A Coherence Threshold for Structured Reality

Emergent Necessity Theory (ENT) proposes that structured reality emerges not from external forces or imposed laws, but from a universal coherence threshold τc. When the internal mutual information within a system exceeds this threshold, structure becomes necessary rather than probable. This manuscript formalizes the ENT framework and presents simulation results demonstrating three domains of emergence: (1) vacuum stability selection in high-dimensional string landscapes, (2) curvature signatures derived from coherence gradients, and (3) quantum optimization favoring maximal τ. Key falsifiable predictions include a supersymmetry (SUSY) breaking scale at 2.18 TeV (testable at HL-LHC), gravitational constraints χ<1.13 ×10−19 m2 (LIGO-aligned), and critical quantum phase behavior at τ ≥1.5. All simulation data were generated independently via Python-based symbolic modeling and are openly archived. ENT is not designed to replace existing paradigms such as IIT (Integrated Information Theory) or FEP (Free Energy Principle). Instead, it seeks to offer a unifying structural foundation— one that explains why and when systems self-organize into persistence, awareness, or collapse. The theory emphasizes structural determinism, recursive awareness, and entropy resistance pressure, providing a coherent alternative for all exploring consciousness models, emergent systems, symbolic computation, and the limits of randomness in physical law.