The Axiom Lattice of Unified Resonance Cosmology (V4): A Seven-Tier Resonance Framework Spanning Physics, Complexity, Biology, and Cognition

The Axiom Lattice of Unified Resonance Cosmology (URC) formalizes the foundational laws governing resonance-driven systems across physical, biological, cognitive, and computational domains. In this V4 edition, the lattice incorporates a new Tier 0: the Meta-Axioms of the Unified Resonance Topology Framework (URTF), which define the topological requirements—geometry fitness, tension gradients, oscillatory debt, and constraint-priority gating—that underlie all coherent oscillatory behavior. Building on these meta-axioms, the lattice organizes thirty-two domain-level axioms into seven tiers, spanning generative structure, dynamic behavior, relational transitions, continuum mechanics, cross-domain invariants, and observer-embedded resonance. Together, these tiers articulate the multi-level logical architecture of resonance systems and provide the theoretical backbone linking the broader URC ecosystem, including the Resonant Self-Consistency Architecture (RSCA), the Architecture of Oscillatory Systems (AOS), Temporal Resonance Observation (TRO), XY Continuum Geometry (XYCON), and the Unified Resonance Topology Framework (URTF). This document serves as the formal structural map of the field, defining the governing principles that constrain, permit, and unify resonance behavior across scales and substrates.