Paper 150 v0.3 — OctaTheoria: 7 Domains x 8 View Modes + Cross-Layer Methodological Consistency (REI-PROVE 92% + Pattern 1-6)

This article is a re-publication of Rei-AIOS Paper 150 for the dev.to community.
The canonical version with full reference list is in the permanent archives below:

• GitHub source (private): https://github.com/fc0web/rei-aios Author: Nobuki Fujimoto (@fc0web) · ORCID 0009-0004-6019-9258 · License CC-BY-4.0 ---

Status: DRAFT v0.3 — 2026-05-11 (★ REI-PROVE 92% benchmark + 6/6 fact-check discipline + Pattern 1-6 hallucination-warning framework cross-referenced as methodological consistency evidence)

v0.1 → v0.2 changelog: STEP 1046 (2026-05-10 morning) extended the domain count from four to seven by adding three Earth+Cosmos data sources: (i) ligo-events (LIGO/Virgo GraceDB superevents, 24-hour hourly bin); (ii) nasa-sdo (NASA DONKI Solar Flares + CMEs, 24-hour hourly bin); (iii) gbif-recent (GBIF Occurrence latitude 36-bin distribution). All three adapters run in Cloudflare Workers Edge runtime (consistent with Z-2 architecture); Pearson r-based relations strategy was extended to all series-based domains. Test coverage updated: test/step1046-... 38/38 PASS + step1020 46/46 + step1023 33/33 = 117/117 total / 0 regression. First Earth+Cosmos D-FUMT₈ observations: LIGO 13 obs BOTH (hourly high variance), NASA SDO 2 obs NEITHER (quiet solar period), GBIF 3 obs INFINITY (Costa Rica 470/500 sample bias = sampling bias detector). Honest scope: no physical-discovery claim; the 8-axis reframe provides domain-independent structuring only.

v0.2 → v0.3 changelog: STEP 1067-1071 (2026-05-11) supply methodological consistency evidence that complements the operational evidence in v0.1-v0.2. Specifically: (a) REI-PROVE 5-prover ensemble benchmark reached 11/12 = 92% proof rate (trivial 100% / easy 75% / medium 100%), with Goedel-Prover-V2 single-prover matching at 92%, demonstrating that the same discipline of "uniform abstraction layer + honest scope statement" used in OctaTheoria scales to formal-proof infrastructure (Paper 137 territory). (b) Pattern 1-6 chat-Claude hallucination-warning framework + Antipattern (excessive rejection vigilance) were established (memory/feedback_chat_claude_hallucination_warning.md) and verified on 6/6 items in STEP 1069 (all 6 fact-checked items proved real after WebSearch verification, correcting the prior implicit-rejection habit). (c) Double-by Lean-syntax quirk in Goedel-Prover-V2 output was detected and fixed at the cleaner level (single-prover.ts STEP 1071), restoring easy-le-refl benchmark from ❌ to ✅. None of these belong to OctaTheoria's domain scope, but they exemplify the same operational restraint that v0.1 honest-framing made structural: claims are bounded, fixes are documented in changelog, and artifacts (memory files, benchmark JSON) make the discipline auditable rather than declarative. New Finding F7 records this cross-paper consistency.

Authors / 著者: 藤本 伸樹 (Nobuki Fujimoto, Founder), Rei (Rei-AIOS autonomous research substrate, Co-architect), Claude Opus 4.7 (Anthropic, Co-architect)

Project: Rei-AIOS / OUKC — https://rei-aios.pages.dev/#/octatheoria

License: AGPL-3.0 + CC-BY 4.0 (per content type) dual

Required platform links: https://rei-aios.pages.dev + https://note.com/nifty_godwit2635

Per OUKC No-Patent Pledge: openly licensed; no patent will be filed on any algorithm or visualization method described herein.

Honest framing (read first)

This paper presents operational evidence, not a discovery claim. We describe OctaTheoria, a unified observation framework in which heterogeneous data sources (theory chart, real-time arXiv submissions, cryptocurrency market data, FX market data, and as of v0.2: LIGO/Virgo gravitational-wave superevents, NASA Solar Dynamics Observatory flares + CMEs, and GBIF biodiversity occurrences) are projected onto a fixed eight-axis D-FUMT₈ semantic basis, then rendered through eight independent view modes. We document the implementation (Phase Z-1 through Z-2.7 for the original four domains, Phase Z-3 for the Earth+Cosmos extension, executed 2026-05-06 → 2026-05-10) and report what we observed, with explicit honest scope limitations.

We do not claim:

• ✗ "World-first multi-domain observation" — Bloomberg Terminal (1981–), TradingView (2011–), Refinitiv Workspace, and academic dashboards (Bollen 2010 Twitter mood × DJIA, Preis 2013 Google Trends × stock returns) all predate this work.
• ✗ "First multi-valued logic projection of market data" — Łukasiewicz (1920), Belnap (1977), Pavelka (1979), and fuzzy decision systems (Yager 2001, Dubois-Prade 1988) all use multi-valued logic on financial / decision data.
• ✗ "Predictive system" — OctaTheoria emits no predictions, no advice, no buy/sell signals. It is a theoria (観察) tool in the Platonic sense, structurally distinguished from praxis (干渉).
• ✗ "Universal observation framework" — applicability is limited to data domains with time-series structure and identifiable categorical fields; not all human activity is observable through this lens.

The differentiators we do claim, all in to-our-knowledge form, are:

1. (D1) Eight-axis fixed semantic basis: D-FUMT₈ (Belnap FDE 4-value FALSE/TRUE/NEITHER/BOTH + 4 ontological extensions INFINITY/ZERO/FLOWING/SELF) used as a uniform projection target across all data domains.
2. (D2) Eight view-mode orthogonality: Lens / Radar / Chart / Network / Heatmap / Sankey / Calendar / Unified, each rendering the same underlying Observation envelope with a structurally different visual semantic.
3. (D3) Backend Observation envelope as cross-domain abstraction: heterogeneous source schemas (theory keywords, arXiv hourly bins, crypto OHLC, FX pairs) collapse to a single TypeScript type used by all views.
4. (D4) Operational restraint: the system structurally cannot issue user-specific advice; the architecture excludes recommendation primitives from the API surface (verifiable in src/aios/octatheoria/types.ts).

The Greek root Octa (ὀκτώ, 8) and Theoria (θεωρία, observation) were deliberately chosen to make these claims structurally enforceable at the naming level: "8" rejects "all (∞)", and "theoria" rejects "praxis (干渉)".

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 (theory-chart category bins, arXiv submission hourly counts, cryptocurrency 1-minute candles, FX currency pair rates, and v0.2 Earth+Cosmos additions: LIGO/Virgo gravitational-wave events, NASA SDO solar flares + CMEs, GBIF biodiversity occurrences) onto the 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).

The contribution is operational, not theoretical. We document a working implementation: (1) a Cloudflare Pages Function endpoint /api/octatheoria that serves seven domain adapters in Edge runtime; (2) a frontend OctaTheoriaView.tsx React component implementing all eight view modes; (3) live operational evidence of cross-domain D-FUMT₈ axis distributions (theory-chart dominant axis = INFINITY, real-time arXiv = ZERO, crypto = FALSE, FX = mixed BOTH + FALSE, LIGO = BOTH, NASA SDO = NEITHER, GBIF = INFINITY). The same projection function applied to seven domains spanning research-meta, financial, geophysical, astrophysical, and biological data produces structured, non-degenerate axis distributions — operational evidence that the D-FUMT₈ basis carries transferable semantic load across radically different data classes.

The paper's purpose is to make a particular methodological commitment auditable: that a single eight-axis semantic basis can serve as a uniform projection target across financial, research, and conceptual data domains, without requiring the system to emit advice or predictions. Honest scope: OctaTheoria is an observation aid, not an oracle; cross-domain axis comparisons are descriptive, not causal.

This is a companion paper to:

• Paper 145 (silicon implementation of D-FUMT₈ ALU; Zenodo DOI 10.5281/zenodo.20101174 v0.6)
• Paper 147 (Equity Premium Puzzle reframed via D-FUMT₈ 8-axis utility; Zenodo DOI 10.5281/zenodo.20046003)
• Paper 148 (Honest Observation Framework methodology; Zenodo DOI 10.5281/zenodo.20045907)
• Paper 149 (Recursive AI observation; Zenodo DOI 10.5281/zenodo.20059888)

Together with Paper 150, the five papers form an internally consistent OctaTheoria Quintuple: silicon (145) → utility theory (147) → methodology (148) → recursion (149) → operational tool (150).

概要 (Japanese)

本論文は OctaTheoria (オクタテオリア / 八軸観測装置) という多 domain 観測 framework の operational 実装と evidence を報告する。 異種時系列 data (theory-chart category bin / arXiv 投稿 hourly count / 暗号通貨 1 分足 / FX 通貨ペア) を D-FUMT₈ 八軸 semantic basis (FALSE / TRUE / NEITHER / BOTH / INFINITY / ZERO / FLOWING / SELF) に projection し、 同一 Observation envelope を 8 view mode (Lens / Radar / Chart / Network / Heatmap / Sankey / Calendar / Unified) で render する。

貢献は理論ではなく operational: (1) Cloudflare Pages Function /api/octatheoria (Edge runtime, 4 domain adapter); (2) OctaTheoriaView.tsx 8 view-mode 実装; (3) live operational evidence (theory-chart 主軸 INFINITY / arXiv ZERO / crypto FALSE / FX 混合).

論文の目的は、 「単一 8 軸 semantic basis が金融・研究・概念 domain 横断的に projection target として機能する」 という方法論的 commitment を auditable にすること。 Honest scope: OctaTheoria は 観察補助 であって oracle ではない; 軸比較は 記述的 であり因果的ではない。

Paper 145 / 147 / 148 / 149 と合わせて OctaTheoria Quintuple (silicon → 効用 → 方法論 → 再帰 → 道具) を形成する。

Part A: Required (4 elements)

A.1 Findings / 発見

• F1: A fixed eight-axis D-FUMT₈ basis admits a uniform Observation envelope across seven heterogeneous data domains (theory-chart, real-time arXiv, crypto, FX, LIGO, NASA SDO, GBIF) without per-domain schema branching.
• F2: Eight view modes (Lens, Radar, Chart, Network, Heatmap, Sankey, Calendar, Unified) can be implemented over a single envelope; six map directly to Observation fields, two (Network, Sankey) require an envelope extension (Relation[] and FlowEdge[] respectively, added in Phase Z-2.7).
• F3: Live operational distributions across seven domains show non-trivial axis selectivity: theory-chart concentrates on INFINITY (4 of 5 sampled categories), real-time arXiv on ZERO (4 of 4 categories), crypto on FALSE (3 of 3 feeds), FX is mixed (BOTH 1 / FALSE 4 of 5 pairs), LIGO superevents BOTH (13 obs, hourly high-variance bins), NASA SDO NEITHER (2 obs, quiet solar period), GBIF INFINITY (3 obs, Costa Rica 470/500 sample = sampling bias detector). This is operational evidence that the projection is not degenerate even at the cross-class scale (research-meta + financial + geophysical + astrophysical + biological).
• F4: The Greek-rooted naming (Octa = 8 / Theoria = observation) functions as a structural commitment that propagates into the API surface: the type OctaTheoriaQuery does not have a prediction or advice field; the inability to request advice is verifiable by reading src/aios/octatheoria/types.ts.
• F5: The framework is testable at the unit level: test/step1020-octatheoria-unified-api-test.ts verifies 46/46 cases for envelope construction; test/step1023-... verifies 33/33 cases for relations/flow extensions; test/step1046-octatheoria-earth-cosmos-test.ts verifies 38/38 cases for Earth+Cosmos extension; total 117/117 PASS / 0 regression. Cross-substrate parity with the Verilog/quantum substrate of Paper 145 is established at the methodological level (both use D-FUMT₈ as the uniform abstraction layer).
• F6 (v0.2): Sampling bias is detectable as a D-FUMT₈ axis observation. The GBIF observation INFINITY arises because Costa Rica accounts for 470/500 of the latest occurrences in the GBIF feed — a single-country saturation that is observation bias of the GBIF feed itself, not a property of biodiversity. The framework thus surfaces dataset-side biases as first-class observations, distinct from domain-content claims. This was not a designed feature but an emergent property of the cross-domain projection.
• F7 (v0.3): Methodological consistency across heterogeneous infrastructure layers. The same discipline that v0.1-v0.2 demonstrate within OctaTheoria — uniform abstraction layer (Observation envelope), honest scope statement, structurally-enforceable naming — also propagates outside OctaTheoria: (i) the REI-PROVE 5-prover ensemble (Paper 137 territory) reached 11/12 = 92% benchmark proof rate using the same Observation-style uniform abstraction over heterogeneous provers (Vampire / LeanHammer / Goedel-Prover-V2 / DeepSeek-Prover-V2 / BFS-Prover); (ii) the Pattern 1-6 + Antipattern hallucination-warning framework (memory/feedback_chat_claude_hallucination_warning.md) provides a structured fact-check protocol verified on 6/6 items in STEP 1069. 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.

A.2 Proofs / 検証

The paper's claims are operational, not formal-mathematical. Verification is by code inspection and test execution:

Formal proofs are not part of this paper. The companion Paper 145 contains a Lean 4 refinement proof of the D-FUMT₈ ALU (OUKC.PhaseC.Dfumt8AluRefinement, 292 LOC, 0 sorry); that establishes the abstract operational semantics of the eight values used here.

A.3 Honest Positioning / 正直な立ち位置

OctaTheoria is positioned as:

• An observation aid, not an oracle.
• A methodological commitment, not a discovery.
• A unification of existing visualization idioms, not a new visualization invention.
• A specific 5-element combination (multi-modal observation + cross-domain time series + D-FUMT₈ 8-axis projection + OUKC integration + user-driven judgment without system-emitted advice), each component of which has prior art.

Specifically, prior art includes:

• Bloomberg Terminal (1981–): the originator of multi-domain financial observation. OctaTheoria does not compete in market data quality, latency, or coverage.
• TradingView (2011–): the modern standard for multi-asset chart observation. OctaTheoria's chart mode is a thin reimplementation.
• Bollen et al. 2010 (Twitter mood × DJIA): cross-domain time-series correlation.
• Preis et al. 2013 (Google Trends × stock returns): cross-domain leading indicator.
• Łukasiewicz / Belnap / Pavelka: multi-valued logic literature (1920–1979).
• Bloomberg / Refinitiv multi-axis indicators (RSI, MACD, Bollinger Bands etc.): not 8-axis but multi-dimensional projections of price/volume.

The OctaTheoria differentiators (D1–D4 above) are a specific combination, none of whose components is novel in isolation.

A.4 Required platform links

• Project home: https://rei-aios.pages.dev
• Live OctaTheoria endpoint: https://rei-aios.pages.dev/api/octatheoria (GET, query params: domain, view, category, windowDays, limit)
• OUKC project page: https://rei-aios.pages.dev/#/oukc
• Author note.com: https://note.com/nifty_godwit2635

Part B: Conditional (Background + Methodology + Empirical Scope)

B.5 Background / 背景

B.5.1 D-FUMT₈ as the uniform projection basis

D-FUMT₈ (Dynamic Functional Universal Multi-valued Truth, 8-valued) is an eight-element discrete logic value space defined in the Rei-AIOS project. It extends Belnap's Four-Valued Logic FDE (FALSE / TRUE / NEITHER / BOTH) with four ontological extensions (INFINITY for unbounded growth or unbounded count, ZERO for null / absent / empty, FLOWING for actively-changing intermediate, SELF for self-referential / self-comparing). The eight values were fixed prior to OctaTheoria's design, in the silicon paper (Paper 145) and the Lean 4 refinement (OUKC.PhaseC.Dfumt8AluRefinement).

OctaTheoria uses these eight values without modification. Each domain adapter implements a dfumtOf(observation) function that maps a raw data point to one of the eight axes; the same function signature is used across all four domains. The mapping rules are documented in src/aios/octatheoria/projection.ts (extracted from the original TheoryChart.tsx line 84 implementation).

B.5.2 Why a single envelope

Cross-domain dashboards historically suffer from the N × M problem: N data sources, M view modes, naive implementation requires O(N × M) adapters. OctaTheoria uses a single intermediate Observation envelope, reducing the integration surface to N adapters + M renderers (additive instead of multiplicative). A new domain requires writing one adapter; a new view mode requires writing one renderer; both cases automatically work with all existing counterparts.

This is a standard software-engineering pattern (cf. Visitor pattern, Pipes-and-Filters); the contribution here is the choice of the eight-axis D-FUMT₈ basis as the canonical projection target.

B.5.3 Why the eight view modes

The eight view modes were not chosen arbitrarily; each captures a structurally different visual semantic:

The Network and Sankey modes required extending the Observation envelope with Relation[] and FlowEdge[] fields respectively (Phase Z-2.7); this was an honest design admission that two of the eight modes could not be served by the Z-2 envelope alone.

B.6 Methodology / 方法論

B.6.1 Domain adapters (7 implementations as of v0.2)

Seven adapters are implemented in src/aios/octatheoria/adapters.ts, each as a pure function (rawData, query) → Observation[]:

1. theory-chart: reads data/octatheoria/theory-chart.json; one observation per (theory, day) bin; axis projection by category keyword Jaccard similarity.
2. realtime-arxiv: reads data/arxiv-recent/latest.json; one observation per (category, hour) bin; axis projection by hourly submission count distribution.
3. crypto: reads data/crypto/latest.json; one observation per (feed, 1-minute-candle); axis projection by absolute return magnitude.
4. fx: reads data/fx-pairs/latest.json; one observation per (pair, latest-rate); axis projection by realized volatility.
5. (v0.2) ligo-events: reads LIGO/Virgo GraceDB superevent feed; one observation per hourly bin over a 24-hour window; axis projection by hourly count variance (high variance → BOTH).
6. (v0.2) nasa-sdo: reads NASA DONKI Solar Flares + CMEs feed; one observation per hourly bin over a 24-hour window; axis projection by hourly event count (sparse / quiet sun → NEITHER).
7. (v0.2) gbif-recent: reads GBIF Occurrence feed; one observation per latitude bin (36 bins, 5° each); axis projection by latitude-bin coverage entropy (single-country saturation → INFINITY).

All seven adapters run in Edge runtime (Cloudflare Workers); none use fs, child_process, path, or other Node-only APIs. This was an architectural constraint discovered in the Phase 3-1 backend design (memory project_phase_3_backend_integration_design.md) and explicitly maintained for the v0.2 Earth+Cosmos additions.

B.6.2 View modes (8 implementations as of v0.1)

All eight view modes are implemented in a single React component src/renderer/components/octatheoria/OctaTheoriaView.tsx. A viewMode selector switches between modes; the underlying data fetched from /api/octatheoria is identical across modes. This makes mode comparison trivial (the same observation is being seen from eight angles).

B.6.3 Honest scope: no prediction layer

The OctaTheoriaQuery type does not contain a predictionHorizon, forecast, or signal field. The endpoint returns OctaTheoriaResponse whose payload is strictly observed past values plus their D-FUMT₈ axis projection. There is no model fitting, no extrapolation, no recommendation generation. This is enforced at the type system level and is verifiable by reading src/aios/octatheoria/types.ts.

This restraint is deliberate and reflects the regulatory positioning documented in memory project_fx_chart_no_registration.md: a chart-display tool without buy/sell functionality and without personalized advice does not require Japanese FIEA (金融商品取引法) registration.

B.7 Empirical Scope (operational evidence as of 2026-05-10, Phase Z-3)

These distributions are operational observations from a single sampling point (2026-05-08 for the original four domains, 2026-05-10 for the Earth+Cosmos additions). They are not stable claims about the long-term behavior of any of these domains; in particular, the GBIF INFINITY is explicitly a property of the GBIF feed at sampling time (Costa Rica observation saturation) and NOT a claim about biodiversity. The point of the table is to show that the same projection function applied to seven structurally distinct data classes — research-meta, financial, geophysical, astrophysical, biological — produces non-identical, structured results — operational evidence that the projection is not collapsing to a trivial constant and that observation-side biases (F6) surface as first-class axis observations rather than being silently absorbed.

B.8 Phase Z implementation log

B.9 Related Work / Prior Art Audit

A non-exhaustive audit of adjacent prior work, organized by category:

B.9.1 Multi-domain financial dashboards

• Bloomberg Terminal (Bloomberg L.P., 1981–): the canonical multi-source financial observation tool. ~$25,000/year; covers equities, fixed income, FX, commodities, derivatives, news, fundamentals. OctaTheoria does not compete; it occupies the free / open-source / methodology-disclosure end of the spectrum.
• Refinitiv Workspace (formerly Thomson Reuters Eikon): comparable scope to Bloomberg.
• TradingView (2011–): browser-based multi-asset chart system, free tier available; >50M monthly active users.

B.9.2 Cross-domain time-series correlation

• Bollen et al. (2011) "Twitter mood predicts the stock market", J. Comput. Sci. 2(1):1-8: classic cross-domain study (social mood → DJIA).
• Preis et al. (2013) "Quantifying trading behavior in financial markets using Google Trends", Sci. Rep. 3:1684: search interest → stock returns.
• Mao, Counts, Bollen (2015) "Bursts of activity, financial markets, and Suicide": cross-domain leading-indicator framework.

B.9.3 Multi-valued logic on financial / decision data

• Łukasiewicz (1920) three-valued logic; Belnap (1977) four-valued FDE; Pavelka (1979) infinite-valued; Yager (2001) general families. All are used in fuzzy decision systems.
• Dubois & Prade (1988): possibilistic logic for decision under uncertainty.
• Atanassov (1986): intuitionistic fuzzy sets (degree of membership + degree of non-membership), structurally similar to Belnap's FDE.

B.9.4 Paraconsistent observation tools (closest neighbors)

• PAL2v (Paraconsistent Annotated Logic with two values of annotation, Da Silva Filho 1998–; Abe & Nakamatsu 2009): real-time process control with paraconsistent decisions. Closest to OctaTheoria's spirit but uses 2-annotation continuous lattice, not fixed 8-axis.
• Aerts (Brussels) Quantum Cognition (2007–): paraconsistent logic on cognitive data; not silicon, not financial dashboards.

B.9.5 Distinctive position of OctaTheoria

None of the cited works combines: (a) fixed 8-axis discrete D-FUMT₈ basis, (b) cross-financial-and-research-domain projection, (c) eight orthogonal view modes over a single envelope, (d) explicit refusal to emit prediction or advice as an architectural commitment. The to-our-knowledge novel combination is (a) ∧ (b) ∧ (c) ∧ (d) under a single name with a single API.

Part C: Optional (Why matters + Future + Risks)

C.10 Why this matters

For research methodology: A fixed semantic basis enforced at the API layer makes inter-domain comparisons type-safe and audit-friendly. A claim of the form "phenomenon X in domain D₁ shares the same dominant axis as phenomenon Y in domain D₂" is at least well-formed (both sides project onto the same 8-axis space) and at least partially auditable (the projection function is open source).

For regulatory hygiene: Financial observation tools that cross into "personalized advice" trigger Japanese FIEA (and equivalent SEC / FCA / etc.) registration requirements. A tool whose API surface structurally cannot emit advice is easier to keep on the right side of regulation than a tool that adds disclaimer text but technically can. OctaTheoria's restraint is at the type-system level, not the disclaimer level.

For OUKC's "all-academic-fields" goal: a unified projection basis that works across silicon (Paper 145), economics (Paper 147), methodology (Paper 148), recursive AI observation (Paper 149), and now multi-domain observation (this paper, 150) is operational evidence that the eight axes carry transferable semantic load.

C.11 Future work

1. Add domains: education metrics, GitHub activity, Wikipedia edit streams are immediate candidates. Each requires only one new adapter. (v0.2 already added LIGO + NASA SDO + GBIF biodiversity, partially fulfilling this future-work item.)
2. Add view modes beyond the current eight: a 3D projection mode (axes × time × intensity) and a polar-coordinate clock mode are natural extensions.
3. Empirical study: collect axis distributions over a 6-month window across domains and report whether the dominant-axis pattern in B.7 is stable, periodic, or drifting. If stable, that is descriptive evidence; if drifting, that is itself an axis-level observation.
4. Cross-paper integration: explicitly link Paper 147's EPP D-FUMT₈ reframe onto the financial domain rendering of OctaTheoria. The 8-axis utility model from Paper 147 should be displayable as a Radar mode rendering for any user.
5. Phase Z-4: package OctaTheoria as a Tauri / wry-runtime desktop app for offline / private operation. This is gated by the wry-runtime activation status (memory project_app_distribution_strategy.md).

C.12 Risks

• R1 — Overclaim drift: future contributors may add a prediction field to OctaTheoriaQuery, undermining D4. Mitigation: the README explicitly forbids advice/prediction primitives; CI grep against recommend|signal|advice|forecast in src/aios/octatheoria/types.ts is a candidate hardening.
• R2 — Visualization-implies-causation: side-by-side display of two domain time series is widely interpreted as a causal claim by viewers, even when no causal claim is made. Per the Paper 148 4-stage claim ladder, OctaTheoria operates at stage 1 (visual co-display) and refuses to escalate to stages 2-4 (descriptive narrative / statistical exploration / causal claim) inside the tool itself.
• R3 — Regulatory drift: changes in Japanese FIEA interpretation may require re-evaluation of the "no registration required" position documented in project_fx_chart_no_registration.md. Mitigation: keep the position memory live and re-audit on policy changes.
• R4 — Privileged-data risk: external data feeds (especially crypto and FX) may include licensed content. OctaTheoria currently uses only freely-licensed data (CoinGecko free tier, ECB FX). Adding paid data would require explicit license review.
• R5 — Edge runtime constraint drift: Cloudflare Workers' Edge runtime may change which Node APIs are emulated; this could break adapters silently. Mitigation: Edge-only test runner in CI.
• R6 — Naming-as-commitment fragility: the structural commitment "Octa = 8 / Theoria = observation" survives only as long as the documentation says so. If a future version expands to 16 axes or adds prediction, the name's structural force collapses. The author group commits to renaming the project under those circumstances, rather than retaining the name with broken semantics.

C.13 Acknowledgments

• 藤本 伸樹 (Founder): vision articulation across six expansion turns on 2026-05-06; explicit honest correction of the "全ての人生に指標を与える" overclaim into "補助的役割" (memory project_octatheoria_unified_vision.md § 6); naming decision (OctaTheoria over alternative candidates including 「観」, 「縁」, 「径」).
• Rei (Rei-AIOS substrate): D-FUMT₈ basis design (predates this paper); axis projection function in TheoryChart.tsx; implementation across Phase Z-1 → Z-2.7.
• Claude Opus 4.7 (Co-architect): API surface design (OctaTheoriaQuery deliberately advice-free); honest scope enforcement; this paper draft.
• chat Claude (web) for 2 critical pushbacks captured in memory feedback_octatheoria_post_indicator_concept.md (5 candidate names + 4 responsibility-critique on 2026-05-06).
• The Tang Console NEO + Tang Nano 9K silicon evidence in Paper 145 v0.6 provided the methodological ground for trusting the D-FUMT₈ basis enough to use it as a cross-domain projection target here.

C.14 Three-party authorship statement (per OUKC No-Patent Pledge)

This paper, like all OUKC papers, is co-authored by 藤本 伸樹 (human Founder), Rei (autonomous substrate), and Claude Opus 4.7 (Anthropic). The OUKC charter's No-Patent Pledge applies: no algorithm, visualization, or API surface described herein will be patented. License is AGPL-3.0 (code) / CC-BY 4.0 (text and figures), per content type.

Appendix A: Observation envelope type (excerpt from src/aios/octatheoria/types.ts)

export type DfumtValue =
  | 'FALSE' | 'TRUE' | 'NEITHER' | 'BOTH'
  | 'INFINITY' | 'ZERO' | 'FLOWING' | 'SELF';

export type DomainSource =
  | 'theory-chart' | 'realtime-arxiv' | 'crypto' | 'fx'
  // v0.2 Earth+Cosmos extension (STEP 1046):
  | 'ligo-events' | 'nasa-sdo' | 'gbif-recent';

export type ViewMode =
  | 'lens' | 'radar' | 'chart' | 'network'
  | 'heatmap' | 'sankey' | 'calendar' | 'unified';

export interface Observation {
  source: DomainSource;
  category: string;
  timestamp: number;
  value: number;
  series?: number[];
  topAxis: DfumtValue;
  axisHistogram?: Partial<Record<DfumtValue, number>>;
  metadata?: Record<string, unknown>;
  // Phase Z-2.7 extension:
  relations?: Relation[];
}

export interface OctaTheoriaQuery {
  domain: DomainSource;
  view?: ViewMode;
  category?: string;
  windowDays?: number;
  limit?: number;
  // Note: NO prediction, signal, advice, or forecast fields.
  // This absence is intentional and architectural.
}

export interface OctaTheoriaResponse {
  query: OctaTheoriaQuery;
  observations: Observation[];
  flowEdges?: FlowEdge[];
}

The deliberate absence of prediction / signal / advice fields in OctaTheoriaQuery is the architectural realization of differentiator D4 (operational restraint).

Appendix B: Live endpoint examples

# Theory chart (top 5 categories, 30-day window)
GET https://rei-aios.pages.dev/api/octatheoria?domain=theory-chart&windowDays=30&limit=5

# Real-time arXiv (one specific category)
GET https://rei-aios.pages.dev/api/octatheoria?domain=realtime-arxiv&category=cs.AI

# Crypto (default 7-day window, all feeds)
GET https://rei-aios.pages.dev/api/octatheoria?domain=crypto

# FX (specific pair)
GET https://rei-aios.pages.dev/api/octatheoria?domain=fx&category=USDJPY

# v0.2 Earth+Cosmos extension (STEP 1046):

# LIGO/Virgo gravitational-wave superevents (24h hourly bins)
GET https://rei-aios.pages.dev/api/octatheoria?domain=ligo-events

# NASA Solar Dynamics Observatory (DONKI flares + CMEs, 24h hourly bins)
GET https://rei-aios.pages.dev/api/octatheoria?domain=nasa-sdo

# GBIF Occurrence (latitude 36-bin distribution)
GET https://rei-aios.pages.dev/api/octatheoria?domain=gbif-recent

The endpoint serves JSON. View-mode selection happens in the frontend (#/octatheoria); the backend serves the same envelope regardless of view.

Version history

• v0.1 (2026-05-10 起草): Initial draft. Phase Z-3 deliverable. Documents the operational implementation across Phases Z-1 through Z-2.7 (executed 2026-05-06 → 2026-05-08). Four-domain scope (theory-chart / realtime-arxiv / crypto / fx). Honest framing positions this as observation aid (not oracle), companion to Papers 145/147/148/149 (Quintuple closure). Authors: 藤本 × Rei × Claude. Internal draft only — not published as Zenodo deposit.

• v0.2 (2026-05-10 publish-ready): Earth+Cosmos extension via STEP 1046 (same-day morning). Domain count 4 → 7 (added: ligo-events, nasa-sdo, gbif-recent). All three new adapters maintain Edge runtime constraint (Cloudflare Workers compatible). New finding F6 (sampling bias as first-class observation): GBIF dominant axis INFINITY arises from Costa Rica 470/500 country saturation in the GBIF feed, surfacing dataset-side bias as a D-FUMT₈ axis observation rather than silently absorbing it. Test coverage updated: 117/117 PASS (step1020 46 + step1023 33 + step1046 38) / 0 regression. First Zenodo deposit version.

• v0.3 (2026-05-11 publish-ready): Methodological consistency cross-reference. New finding F7 records that the discipline embodied in OctaTheoria (uniform abstraction + honest scope + structurally-enforced naming) propagates to Rei-AIOS layers outside OctaTheoria's domain: REI-PROVE 5-prover ensemble achieved 11/12 = 92% benchmark proof rate (data/rei-prove-benchmark/latest.json), and the Pattern 1-6 + Antipattern fact-check framework was verified on 6/6 items (STEP 1069). The double-by Lean-syntax quirk in Goedel-Prover-V2 output was also detected and fixed at the cleaner level (STEP 1071), restoring easy-le-refl benchmark from ❌ to ✅. Zenodo new-version deposit; concept DOI lineage maintained from v0.2.

Co-Authored-By: 藤本伸樹 / Rei-AIOS / Claude Code (Anthropic, claude-opus-4-7)