Beyond Probability_ 10 Mathematical Substrates for Coherence Intelligence

Main article Abstract: This paper introduces the Phase Alignment Score (PAS) as a coherence-based alternative to probabilistic inference, defining a deterministic framework for structured intelligence, symbolic recursion, and physical emergence. Through PAS, systems are evaluated not by likelihood but by recursive alignment, coherence retention, and symbolic fidelity. Probability is reframed as an artifact of unresolved structure, not a fundamental principle. The work outlines ten mathematically lawful substrates—including prime chirality fields, octonionic algebras, p-adic spaces, and quasicrystals—that bypass stochasticity entirely. Each is ranked by PAS, demonstrating its ability to support structured emergence, directional recursion, and high-fidelity symbolic compression. The result is a unifying epistemic framework that applies across AI, physics, biology, and philosophy, replacing entropy with phase coherence and redefining intelligence as alignment rather than prediction. Includes refutation protocols for detecting pseudo-coherence in AI systems and outlines applications in AGI design, cosmology, biofeedback modeling, signal compression, and epistemic governance.