What question did this study set out to answer?

This research aims to establish a unified information-geometric framework connecting logic, computation, and physics through the concept of reflexive reality.

June 11, 2026Open Access

Mathematical Foundations of Reflexive Reality: A Unified Information-Geometric Framework for Physics

Key Points

This research aims to establish a unified information-geometric framework connecting logic, computation, and physics through the concept of reflexive reality.
Developed a mathematical framework known as the Mathematical Foundations of Reflexive Reality (MFRR).
Conducted experiments (TE_2.1) with 11 different tests and over 710 runs, utilizing Python for validation.
Formulated and validated 17 closure theorems, including the Two-Layer PSC Theorem with associated group symmetries.
The framework uniquely identifies the gauge group SU(3)×SU(2)×U(1) with three generations of particles.
Achieved a high precision of results with sub-percent accuracy through 57,337+ experimental runs.
Resolved the black-hole information paradox and derived significant physical phenomena from information-theoretic constraints.

Abstract

The Mathematical Foundations of Reflexive Reality (MFRR) establishes a unified framework in which logic, computation, and physics are aspects of one self-defining process. A universe can exist consistently only if its laws are internal, reflexively executed, and energetically self-accounting. The central construct—Transputation (\ (\) ) —realizes lawful internal adjudication of computational degeneracies, producing Perfect Self-Containment (\ (\) ). The forcing of transputation as the unique internal adjudicator under closed-choice conditions is machine-proved in a companion Lean development (zero sorry; Strong Transputational Universality, STU). Seventeen closure theorems connect logic, energy, geometry, thermodynamics, and theory space. The pinnacle structural result is the Two-Layer PSC Theorem: Layer~I (hard PSC axioms) uniquely forces gauge group SU (3) × SU (2) × U (1) with Ngen 3; Layer~II (Presentation Invariance/MDL) selects Ngen=3 as the unique PSC-optimal solution. The framework further resolves the black-hole information paradox via reversible transputation (^-1 =I), derives ensemble quantum decoherence as the origin of GKSL dynamics without external environment, and establishes three universal information-energetic laws: (i) ~superlinear energy amplification (α: 1. 01→ 1. 83) quantifying the quantum-to-classical transition; (ii) ~the Information Profit Principle (Gen/Drain >1. 13=1+Λ/2) governing all self-organization; (iii) ~decoherence as profit-accounting corruption by additive external noise. Part~V realizes MFRR constructively via steel-man experiments (TE₂. 1: 11 experiments, 710 runs) deriving gravity, quantization, entanglement, and wormhole formation from information-theoretic constraints alone, and via five advanced theorems (TE₂. 2–TE₂. 6) proving PSC-optimality of SM, nuclear physics, unitarity, ΛCDM, and Δ-machine necessity. The framework is verified by the ΛΩ-RCP, TE₁, and TE₂ validation programs: 297 first-party Python modules, 57, 337+ experimental runs, 15, 894+ result files, confirming core predictions to sub-percent precision.

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