The Ω-Ψ Framework and TPC-IP Protocol Suite: Mathematical Foundations for Cognitive Interoperability

This paper proposes the Ω-Ψ Framework, a philosophical and mathematical approach to a longstanding problem in philosophy of mind: how to compare cognitive systems with radically heterogeneous architectures (human, artificial, hybrid) without committing to specific metaphysical positions on phenomenal consciousness. Building on the Theory of Conscious Potentiality (TPC), the framework develops Ω-space, a four-dimensional metric space quantifying cognitive potential along model complexity, temporal horizon, meta-modeling, and adaptive flexibility, and Ψ-space, an eight-dimensional dyadic space modeling cognitive resonance between systems. The paper articulates the framework's epistemic commitments explicitly: it operationalizes capacities relevant to consciousness studies (after Chalmers, Tononi, Clark) without claiming to resolve the Hard Problem, and it distinguishes empirically supported components from logically coherent and speculative ones. Companion technical specifications (RFC-style protocols for cognitive interoperability) are provided as supplementary material at the linked Zenodo DOI; the philosophical core of the framework is presented self-contained in this manuscript. Empirical validation of the measurement protocol for AI systems is reported in a separate companion preprint.