyes 2026: abstract reading 完了 (2026-06-29), STEP 1246 candidate (separate decision)
- Niu 2026: abstract + withdrawal status 確認完了 (2026-06-29), redirect to Rozier-Terracol 2025

**Reading 3/3 before any new STEP** = Janik incident protocol enforced.

## Updated v0.1 publish gate
1. **Original**: novelty beyond Lagarias 1985 / Jacobsthal / Janik syracuse-confinement
2. **NEW**: novelty beyond Chang 2026's 29-paradigm exhaustion (currently nothing identified)
3. **NEW**: full chapter-level reading of Chang 2026 (current: abstract only)
4. Reyes 2026 Lean 4 formalization (STEP 1246 candidate) = **separate artifact** from dossier

## Recommendation
- dossier remains **SHELVED**
- Add Chang 2026 to references
- Defer Reyes 2026 Lean 4 formalization decision to separate STEP discussion (not under this dossier)

## Honest scope discipline
- [[feedback-no-rush-publication]]: dossier v0.1 publish gate strengthening = 急がず ゆっくりと適用
- [[feedback-world-uniqueness-claim-controllable]]: Reyes 2026 「first Lean 4」 claim は audit 後のみ可能
- [[feedback-evaluation-symmetry-principle]]: Chang 2026 superset 認識 = inflate せず deflate せず (dossier §3 が 「small/honest」 を再 articulate)
- [[feedback-chat-claude-hallucination-warning]] Antipattern: Niu 2026 withdrawal を見逃して引用しないように redirect 明示 (Pattern 5 防止)
- STEP 690-696 Janik 教訓 reframe operational (reading 3/3 完了 before any §3 update)

## 関連
- [[project-session-2026-06-28-cotnoir-recapture-step1240-trilogy]] (2026-06-28 session 親)
- [[project-step1228x-paper-draft-literal-ban-2026-06-28]] (本 turn 8th iteration hardening)
- [[project-invention-2026-06-27-downgrade-approve-zlb-plus-4-reject-pipeline-leak-12]]
- [[project-step1225-cron-timing-root-cause-forensics-2026-06-28]]
- [[project-paper171-rei-internal-review-2026-06-28]]
- [[project-kapsner-2020-engagement-note-2026-06-29]]
- [[project-posina-roy-2024-fetch-hold-2026-06-29]]
- [[feedback-no-rush-publication]]
- [[feedback-world-uniqueness-claim-controllable]]
- [[feedback-evaluation-symmetry-principle]]
- [[feedback-chat-claude-hallucination-warning]]