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Rei-AIOS Papers Series' Articles

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Paper 143 — Cross-Cultural Convergence: Rei-AIOS Reaches Mikami's 1953 Japanese Wa-Ga Thesis (11/11)

Paper 143 — Cross-Cultural Convergence: Rei-AIOS Reaches Mikami's 1953 Japanese Wa-Ga Thesis (11/11)

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7 min read
Paper 148 — Honest Observation Framework for AI-Assisted Research Tools (Rei-AIOS / OUKC)

Paper 148 — Honest Observation Framework for AI-Assisted Research Tools (Rei-AIOS / OUKC)

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12 min read
Paper 147 — Eight-Valued Utility and the Equity Premium Reframe (Rei-AIOS / OUKC)

Paper 147 — Eight-Valued Utility and the Equity Premium Reframe (Rei-AIOS / OUKC)

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14 min read
Paper 149 — Recursive AI Observation as D-FUMT-8 SELF-loop Operational Evidence: When the AI Observatory Includes Itself (Rei-AIOS / OUKC)

Paper 149 — Recursive AI Observation as D-FUMT-8 SELF-loop Operational Evidence: When the AI Observatory Includes Itself (Rei-AIOS / OUKC)

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11 min read
Paper 145 — First D-FUMT-8 Silicon with SELF-reflexive Logic Primitive (Three-Substrate Cross-Verification: FPGA + Aer + IBM Heron r2 Real Hardware)

Paper 145 — First D-FUMT-8 Silicon with SELF-reflexive Logic Primitive (Three-Substrate Cross-Verification: FPGA + Aer + IBM Heron r2 Real Hardware)

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23 min read
Paper 145 v0.6 — First D-FUMT-8 Silicon with SELF-reflexive Primitive (Four-Substrate Cross-Verification)

Paper 145 v0.6 — First D-FUMT-8 Silicon with SELF-reflexive Primitive (Four-Substrate Cross-Verification)

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38 min read
Paper 150 v0.2 — OctaTheoria: Unified Multi-Domain Observation Framework with Eight-Axis D-FUMT-8 Projection (Seven Domains x Eight View Modes)

Paper 150 v0.2 — OctaTheoria: Unified Multi-Domain Observation Framework with Eight-Axis D-FUMT-8 Projection (Seven Domains x Eight View Modes)

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

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

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20 min read
Paper 152 v0.1 — Sigma-Cascade Observation of Collatz Orbit Confluence: Empirical Peak-Merge Enumeration and the n=96k Hypothesis

Paper 152 v0.1 — Sigma-Cascade Observation of Collatz Orbit Confluence: Empirical Peak-Merge Enumeration and the n=96k Hypothesis

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12 min read
Paper 152 v0.2 — Sigma-Cascade Observation of Collatz Orbit Confluence: Lean 4 Mechanized Closures + 3-Adic Isolation Theorem + Honest Correction E2

Paper 152 v0.2 — Sigma-Cascade Observation of Collatz Orbit Confluence: Lean 4 Mechanized Closures + 3-Adic Isolation Theorem + Honest Correction E2

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19 min read
Paper 152 v0.3 — Sigma-Cascade Collatz: 10^9 Scan + G_3 Subgraph Framework + Erratum E3 + Lemma 5d.1 Lean 4 Mechanized

Paper 152 v0.3 — Sigma-Cascade Collatz: 10^9 Scan + G_3 Subgraph Framework + Erratum E3 + Lemma 5d.1 Lean 4 Mechanized

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26 min read
Paper 63 v0.2 — SNST Supplement: PSLQ Phi^2=Psi+2 + PySR x CICY3 Negative Finding + Tao 67 Connections

Paper 63 v0.2 — SNST Supplement: PSLQ Phi^2=Psi+2 + PySR x CICY3 Negative Finding + Tao 67 Connections

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7 min read
Paper 153 v0.1 — Phi-Catalog: A Notation for Impossibility-Possibility Extensions (9 Historical Cases)

Paper 153 v0.1 — Phi-Catalog: A Notation for Impossibility-Possibility Extensions (9 Historical Cases)

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11 min read
Paper 153 v0.2 — Phi-Catalog: Case 6 (Riemann ZCSG) + Forward Application Self-Test + Berry-Keating Numerical Study

Paper 153 v0.2 — Phi-Catalog: Case 6 (Riemann ZCSG) + Forward Application Self-Test + Berry-Keating Numerical Study

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10 min read
Paper 155 v0.2 — Semantic Dyson Sphere (Beyond-Shannon Recovery as Civilizational Footprint, Lean 4 Mechanized)

Paper 155 v0.2 — Semantic Dyson Sphere (Beyond-Shannon Recovery as Civilizational Footprint, Lean 4 Mechanized)

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17 min read
Paper 144 v0.3.1 — OUKC: An AI-Friendly Multilingual Worldview Commons (Founding Document)

Paper 144 v0.3.1 — OUKC: An AI-Friendly Multilingual Worldview Commons (Founding Document)

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20 min read
Paper 154 v0.0 (OUTLINE) — Rei as a Formal-Verification Compilation Pass for AI-Generated Mathematics

Paper 154 v0.0 (OUTLINE) — Rei as a Formal-Verification Compilation Pass for AI-Generated Mathematics

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13 min read
Paper 157 - Octonion-Axiomatic Dual Independence: 7 Imaginary Units || 7 Axioms, Machine-Checked in Lean 4 (OUTLINE)

Paper 157 - Octonion-Axiomatic Dual Independence: 7 Imaginary Units || 7 Axioms, Machine-Checked in Lean 4 (OUTLINE)

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21 min read
Paper 159 - A Two-Layer D-FUMT-8 Reconstruction of Priest-Garfield's Inclosure Schema for Nagarjuna's Catuskoti (OUTLINE v0.1)

Paper 159 - A Two-Layer D-FUMT-8 Reconstruction of Priest-Garfield's Inclosure Schema for Nagarjuna's Catuskoti (OUTLINE v0.1)

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16 min read
Paper 159 v0.2 - A Two-Layer D-FUMT-8 Reconstruction of Priest-Garfield's Inclosure Schema (LEAN-4-BUILT, zero axiom dependence)

Paper 159 v0.2 - A Two-Layer D-FUMT-8 Reconstruction of Priest-Garfield's Inclosure Schema (LEAN-4-BUILT, zero axiom dependence)

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24 min read
Paper 160 v0.2 - Inversion vs Deconstruction in D-FUMT-8 (Lean 4 verified, zero axiom)

Paper 160 v0.2 - Inversion vs Deconstruction in D-FUMT-8 (Lean 4 verified, zero axiom)

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28 min read
Paper 161 v0.1 - Two Regimes of Rest: ZERO and SELF-loop via dynamical systems (5 experiments + 3 Lean files + depth wall 200x breakthrough)

Paper 161 v0.1 - Two Regimes of Rest: ZERO and SELF-loop via dynamical systems (5 experiments + 3 Lean files + depth wall 200x breakthrough)

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22 min read
Paper 161 v0.2 HARDWARE-VERIFIED - Two Regimes of Rest: 18 Lean theorems exit-0 + IBM Heron r2 real-hardware (27 CZ, depth 51, 1.82% leakage)

Paper 161 v0.2 HARDWARE-VERIFIED - Two Regimes of Rest: 18 Lean theorems exit-0 + IBM Heron r2 real-hardware (27 CZ, depth 51, 1.82% leakage)

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25 min read
Paper 145 v0.8 — D-FUMT-8 Phase 4 Quine-McCluskey Simplification + Finding F11 Engineering-Correctable Relaxation Bias on IBM Heron r2

Paper 145 v0.8 — D-FUMT-8 Phase 4 Quine-McCluskey Simplification + Finding F11 Engineering-Correctable Relaxation Bias on IBM Heron r2

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48 min read
Paper 163 v0.1 — Institution + Bilattice + SELF<->Lawvere: Four-Step Operational Integration with Lean 4 Axiom-Free Constructive Proofs

Paper 163 v0.1 — Institution + Bilattice + SELF<->Lawvere: Four-Step Operational Integration with Lean 4 Axiom-Free Constructive Proofs

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10 min read
Paper 164 v0.1 — infinity-cosmoi Skeleton + Tetradic Completion of rhymeOrTheorem: 4-Step Continuation of Paper 163

Paper 164 v0.1 — infinity-cosmoi Skeleton + Tetradic Completion of rhymeOrTheorem: 4-Step Continuation of Paper 163

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18 min read
Paper 165 v0.1 — Existence Proof Garden: Interactive Synthesis of Piantadosi-Chomsky Debate, Modal Duality, and Adjunction

Paper 165 v0.1 — Existence Proof Garden: Interactive Synthesis of Piantadosi-Chomsky Debate, Modal Duality, and Adjunction

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11 min read
Paper 166 v0.1 — A Lean 4 Axiom-Free Formalization of Exit-Layer Collatz Convergence as a Stream Coalgebra: A Record Following Kim (2008)

Paper 166 v0.1 — A Lean 4 Axiom-Free Formalization of Exit-Layer Collatz Convergence as a Stream Coalgebra: A Record Following Kim (2008)

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24 min read
Paper 167 v0.1 — Sophie Germain Primes: Barrier-Side Observations + Lean 4 Axiom-Free Conjunction-Wall (Rei-AIOS)

Paper 167 v0.1 — Sophie Germain Primes: Barrier-Side Observations + Lean 4 Axiom-Free Conjunction-Wall (Rei-AIOS)

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16 min read
Paper 158 v0.2 — The Collatz Exit Layer: Zero-Sorry Lean 4 Formalization of m_p = (4^p 1)/3, and an Honest Map of the Seven-Route Wall Beyond

Paper 158 v0.2 — The Collatz Exit Layer: Zero-Sorry Lean 4 Formalization of m_p = (4^p 1)/3, and an Honest Map of the Seven-Route Wall Beyond

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17 min read