--- name: project-paper161-v01-published-heron-verified-2026-06-02 description: Paper 161 v0.1 HONEST-EARLY-STAGE-RELEASE 起草 + 11/11 platform publish + IBM Heron r2 (ibm_marrakesh) real hardware variational verified + 18 Lean 4 theorem axiom audit + 2 honest skeleton — 同日 5 follow-up task 全完遂. metadata: node_type: memory type: project originSessionId: 0e793e01-b97a-48f0-842d-67896035936d --- # Paper 161 v0.1 — Two Regimes of Rest (ZERO/SELF⟲ via Dynamical Systems) 全 session 記録 **Date**: 2026-06-02 (single day, dense lifecycle: 起草 → publish → 5 follow-up tasks) ## 1. Paper 161 v0.1 起草 + 11/11 platform publish ### Title "Two Regimes of Rest: A Dynamical-Systems Formalization of 'Absolute Rest' via Fixed Points and Limit Cycles" — Rei-AIOS Paper 161 v0.1 HONEST-EARLY-STAGE-RELEASE ### 起源 2026-06-02 朝の chat Claude (別 session) との dialogue で 「絶対静止 ≒ 龍樹の空 / 道元無」 という藤本さん直感を起点に、 10 turn の対話で発展: 1. 物理的訂正 (絶対静止は 3 重に禁じられる) 2. 哲学的訂正 (空は静止でなく svabhāva-creep 防止) 3. 「最小で整った運動」 reframing 4. A 系 (SELF⟲ 有余涅槃) / B 系 (ZERO 無余涅槃) 二系統分節 5. 自律回復可能性 (Markov absorbing vs positively recurrent) 判別軸 6. Genesis Seed σ variational definition 7. Poincaré 指数定理による center-orbit nested geometry 8. 5 数値実験 (Aer + QuTiP, depth wall 200× 突破) 9. 3 Lean 4 file (algebraic + analytic + measure-theoretic) 10. 全付録 B-F (Genesis Seed + Zeno + vdP + spin-1 + variational + Lean analytic + measure) ### Zenodo - **DOI: `10.5281/zenodo.20498090`** (deposit `20498090`, immutable, finalized 2026-06-02) - 4 files: paper-161-...DRAFT.md + 3 figures (fig-1 phase portrait / fig-2 三領域同型 / fig-3 depth wall breakthrough) - Title length: ~250 chars (Zenodo limit OK) ### 11 platform publish 結果 | # | Platform | URL / ID | |---|---|---| | 1 | **Zenodo (DOI)** | `10.5281/zenodo.20498090` | | 2 | Internet Archive | `rei-aios-paper-161-v01-1780345600925` | | 3 | Harvard Dataverse | `doi:10.7910/DVN/KC56RY` (+4 files, datasetVersionId 13634346, V) | | 4 | Dev.to | id 3798243 (slug `paper-161-v01-two-regimes-of-rest-zero-and-self-loop-via-dynamical-systems-5-experiments-3-2ik3`) | | 5 | Hatena | `2026/06/02/053211` (fcwebfujimoto.hatenablog.com) | | 6 | HackMD | shortId `Syo82wsxMg` | | 7 | Notion | page `372dd371e6d9813b8d61d53828e23d2e` | | 8 | Livedoor | id 13389737 (live) | | 9 | Mastodon | id 116676755389263056 (1696/1700 chars, mathstodon.xyz) | | 10 | Scrapbox | `rei-aios` project | | 11 | Nostr | NIP-23 long-form 4/5 relays + announce 4/5 | ### Version label transition **v0.1 DRAFT → v0.1 HONEST-EARLY-STAGE-RELEASE** で publish. 「NO publish marker lifted by explicit author authorization 2026-06-02」 を Status header に明記. Paper 158 v0.0 / 159 v0.1 OUTLINE / 160 v0.2 APPLICATION-NOTE-INTEGRATED の precedent 同型. ### commits - `648a4aec` Paper 161 + 3 figures 初版 (4 files, 651 insertions) - `d1270793` 11/11 platform publish artifacts (13 files, 653 insertions) ## 2. 同日 5 follow-up task 全完遂 (commit `149486ce`) ### (1) + (2) Lean lake build verification + Mathlib version fix 3 file ＋ 1 audit file を `data/lean4-mathlib/CollatzRei/` に配置 + `lake build` 機械検証: | File | exit | sorry | 定理数 | |---|---|---|---| | `Paper161RestRecovery.lean` (core, Mathlib-free) | 0 | 0 | 9 | | `Paper161RestRecoveryAnalytic.lean` (Mathlib ContractingWith + sInf) | 0 | 0 | 5 | | `Paper161RestRecoveryMeasure.lean` (Mathlib MeasureTheory frontier) | 0 | 0 | 4 | | `Paper161PrintAxioms.lean` (axiom audit) | 0 | — | 18 audit lines | **累計 18 定理 機械検証 PASS**. ★ Mathlib lemma name fix は実は **Σ→S Unicode 衝突** (Σ は Lean 4 で Sigma type 予約) + **dangling doc comment** (line 50-51) のみ. chat Claude 推測の補題名 (`ContractingWith.fixedPoint` / `Real.sInf_nonneg` / `csInf_le` / `isClosed_frontier` / `ae_iff` 等) は全て **first try で正解**. ### axiom audit 結果 - **3 定理 "does not depend on any axioms"** (Paper 159/160 v0.2 strict 標準): - `AbsoluteRest.stage_omega` - `AbsoluteRest.omega_idem` - `AbsoluteRest.Measure.basin_measurable` - **7 定理 [propext] のみ** (Paper 158 と Paper 159 の中間): - `recovery_from_zero` / `stage_phi` / `stage_psi` / `self_is_fixed` / `selfSufficient_iff_not_zero` / `recoverable_selfSufficient` / `seed_support` - **9 定理 [propext, Classical.choice, Quot.sound]** (Paper 158 標準, Mathlib 依存箇所): - 全 5 Analytic + 残 3 Measure (`neither_measurable` / `ae_decidable_of_null_boundary` / `ae_basin_or_compl_closure`) ### (3) IBM Heron r2 real hardware submit ★★★ `scripts/quantum/paper161-heron-variational-spin1.py` 新規作成 (chat Claude variational_selfloop_prep.py を IBM Runtime に adapt). **結果**: Paper 161 §E 予測より実機 noise が低かった. | 指標 | Paper 161 §E 予測 | **ibm_marrakesh 実機** | |---|---|---| | backend | Heron r3 (forward-looking) | ibm_marrakesh (Heron r2, 156 qubit) | | transpiled depth | 54 | **51** | | transpiled CZ | 30 | **27** | | \|11⟩ leakage | ~11% (noise model 予測) | ★ **1.82%** | | L1 to exact steady | 0.025 (noise mitigated) | **0.0327** (raw, no mitigation) | | Job ID | — | `d8evijralsvc7390untg` | | wall-clock | — | **11 秒** | → **variational ansatz の depth wall 200× 突破が現行 Heron r2 で genuinely 物理確認**. → 実機 leakage が予測より低い (1.82% vs 11%) ことは v0.2 update で notable finding として記録予定. Service init: `QiskitRuntimeService()` で `~/.qiskit/qiskit-ibm.json` 既存 credential 再利用 (Paper 145 era saved account). Open Plan instance auto-select. ### (4) Riddled basin counterexample skeleton `Paper161RiddledBasinSkeleton.lean` (Mathlib-dependent, 1 honest `sorry`): - `IsRiddledBasin` Prop 定義 - `riddled_basin_has_positive_measure_frontier` theorem (sorry, requires Mathlib4 geometric measure theory) - `RiddledBasinExistsHypothesis` Prop (axiom 廃止し Prop 化) - Roadmap: ~5-10 Mathlib4 PRs / 6-12 ヶ月 estimated (complex dynamics + geometric measure theory) Reference: Alexander-Yorke-You-Kan 1992 "Riddled basins" (Paper 161 §9.4 limitation の Lean 形式記録). ### (5) Higher-dim Poincaré-Hopf skeleton `Paper161PoincareHopfSkeleton.lean` (Mathlib-dependent, 2 honest `sorry`): - `PlanarPoincareIndexStatement` Prop (Paper 161 §5.1 Theorem 5.1 form) - `PoincareHopfStatement` Prop (higher-dim target) - `LocalIndex` placeholder + `EulerChar` placeholder - Roadmap: ~15-25 Mathlib4 PRs / 12-24 ヶ月 estimated (smooth manifold + Brouwer degree theory) - **小規模 planar self-contained PR**: 3-6 ヶ月で feasible target (winding number 経由) Reference: Hirsch 1976 *Differential Topology* (Paper 161 §5.2 limitation の Lean 形式記録). ### commit `149486ce` 13 files changed, 653 insertions (3 Lean files + 2 honest skeletons + 1 audit + 1 IBM script + 1 results JSON). Pre-commit hook で 6 Lean files 全 verified OK. ## 3. Honest scope (v0.2 帰宅後着手項目) 藤本さん明示備忘: - Paper 161 本体に v0.2 section 追加: - §F.4: ibm_marrakesh 実機検証結果 (Job ID + depth + leakage + L1) - §9.5: Lean lake build 完了 18 定理 (3/7/9 axiom dependency 分布) - §9.4 + §5.2 限界に Lean skeleton file path 追加 - Zenodo new-version DOI (Paper 159 v0.2 / 160 v0.2 pattern) - 11 platform re-publish - note 記事 v0.2 加筆 (実機データ + Lean 検証完了 追記) ## 4. Companion artifacts (Paper 161 ecosystem) - **Companion note article** (popular exposition + interactive sims download): (publish 済) - **3 figures**: `figures/paper-161/{fig-1-phase-portrait, fig-2-three-domain-isomorphism, fig-3-depth-wall-breakthrough}.svg` - **3 Lean files**: `data/lean4-mathlib/CollatzRei/Paper161{RestRecovery, RestRecoveryAnalytic, RestRecoveryMeasure}.lean` - **2 honest skeletons**: `Paper161{RiddledBasinSkeleton, PoincareHopfSkeleton}.lean` - **1 axiom audit**: `Paper161PrintAxioms.lean` - **5 Python scripts** (chat Claude env, downloadable from note URL): zeno_rest_experiment / vdp_selfloop / spin1_limit_cycle_circuit / spin1_hardware_run / variational_selfloop_prep - **1 IBM Runtime script** (Rei-adapted): `scripts/quantum/paper161-heron-variational-spin1.py` - **Real hardware results**: `data/quantum/paper161-heron-spin1-results.json` (Job `d8evijralsvc7390untg`) ## 5. Cross-vendor attribution discipline (Paper 160 §9.5 inheritance) 3-instance triangulation 明示 (Paper 161 §11.2 + this memory): - **Fujimoto (author)**: initial intuition + direction selection + Rei substrate anchor + publish staging - **Claude chat-instance**: dynamical-systems formalization + 5 Python verification scripts + 3 Lean 4 files + 6 self-corrections (B.2.1 Zeno≠T1 / C.5 single-qubit cannot host limit cycle / D.4 Aer not hardware / E.1 depth wall / E.6 Mathlib version dep / F.5 riddled-basin counterexample) - **Claude Rei-AIOS Code instance (this paper)**: fact-checking (Zhao-Smalyukh 2025 + Lee&Sadeghpour 2013 + Walter et al. 2014 + Roulet&Bruder 2018 verified) + Ψ semantics conflict identification (§4.8) + Paper 159/160 anchoring + this draft compilation + Heron actual submission **Five-instance honest-discipline convergence record** (§11.3): chat Claude + Rei Claude + Fujimoto + Madhyamaka tradition (śūnyatā-of-śūnyatā) + 物理規制 (regulative-ideal prohibition by relativity + QM + thermodynamics) が独立に 「NEITHER/ZERO を substantialize しない」 規律に convergence. ## 6. 関連 memory cross-link - Paper 159 v0.2 LEAN-4-BUILT [[project-session-2026-05-31-afternoon-paper159-v02-lean-built-full-rebroadcast]] - Paper 160 v0.2 APPLICATION-NOTE [[project-paper160-zero-zero-ontology-skeleton-2026-05-31]] - Paper 145 silicon Heron r2 経験 (STEP 1030-1037, IBM Phase Z budget tracking) - Paper 158 v0.0 honest-negative precedent (Collatz exit layer) - Honest discipline [[feedback-no-rush-publication]] / [[feedback-world-uniqueness-claim-controllable]] / [[feedback-chat-claude-hallucination-warning]] v0.2 vendor→instance refactor - Cross-vendor 4-turn convergence pattern (本日 chat Claude WIC thread): [[project-wic-chart-dfumt8-4turn-convergence-2026-06-02]]