The Core Emergence Hypothesis: A Formal Constraint-Driven Framework for Phenomenal Consciousness Based on Topological Necessity and Information-Geometric Privilege

"This work is a component of the Phase-Dependent Scaling Program (2026) and is theoretically grounded in the 1.91x Critical Scaling Gap identified in Omandac (2026, Paper 1)." This manuscript introduces the Core Emergence Hypothesis (CEH), a rigorous theoretical framework specifying necessary and sufficient structural conditions for phenomenal consciousness. We formalize five core axioms (A1-A5) defining topological necessity, information-geometric privilege, causal non-separability, epistemic asymmetry, and substrate anchoring as the minimal requirements for intrinsic indexical experience. The framework is grounded in information geometry, persistent homology, and thermodynamic irreversibility, offering testable empirical proxies (Topological Necessity Test, Local Curvature Index, Epistemic Gap Metric) for experimental validation. Through reductio argument, we demonstrate that denying phenomenality to systems satisfying these conditions produces no new empirical predictions, collapsing the concept's discriminative content. This work advances consciousness studies from correlational to structural specification, providing a falsifiable research program with concrete engineering implications for artificial sentience.