A Mathematical Physics Framework Based on the Axiomatic System of Observer and Causal Closure

This paper presents a unified theoretical framework---the Hierarchical Spacetime Topology and Cognitive Causality (HSTC) theory---built upon three fundamental meta-propositions concerning observers and causal closure. From these, a system of nine axioms (B1--B5, C1--C4) is derived, establishing an ontology-cognition dual-layer structure. The framework yields a chain of necessary derivations: the real number continuum emerges as the unique optimal cognitive substrate when a finite observer confronts a deep discrete ontology at macroscopic scales; calculus and linear differential equations follow as the optimal tools for local approximation and global prediction; and under four distinct cognitive limits---macroscopic low-velocity, high-velocity flat-spacetime, strong gravitational self-reference, and microscopic erosion---linear differential equations uniquely degenerate into Newtonian mechanics, special relativity, general relativity, and quantum mechanics, respectively. Beyond reproducing known physics, the theory traces the inverse fine-structure constant to a prime number (137) of topological origin, with its decimal part arising from vacuum polarization induced by a cross-hierarchical erosion operator. Testable physical predictions are given for quantum decoherence, black hole singularities, and classical chaos. The meta-propositions and axiom system were independently formulated by the author; logical derivation and cross-validation were conducted through human--AI interaction, with all conclusions verified by the author.