COMPLEX BINARITY THEORY: COMPLETE THEOREM VOLUME

Complex Binarity Theory: Complete Theorem Volume (v1.0) This document presents the formal corpus of Complex Binarity Theory (CBT), a geometric extension of classical binary logic designed to model structural complexity under accumulated transition and stress. When structural complexity exceeds the resolution capacity of classical binary operators, distinct system states collapse into indistinguishable outputs. CBT introduces an orthogonal transition axis that preserves binary decision structure while extending representational resolution in the dynamic domain. The theory models systems as finite weighted graphs equipped with: a resonance amplification operator (λ_eff), a structural deficit metric (L_def), deterministic cascade admissibility conditions, spectral invariants (ρ, λ₂), an orthogonal temporal axis, and a triadic memory structure (p_e, p_p, F). Within this framework, structural transitions are defined deterministically rather than probabilistically. The theory establishes minimal cascade conditions, compensation bounds, coupling amplification properties, and proves the asymptotic completeness of attractor classification under stated model assumptions. This release contains the full mathematical specification of the theory. Computational implementations and calibration layers are not included. Version: v1.0March 2026