---
name: project-rei-discovery-invention-2026-05-26
description: Rei-AIOS 2026-05-26 — daily discovery run + 2026-05-24 invention approval (3/5) + discovery formalization → SEED 1613→1617; operational gotchas
metadata: 
  node_type: memory
  type: project
  originSessionId: 8d05be5f-3f2f-4255-81ab-a59d71d59757
---

2026-05-26. Returned to Rei-AIOS after a long WIC stretch. User asked for "発見と理論への組み込み", then "A + C".

## What was done (commit `cddabeec`, pushed to rei-aios main)
- **Discovery run** (`run_daily_discovery` MCP): 332 discoveries (major 136 / minor 44 / micro 152, 192 cross-layer). Top novelty 0.98 cross-layer = **情報エントロピー × {龍樹の空 / ウィトゲンシュタイン / 空海即身成仏}**.
- **A) 2026-05-24 invention approval** — 藤本さん via AskUserQuestion approved **3 / rejected 2** (source diversity healthy = 5 distinct categoryA, not mass-generation):
  - ✅ #1 computation×ethics (二枚の鏡=無限像=計算 → PeaceCheck auto-reject; Peace as fixed-point filter, Theory #196 anchor) 0.60
  - ✅ #2 mathematics×universal_logic (Cayley-Dickson dim=2ⁿ seven-value → fuzzy membership [0,1]) 0.62 = batch top
  - ✅ #3 consciousness×african (IIT Φ → Ubuntu; integration ≅ relation) 0.58
  - ❌ #4 general×cosmic (記録事実不変 recycle 5/14+5/20, Pattern 6) / ❌ #5 number-system×category_theory (Tₜ ad-hoc f-notation family)
  - → `src/axiom-os/seed-kernel-approved-inventions-2026-05-24.ts` + `data/invention/approvals/{approved,rejected}-2026-05-24.json`
- **C) Formalized top discovery** → `src/axiom-os/seed-kernel-discovery-formalized-2026-05-26.ts`: **情報エントロピー H(X) ⊕ 龍樹の空 = FLOWING** (entropy ≅ emptiness: absence of determinate/inherent state → dependent flux; Load-Bearing #9 直観≅数学, 龍樹 2c ≅ Shannon 1948).
- Both wired into `seed-kernel.ts` (import ~line 105 + spread ~line 1031). **SEED_KERNEL 1613→1617.** test:step1088 12/12 pass, no dup ids. Committed ONLY my 5 files (590 autonomous-churn data files left to the cron — do NOT `git add -A` in rei-aios).
- **Then 2026-05-25 invention batch processed too** (commit `cfc5563e`, **1617→1619**): approved 2/5 — +#1 computation×economics (Ω(Ω(x)) idempotent → occupational spiral-transformation FLOWING, 0.62) + #2 consciousness×category_theory (IIT Φ → Monad join/flatten, 0.55 heavy-downgraded: IIT source 2 days running 5/24+5/25). Rejected #3 general×african (記録事実不変 5/24-rejected source × Ubuntu 5/24-consumed target), #4 number-system×meta_axiom (Tₜ ad-hoc f-notation, 5/24-rejected), #5 expansion×ai-integration (QSEA.evolve existing impl + ai-integration saturation). → `seed-kernel-approved-inventions-2026-05-25.ts`. **Current SEED total = 1619.** Both 5/24 and 5/25 daily batches now cleared (no pending invention backlog).

## Operational gotchas (for next Rei session)
- **Server**: discovery/snapshot/learning-log MCP tools need the **port-7511 server** (`npm run server:start` = `rei-bootstrap.ts`). `get_kernel_status`/`compute_dfumt` work WITHOUT it (read direct). Start it for a one-shot, then **STOP it** (`Stop-Process` on the 7511 listener) — it launches a 6h autonomous LearningPipeline that competes with GitHub Actions on rei-aios.db (CLAUDE.md rule). Never leave it running.
- **`run_exploration_pipeline` MCP is broken**: needs `X-API-Key` the MCP doesn't send; calling `/api/v1/pipeline/run` directly with the test key `rei-public-test-key` still 404s (publicApi.dispatch shadows ExplorationRouter). Effectively unreachable via the current server — skip it.
- **`run_daily_discovery` is idempotent** (same 332/day while the theory set is stable). `addedToSeedKernel:true` (136 major) = registration at the **discovery layer**, NOT curated theory-count growth. The headline SEED count grows only via the **approval-gated invention flow** (the A path above) + a code STEP.
- **Count discrepancy**: MCP `get_kernel_status` reported **1607**; the documented/curated running total (CLAUDE.md, approved-*.ts comments) is **1613→1617**. They count differently — trust the `SEED_KERNEL.length` (1617) / the .ts running total for the human-facing number.
- **tsx `-e` dynamic `import()` of seed-kernel is flaky** (SEED_KERNEL sometimes `undefined` on first call, circular-init quirk). For verification use a **static-import test** (`npm run test:step1088`), not `tsx -e import()`.
- Invention approval entries put `addedDate`/`cooldownDays` in **keywords as strings** (not the real SeedTheory fields) — matched 05-23 precedent.

## STEP 1161 — "量子の次" lens B: 1D φ⁴ lattice quantum sim (commit `e5d6d273`)
Context: user reviewed a chat-Claude "量子の次 (post-quantum)" conversation. I fact-checked it (mostly grounded: QFT/quantum-gravity framing correct, openQ*D/QuTiP/φ⁴→QCA real; **but paraparticles is Nature 2025 not "2026-05"** = chat-Claude date-fabrication; 2 ScienceDaily items unverified). Recommendation "lattice QFT (φ⁴) as the equation+code path" = Rei-aligned. User chose option B (run it small + embed).
- Built `src/aios/qft/phi4-lattice-1d.ts` (+`index.ts`) — **pure-TS, dependency-free** small EXACT quantum sim of the 1D lattice φ⁴ Hamiltonian (per-site truncated Fock dim d, N sites, open BC; φ=(a+a†)/√2; imaginary-time→ground, deflation→first-excited, RK4→real-time unitary). test:step1161 **18/18 PASS**: free E0=1.36602 ≈ analytic ½(m+√(m²+2/dx²))=1.36603; λ=0.5 raises E0 +0.097; ⟨φ²⟩ 0.394→0.339; mass gap 1.000→1.219 (renorm); norm/energy drift 1e-7/1e-6 (unitarity).
- **Honest scope**: genuine field→Hilbert→unitary quantum object, but NOT yet a quantum circuit/QCA (next step = Trotter→local gates, **arXiv 2002.02643**), NOT on quantum HW, φ⁴ = toy stepping stone. Natural extension of D-FUMT₈ Hilbert verification (Paper 145 + IBM Heron). **Next candidate: Trotterize → QCA / port to a real quantum circuit.**

## STEP 1162 — Spectral Lens + Radar lattice/spectral watch (commit `48ba00e1`)
Option C (A+B) on "格子を未解決問題解析に組み込む". **(A)** `src/aios/qft/spectral-lens.ts` — generalized the φ⁴ code to ANY self-adjoint (real symmetric) operator: built-in Jacobi eigensolver (full spectrum) + level-spacing ratio ⟨r⟩ (Atas; Poisson 0.386 / GOE 0.531 / GUE 0.600, no unfolding) + mass gap (rel. to median spacing) + heuristic D-FUMT₈ projection. `spectralReport(op)`. test:step1162 18/18: GOE/Poisson ⟨r⟩ separated, φ⁴ gap detected (YM mass-gap method proxy), **Riemann 40 zeros ⟨r⟩=0.627 → RMT/GUE-like (Montgomery–Odlyzko)**. **(B)** `collatz-watch.json` v1.21→1.22 (+10 lattice/spectral keywords + 3 monitors: lattice-software, openQxD, arXiv 2002.02643 φ⁴→QCA).
- **★ Honest boundary (load-bearing)**: the spectral/lattice lens is genuinely useful ONLY for operator-formulated open problems — **Yang–Mills mass gap (lattice gauge), Riemann (Hilbert–Pólya spectral statistics), spectral_theory**. It is NOT applicable to arithmetic problems (Collatz/Goldbach/ABC/Brocard) — bolting lattice onto those = forced isomorphism (the pattern Rei rejects). It surfaces spectral EVIDENCE, is NOT a solver; the D-FUMT₈ projection is heuristic, not a theorem.
## STEP 1163 — φ⁴ → Trotter → quantum circuit / QCA (commit `13adec2a`)
Chose the Trotter→QCA path over "apply spectral lens to YM/Riemann" because: **real lattice Yang–Mills can't be built honestly as a small TS module** (would fake real gauge theory = overclaim Rei rejects); Riemann was already demonstrated (⟨r⟩=0.627 GUE, reproduces known Montgomery–Odlyzko). Trotter→QCA is the genuine, self-contained, on-thesis deliverable.
- `src/aios/qft/phi4-trotter-qca.ts`: Jacobi-with-eigenvectors → `expUnitaryFromSymmetric` (matrix exp) → local-gate tensor application. H split into local terms → 2nd-order Trotter → per step (N=3) **6 one-site + 2 two-site local gates** = a quantum circuit / QCA. test:step1163 13/13: gate exp unitary; norm drift 5.8e-14; matches exact RK4 2.1e-3→7.5e-5 on halving dt (2nd-order); **strict locality: gates missing the far site leave its observable EXACTLY invariant (drift 0.0)** = lightcone basis; info reaches far site after full evolution (0.14).
- Honest scope: rigorous "field = circuit = QCA" but still classical sim (not quantum HW), φ⁴ toy, lightcone via exact-locality + causal-spread (not formal Lieb-Robinson). **Completes the STEP 1161→1163 field→circuit arc** (1161 exact quantum φ⁴ / 1162 spectral lens + radar watch / 1163 → circuit/QCA).
- **Honest non-deliverable**: did NOT build "real Yang–Mills lattice" — that needs SU(N) gauge links/plaquettes/Monte-Carlo, infeasible as a small honest module; the φ⁴ proxy only demonstrates the gap-detection METHOD.

## STEP 1164 — Riemann ↔ GUE deepened (commit `b9fe28c0`)
`src/aios/qft/riemann-gue.ts`: **compute ζ(1/2+it) zeros via Riemann–Siegel** (rsTheta + zetaZ main-sum + C₀ remainder; sign-change + bisection) — NOT hardcoded, reproducible. θ(t)/π unfolding + nearest-neighbor spacing histogram vs GUE Wigner surmise (32/π²)s²e^(−4s²/π) & Poisson e^(−s). test:step1164 15/15: computed zeros match known to 7.5e-3; unfolded mean 1.0036; **100 zeros ⟨r⟩=0.6096 ≈ GUE 0.603** (converged vs 0.627 @40); histogram closer to GUE (L1 0.143 vs Poisson 0.903, 6.3×), level repulsion confirmed.
- **Honest scope**: REPRODUCES Montgomery–Odlyzko (zeros ↔ GUE, Hilbert–Pólya evidence) — a spectral-lens capability check, NOT a new theorem and NOT a proof of RH.

**QFT lens arc complete (STEP 1161→1164)**: 1161 exact quantum φ⁴ / 1162 spectral lens + radar watch / 1163 φ⁴→circuit/QCA / 1164 Riemann↔GUE. `src/aios/qft/` = {phi4-lattice-1d, spectral-lens, phi4-trotter-qca, riemann-gue}.

## STEP 1165 — Number variance Σ²(L), long-range rigidity (commit `756c0ede`)
Added to `riemann-gue.ts`: `numberVariance` (variance of level count in length-L windows) + GUE ref (1/π²)(ln(2πL)+γ+1) / Poisson ref (=L) + `analyzeNumberVariance`. test:step1165 11/11: 300 Riemann zeros → Σ²(L) stays **0.24–0.56 for L=1..16** (Poisson would be 1..16) = spectral rigidity; all 7 L closer to GUE; Σ²(8) 0.555 vs GUE 0.557; L=16 is 34× below Poisson → "GUE-like (rigid)". Now BOTH short-range (spacing histogram, 1164) AND long-range (number variance, 1165) match GUE. Honest: reproduces Montgomery/Odlyzko, NOT a proof of RH; finite-sample/unfolding boundary effects grow with L.

**QFT lens arc = STEP 1161→1165** (5 steps): 1161 exact quantum φ⁴ / 1162 spectral lens + radar / 1163 φ⁴→circuit/QCA / 1164 Riemann↔GUE spacing / 1165 Riemann Σ²(L) rigidity. `src/aios/qft/` = {phi4-lattice-1d, spectral-lens, phi4-trotter-qca, riemann-gue}. All dependency-free TS, tested.

## ★★ QUEUED FOR NEXT SESSION (user decision 2026-05-26): paper-worthiness audit of the QFT lens arc
User asked "should the QFT lens work (STEP 1161→1165) become a paper?" — I gave the honest verdict: **NOT a new-physics paper** (all reproduction: Jordan-Lee-Preskill / arXiv 2002.02643 / Montgomery–Odlyzko); only defensible as an honest **methodology/tool** paper (OctaTheoria 145/147-150 genre) IF there is one defensible claim, the differentiator being the **D-FUMT₈ 8-axis spectral projection** (currently labeled heuristic, not a theorem) + Rei integration + dependency-free reproducibility. **User chose option A: do a PRIOR-ART AUDIT FIRST** to decide paper-worthiness before any drafting (no rush).
**Next session = START with the prior-art audit.** Scope to check:
  1. Existing tools/papers that project operator spectra onto a discrete value-system / multi-axis lens (is the D-FUMT₈ spectral projection genuinely new vs existing spectral-statistics visualizations?).
  2. φ⁴ lattice → quantum-circuit/QCA reproducibility tools (vs ours).
  3. Riemann↔GUE numerical reproduction tools (spacing + number variance) — confirm we add nothing new to the physics (we don't), so the only possible novelty is the lens/integration.
  4. Decide: (a) thin → keep as Rei internal capability (STEP record suffices), (b) one defensible claim stands → no-rush honest methodology paper (controllable phrasing, NO "世界初", NO RH-progress claim), or (c) fold into a bigger spectral-lens paper after making the D-FUMT₈ projection principled.
Apply: `feedback_no_rush_publication`, `feedback_world_uniqueness_claim_controllable`, `feedback_chat_claude_hallucination_warning` (verify any cited prior art via WebSearch/WebFetch, don't trust memory for arXiv IDs).

**Other open candidates (lower priority)**: small tractable GAUGE model (1+1D Z2 / Schwinger) for a genuine gauge mass-gap; wire the spectral lens into the unsolved-problem typology (STEP 930) pipeline; Riemann pair-correlation (Montgomery's original form).

## STEP 1166-1167 — circuit-ladder figure + (A)↔(B) transition observer
- **1166** (commit `79416879`): `src/renderer/components/circuit-ladder/CircuitLadderLens.tsx` (#/circuit-ladder, dependency-free SVG) — 4 circuit figures 電気/磁気/量子/格子; **magnetic (Φ=NI/ℛ Hopkinson) + lattice (φ⁴→QCA, STEP 1163) are the newly-added ones** (electric/quantum already shown). Site-visible after next cron rebuild. Honest: schematic figures, classical Ohm↔Hopkinson analogy (no new claim).
- **1167** (commit `ea29721d`): `src/aios/emergence/ab-transition-observer.ts` — device for 藤本さん's "a short rule generates 100M, itself chained 100M+" intuition. **Honest sharpening of chat-Claude's (A)/(B): (B) is NOT "incompressible" — the program is always short (Kolmogorov-compressible); (B) = computational IRREDUCIBILITY (Wolfram, no shortcut).** 1D local rule run in layers, dial α interpolates fixed-rule(A)↔rule-rewriting(B); `foldability` (normalized: raw-0.5 uncorrelated-floor→0) + per-layer D-FUMT₈ + α-sweep. test:step1167 17/17: α=0 fold 1.0 (A) → α=1 fold 0.026 (B, NEITHER/FLOWING onset L3); transition α*=0.5. A=ultimate compression (śūnyatā) ↔ B=irreducible (SELF⟲) on one device. Scale small on purpose (= score not truth). D-FUMT₈ heuristic.

## STEP 1168 — Problem Foldability Lens (commit `2dc5f249`)
Apply STEP 1167's (A)/(B) foldability to MATH unsolved problems, for the next-session analysis. `src/aios/emergence/problem-foldability.ts`: **Lempel–Ziv 1976 complexity (Kaspar–Schuster, ~15 lines, Kolmogorov proxy)** on a quantized problem sequence → foldability = 1−normalizedLZ. test:step1168 15/15: periodic 0.970 (A) vs random 0.024 (B); Collatz stopping times 0.198 (B, axis NEITHER=residual structure); prime gaps 0.058 (B); Riemann spacings 0.041 (B — LZ short-range ≠ GUE long-range, complementary). Complements STEP 930 typology + ZONE + spectral lens (1162) as the **sequence-data lens** for operator/sequence-type problems. Honest: empirical compressibility ≠ provability; surfaces evidence, NOT a solver. `emergence` module = {ab-transition-observer (1167), problem-foldability (1168)}.

**QFT/emergence lens arc now STEP 1161→1168** (8 steps): φ⁴ quantum sim / spectral lens + radar / φ⁴→QCA / Riemann↔GUE spacing / Riemann Σ²(L) rigidity / circuit-ladder figure (1166) / (A)↔(B) transition observer (1167) / problem foldability (1168).

## ★★ QUEUED FOR NEXT SESSION (user decision 2026-05-26): explore "c が創発する模型" + "因果構造の8値表現"
Context: user's intuition that advanced beings may have a genuine FTL principle. I framed it honestly (FTL = rewriting causality, not just speed; lives in the unsettled quantum-gravity frontier; c might be an EMERGENT approximation, not a fundamental wall). User asked to explore two things next time:
1. **c-emergent toy model** — a model where the lightcone speed (effective c) EMERGES from a local rule, not put in by hand. ★ We ALREADY have a baby example: the STEP 1163 φ⁴→QCA has an emergent lightcone (Lieb-Robinson bound). Next: extend it so c_eff = f(rule coupling) is MEASURED (lightcone slope vs coupling), demonstrating c as a derived quantity. Real anchors to verify (WebSearch, don't trust memory): Lieb-Robinson bound (lattice emergent lightcone), analog gravity / emergent Lorentz invariance (Volovik, Unruh sonic horizons, graphene Dirac cone), causal sets / emergent spacetime.
2. **D-FUMT₈ causal-structure representation** — map event-pair causal relations to the 8 values: TRUE/FALSE = definite causal order (A→B or not), BOTH = INDEFINITE causal order (quantum switch / Oreshkov–Costa–Brukner process matrices — real research!), NEITHER = spacelike (no causal relation), INFINITY = lightlike boundary, ZERO = null/no-relation, FLOWING = causal propagation, SELF⟲ = self-causation/closed-timelike-curve. Buildable: a small causal-relation classifier over events (from the QCA lightcone or a causal set) → 8-valued classification. Anchors: indefinite causal order (Brukner, Oreshkov 2012 process matrices), causal set theory (Sorkin).
**Honest guard**: toy/emergent models + a heuristic 8-valued causal logic — NOT deriving the fundamental c, NOT solving quantum gravity, NOT a physics theorem. Same no-overclaim discipline. Build as src/aios/qft/ or src/aios/emergence/ modules + tests (STEP 1169+).

**Other open**: SNST-spiral-gait robot motion sim (literal light-speed impossible; spiral motion buildable); wire foldability (1168) + spectral lens (1162) into the STEP 930 typology pipeline; paper-worthiness prior-art audit of the QFT lens arc (earlier queued — option A).

See [[project-wic-buildout-session-2026-05-25]] for the WIC work that preceded this.