The Core Algebraic Kernels of Spatial Value and Action Flow: Meta-Axioms (MA) and Meta-Transitions (MT)

Abstract

For over two millennia, formal mathematics and standard logic have been confined within the strict walls of bivalent systems, treating truth and falsehood as static, binary endpoints. This structural limitation has forced classical computational architectures to flatten continuous, non-linear natural phenomena into arbitrary intervals, breaking the native physical magnitudes of context-dependent data. This paper establishes the absolute, context-free core underpinning all evolutionary facets by formalizing two dual underlying mathematical engines: Meta-Axioms (MA) and Meta-Transitions (MT). MA governs the spatial value domain, operating as a symmetric, commutative lattice structure where value conservation is strictly preserved over the real continuum ($\overline{\mathbb{R}}$). Conversely, MT governs the continuum action flow domain, operating as an asymmetric, non-commutative monoid structure that captures pure transformation and the algebraic arrow of time. We demonstrate that prior behavioral layers—specifically Relational Logic (RL), Axiomatic Context (AC), Transitional Continuity (TC), and Phase Dynamics (PD)—are isomorphic semantic projections of these primal foundational kernels. By unifying static evaluation logic with irreversible process dynamics under a bounded paraconsistent domain, this foundation reshapes transfinite arithmetic, offering an immutable structural baseline that prevents arithmetic failure and systemic explosion without artificial normalization bias.