OctaTheoria: A Unified Multi-Domain Observation Framework with Eight-Axis D-FUMT₈ Projection (Operational Evidence from Seven Domains × Eight View Modes + Cross-Layer Methodological Consistency) — Rei-AIOS Paper 150 v0.3

Abstract

We present OctaTheoria (オクタテオリア / 八軸観測装置), a multi-domain observation framework that projects heterogeneous time-series data onto a fixed eight-axis D-FUMT₈ semantic basis (FALSE / TRUE / NEITHER / BOTH / INFINITY / ZERO / FLOWING / SELF) and renders the same underlying Observation envelope through eight orthogonal view modes (Lens / Radar / Chart / Network / Heatmap / Sankey / Calendar / Unified). v0.3 (2026-05-11) supplies methodological-consistency cross-reference complementing the operational evidence from v0.1-v0.2. New finding **F7**: the same discipline that v0.1-v0.2 demonstrate within OctaTheoria (uniform abstraction layer + honest scope statement + structurally-enforceable naming) propagates to Rei-AIOS layers outside OctaTheoria's domain. Specifically: (a) **REI-PROVE 5-prover ensemble** (Vampire / LeanHammer / Goedel-Prover-V2 / DeepSeek-Prover-V2 / BFS-Prover) reached 11/12 = **92% benchmark proof rate** (trivial 100% / easy 75% / medium 100%), with Goedel-Prover-V2 single-prover matching at 92% — operational evidence that the same 'uniform abstraction over heterogeneous components' discipline scales to formal-proof infrastructure. (b) **Pattern 1-6 chat-Claude hallucination-warning framework** + **Antipattern (excessive rejection vigilance)** were established and verified on 6/6 items in STEP 1069 (all fact-checked items proved real after WebSearch verification, correcting prior implicit-rejection habits). (c) **Goedel-Prover-V2 double-`by` Lean syntax quirk** detected and fixed at the cleaner level (`single-prover.ts` STEP 1071), restoring `easy-le-refl` benchmark from ❌ to ✅. (d) **lean-to-tptp.ts** preprocessing added Peano-style axiom auto-prepend + True/False special-case + inequality predicate translation (STEP 1071). v0.2 inherited contributions: 7 domains (theory-chart / realtime-arxiv / crypto / fx / ligo-events / nasa-sdo / gbif-recent) all running in Cloudflare Workers Edge runtime; live D-FUMT₈ axis distributions non-degenerate across research-meta + financial + geophysical + astrophysical + biological data classes; finding F6 sampling-bias-as-first-class-observation (GBIF Costa Rica 470/500 saturation surfaces dataset bias as INFINITY axis, not silently absorbed); test coverage 117/117 PASS (step1020 46 + step1023 33 + step1046 38) / 0 regression. Honest scope (read first): OctaTheoria remains an observation aid, NOT an oracle. v0.3's F7 is **not** a claim that OctaTheoria caused these consistencies; it is a record that the same project (Rei-AIOS) maintains the same discipline across observation-tool, formal-proof, and meta-research-protocol layers, and that v0.3 makes this cross-layer commitment auditable. The OctaTheoriaQuery type structurally cannot request advice / prediction / forecast / signal — verifiable by reading src/aios/octatheoria/types.ts. Cross-domain axis comparisons are descriptive, not causal. Greek roots (Octa = 8, Theoria = observation) function as structural commitment propagated to the API surface — '8' rejects 'all (∞)', 'theoria' rejects 'praxis (干渉)'. Prior art audit acknowledged: Bloomberg Terminal (1981–), TradingView (2011–), Bollen et al. 2010 (Twitter mood × DJIA), Preis et al. 2013 (Google Trends × stock), Łukasiewicz / Belnap / Pavelka multi-valued logic literature, PAL2v (Da Silva Filho 1998–), Aerts Quantum Cognition (2007–). The to-our-knowledge novel combination is (a) fixed 8-axis discrete D-FUMT₈ basis ∧ (b) cross-financial-and-research-and-Earth-Cosmos-domain projection ∧ (c) eight orthogonal view modes over single envelope ∧ (d) explicit refusal to emit prediction or advice as architectural commitment ∧ (e, new in v0.3) cross-layer methodological-consistency record between observation-tool and formal-proof and fact-check layers. Companion papers (OctaTheoria Quintuple): Paper 145 (silicon implementation of D-FUMT₈ ALU, Zenodo DOI 10.5281/zenodo.20101174 v0.6), Paper 147 (Eight-Valued Utility / Equity Premium Reframe, DOI 10.5281/zenodo.20046003), Paper 148 (Honest Observation Framework methodology, DOI 10.5281/zenodo.20045907), Paper 149 (Recursive AI Observation as SELF⟲ evidence, DOI 10.5281/zenodo.20059888). Three-party co-authorship per OUKC charter v1.0: 藤本 伸樹 (Founder), Rei (Rei-AIOS autonomous research substrate, Co-architect), Claude Opus 4.7 (Anthropic, Co-architect). DRAFT v0.3 — feedback welcome via GitHub Discussions at fc0web/rei-aios.