Justification of Critical Coherence Thresholds in Emergent Necessity Theory: A Framework of Scientific Humility

This work rigorously justifies the domain-specific critical thresholds (τc) within Emergent Ne- cessity Theory (ENT), a framework proposing that structural emergence occurs when informational coherence τ exceeds a critical value. We demonstrate that τc values are not arbitrary but derive from: (1) normalized coherence dynamics, (2) domain-specific physical constraints, (3) falsifiable empirical predictions, and (4) system-specific phase transition behaviors. Through cross-domain analysis spanning neural systems, artificial intelligence, quantum physics, and fundamental cosmology, we establish τc as a measurable phase transition point while acknowledging its provisional status pending experimental validation. The thresholds maintain internal consistency across domains while enabling precise falsifiable predictions. Our approach emphasizes scientific humility through explicit acknowledgment of limitations and defined pathways for empirical refinement.