axioms: structural closure and falsifiability
the minimal assumptions required for integrodynamics
abstract
this paper formalises the axiomatic foundations of integrodynamics: the unified dynamical theory governing contradiction, symmetry, adaptation, and integrity across epistemic, procedural, and institutional systems. building on the six prior papers of the Integrity series, it consolidates their implicit assumptions into a minimal and complete axiom set from which the full integrity field theory follows. integrity is treated not as a moral property but as a conserved structural quantity governed by free-energy dissipation, symmetry constraints, and evidential collapse under stochastic contradictions. eight axioms are stated defining contradiction observability, free-energy monotonicity, conservation of evidential structure, symmetry-stabilised dynamics, bounded adaptation, and probabilistic irreversibility. from these axioms, the core integrodynamic law is derived, unifying contradiction, symmetry, adaptation, implausibility, and integrity into a single field-theoretic architecture. this paper establishes Integrodynamics as a complete structural theory of integrity, with testable predictions, conservation laws, and a well-defined phase structure.