Exhaustive Validation and Interdisciplinary Analysis of Complex Binarity Theory

Exhaustive Validation and Interdisciplinary Analysis of Complex Binarity Theory This document presents a structured mathematical validation and cross-disciplinary analysis of Complex Binarity Theory (CBT), a formal extension of classical binary logic introducing an orthogonal transition operator. CBT defines the precise structural threshold at which classical binary operators lose injectivity (SC > R (B) ), resulting in systemic over-resolution. To resolve this limitation, the theory introduces a homotopy-invariant transition parameter, preserving path-dependence and accumulated structural stress without abandoning deterministic binary operationality. The validation corpus examines: Spectral resonance amplification (λₑff) and structural deficit (Ldef) Logistic boundary suppression via U (C) = 4C (1 − C) Deterministic cascade conditions Compensation bounds and network coupling limits Industrial load amplification Observer non-embeddedness principle Four asymptotic attractor classifications Comparative analysis demonstrates structural consistency with independent models in: Spectral graph theory Systemic financial risk modeling Epidemiological reproduction matrices Materials rheology and plastic deformation Neural memory consolidation Emerging quantum-pattern and epistemic drift frameworks Additionally, empirical large-scale historical decision analysis confirms that binary operators can remain structurally dominant in complex institutional systems, providing contextual support for CBT’s foundational premises. This validation document complements the formal theorem volume of Complex Binarity Theory and serves as its interdisciplinary analytical extension.