The Axiom Lattice of Unified Resonance Cosmology (V5): A Seven-Tier Resonance Framework Spanning Physics, Complexity, Biology, and Cognition

Abstract (English) — V5 The Axiom Lattice of Unified Resonance Cosmology (V5) presents the formal structural grammar of resonance-driven systems across physical, biological, cognitive, and computational domains. Building on the Meta-Axioms of the Unified Resonance Topology Framework (URTF)—including geometry fitness, tension gradients, oscillatory debt, and constraint-priority gating—this framework organizes thirty-two domain-level axioms into a seven-tier lattice governing the emergence, stabilization, and transformation of coherent systems. Version 5 introduces a critical structural inflection point within the Continuum Vortex tier through the formalization of observer-coupled resonance dynamics. Observation is no longer treated as passive measurement but as an active geometric interaction that reshapes the resonance landscape. As a result, system behavior becomes adaptive and relational: prediction is conditional, stability is context-dependent, and boundaries emerge as reflexive, dynamically reconfiguring structures. Each tier inherits its permissible behaviors through constraint pathways originating in the meta-axioms, linking topological requirements to observable system behavior across scales. This establishes a unified framework in which physical structure, biological organization, and cognitive processes arise from shared resonance-coherence mechanisms. The Axiom Lattice therefore serves as a cross-domain synthesis, integrating the mathematical substrate of Unified Resonance Cosmology (URC) with the topological constraints of URTF and extending into applied frameworks including the Architecture of Oscillatory Systems (AOS), Resonant Self-Consistency Architecture (RSCA), Temporal Resonance Observation (TRO), and XY Continuum Geometry (XYCON). Together, these components define the governing principles that constrain, permit, and unify resonance behavior across scales, substrates, and observational conditions.