The Core Algebraic Kernels of Spatial Value and Action Flow: Meta-Axioms and Meta-Transitions

Abstract

This paper establishes the absolute, context-free core underpinning all evolutionaryfacets by formalizing two dual mathematical engines: Meta-Axioms (MA)and Meta-Transitions (MT). MA governs the spatial value domain, operating asa symmetric, commutative lattice structure where value conservation is strictlypreserved. Conversely, MT governs the action flow domain, operating as an asymmetric,non-commutative monoid structure that captures pure transformation andthe algebraic arrow of time. We demonstrate that prior behavioral layers, suchas Relational Logic (RL) and Axiomatic Context (AC), are isomorphic semanticprojections of these primal kernels, thereby unifying static observation logic withirreversible process dynamics.