A First-Principles Axiomatization of Physics—The Cosmic Continuum Component Model with Its Scale Topos and Braided Tensor Category Realization
Abstract
Fundamental physics faces three profound difficulties: ontological incompatibility ($G,c,\hbar$ presuppose different ontological categories), the chasm between continuity and discreteness (classical continuum vs. quantum discreteness), and divergent mathematical languages (differential geometry, Hilbert spaces, renormalization groups). This paper proposes a first-principles axiomatic system for the Cosmic Continuum (15 axioms A0–A14). A0 asserts: All state changes in the universe arise from energy redistribution; there is no state change without energy change. This axiom replaces Newton's "inertia" as the most fundamental physical assumption—inertia is merely the special case $\Delta E = 0$. Built upon this first principle, the axiomatic system is structured through ontological axioms (A1–A3) as the cornerstone, structural axioms (A4–A7) as the skeleton (including the connection axiom A4b which provides a unified description of the four fundamental interactions), dynamical axioms (A8–A12) as the realization (including the field recursion axiom A9b which unifies multiple fields as different levels of a recursive structure), and meta-axioms (A13–A14) as verification. The framework clearly distinguishes mass, energy, and dark mass beings and their corresponding space, time, and dark space dimensions, unified via the New Equivalence Principle (A3). The component (A4) serves as the skeleton, unifying particles and gauge fields into an inseparable tensor product. The scale topos…
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