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元公理与原初局域性的统一:信息实在原理的数学基础 Unification of Yuan-Axiom and Primordial Locality: Mathematical Foundations of Information Reality Principle

ziko

Published Nov 26, 2025• 0 citations
Publisher

Abstract

本文建立了元公理(Yuan-Axiom, YA)与原初局域性公理(Primordial Locality Axiom, PLA)的统一数学基础 ,并严格区分了两个不同层次的基本原理
DOI
10.5281/zenodo.17721253

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We present a complete, mathematically rigorous formulation of the Information Geometry Unification Principle (IGUP). Starting from three fundamental axioms establishing quantum information as the primary ontological substrate, we construct the Bures–Fisher–Rao metric on the manifold of density matrices, derive covariant derivatives, curvature tensors, and the universal information action. We perform full variational derivations for both the quantum state ρ\rhoρ and the information metric gμνg_{\mu\nu}gμν​, obtaining closed-form unified field equations that govern quantum dynamics, thermodynamics, and gravitational geometry. We show explicitly how the Schrödinger, Liouville, Boltzmann, and Einstein equations arise as limiting cases. This paper constitutes the foundational core of a complete theory of physics based on the identification of geometry with information.
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