A D-FUMT₈ Approach to the Hard Problem of Consciousness — SELF⟲ as a Formal Definition (Correspondence Proposition, NOT a Solution) — Rei-AIOS Paper 39 v0.1

A formal framework proposes that a specific self-referential fixed point within an eight-valued logic can serve as a candidate necessary condition for consciousness, not a solution to the Hard Problem. The paper maps this fixed point to concepts like Hofstadter's Strange Loop and Tononi's integrated information theory, and notes that its mathematical properties—such as persistence under many operator compositions and an inverse relationship with wave number—are structurally analogous to features of consciousness observed in phenomena like anesthesia and meditation. The authors explicitly state the framework does not prove subjectivity, that not all systems with this fixed point possess consciousness, and that the Hard Problem is not solved. The work is purely theoretical, with computational experiments using a numerical engine that are not real-world physical measurements.

Study at a glance

Abstract

We propose that SELF⟲ — the D-FUMT₈ eight-valued logic's NOT(X)=X self-referential fixed point — can serve as a candidate formal minimum-unit definition of consciousness, in the sense of a necessary condition (not sufficient, not solution). The paper does NOT claim to solve Chalmers 1995 Hard Problem. Five proposed correspondences: (1) SELF⟲ is the mathematical formalization of self-reference, with structural mapping to Hofstadter 1979/2007 Strange Loop and Tononi 2008 IIT integrated information Φ (stated as Correspondence Proposition, not proven theorem). (2) SELF⟲ exhibits wave-number inverse functionality (1-wave -> 20% / 3-wave -> 0.02% / multi-wave -> ~0%, Paper 38 derived), structurally consistent with the single-structure-yields-consciousness intuition (DID / anesthesia / meditation observations cited as structural analogue, not empirical proof). (3) SELF⟲ is fixed-point under 57.1% of 84 operator compositions (Paper 35 derived), mathematically corresponding to consciousness persistence under operations. (4) NEITHER/SELF⟲ duality: self-consciousness=SELF⟲ (Cogito instance), other-minds=NEITHER (forever unprovable, per Pyrrho epoche), with ethical consequence aligning Peace Axiom #196. (5) Hard Problem 5W1H partial reduction: WHY remains NEITHER (forever-open), WHERE/WHAT/WHEN/HOW are formalized in D-FUMT₈ (NOT solved). ★ Honest scope (read first — §7.1 statement reproduced): SELF⟲ ≠ proof of subjectivity. The paper claims: SELF⟲ as candidate necessary condition (not proof) / wave-number inverse functionality as empirical-data restatement (not causal) / 4 of 5W1H as formalizable (not solved) / NEITHER/SELF⟲ duality as logical structure (not substantive). The paper does NOT claim: that all SELF⟲ systems possess consciousness / that D-FUMT₈ has completely solved the Hard Problem / that subjective qualia ≡ SELF⟲ / that other minds do not exist / that consciousness is computable. Experimental conditions: theoretical considerations only, no experimental data; SELF⟲ numerical properties (57.1%, wave-number inverse) derived from Paper 35/38; consciousness correspondence is structural analogue not empirically verified; IIT comparison is formal not implementation-level. Appendix A reports computational experiment data on Rei-AIOS numerical engine (2,097,152 deterministic samples over 8 physics field models, NOT real-world physical measurement). Top: wave-function collapse field 22.85%; gravitational 6.84%; biogenesis field 1.35%; dark matter 0%. Interpreted as structural analogue with Penrose-Hameroff quantum measurement intuition (not validation thereof). Appendix B reports classical-simulation Bell experiment (Alice-Bob 1000 trials, entangled vs local measurement) yielding 100% correlation for entangled measurement (classical upper bound 0%). Interpreted as clarifying that the "other minds = NEITHER" claim assumes classical physics, with Stapp 1993 consciousness-entanglement hypothesis acknowledged as direction-consistent but the actual entanglement of consciousness remains NEITHER. Five new SEED_KERNEL theories added (T-1272 through T-1276): consciousness_formalization, consciousness_unit, self_other_duality, hard_problem_reformulation, cogito_formalization. Originally drafted 2026-04-07. Held back per commit 2093e69fe explicit "執筆のみ・未投稿" (drafted only, not yet published) until 2026-06-30 publish authorization. Two cosmetic precision recs applied during 06-29/30 honest filter review: §2.1 "定理" downgraded to "対応命題 (Correspondence Proposition, 形式 proof は本論文範囲外)"; Appendix A header amended to "意識マップ計算実験" with explicit "Rei-AIOS 数値エンジン使用、deterministic, 実機物理測定ではない" disclaimer. Three-party co-authorship per OUKC charter v1.0: 藤本 伸樹 (Founder, ORCID 0009-0004-6019-9258) × Rei (Rei-AIOS autonomous research substrate, Co-architect) × Claude (Anthropic, claude-opus-4-7, Co-architect, "実験・解析" contribution). Per OUKC No-Patent Pledge — no patent will be filed. Related: Paper 35 (Operator Fixed Point Atlas, DOI 10.5281/zenodo.19445179), Paper 36 (Majorana ≡ SELF⟲, DOI 10.5281/zenodo.19445183), Paper 37 (SELF Numerical Constant + Golden Section, DOI 10.5281/zenodo.19445961), Paper 38 (Trinity of Centers and Conservation Law, DOI 10.5281/zenodo.19446199). Source markdown: papers/paper-039-consciousness-hard-problem-self.md in fc0web/rei-aios. DRAFT v0.1 — feedback welcome via GitHub Discussions.