Phase-Dependent Scaling in Noisy Dicke Systems: The Omandac Law, the 6/π Binding Proof, and Empirical Convergence to the 0.0417 Singularity (v4.0)

Key Points

• To provide empirical validation of the Omandac Law and explore phase-transition dynamics in neural populations.
• Derived first-principles for binding proof between quantum manifolds and spiking networks.
• Identified resonant tail firing rate as empirical evidence for the 0.0417 ground-state attractor in neural populations.
• Mapped phase gradients to characterize transitions between information states.
• Established Omega = 6/pi as critical for impedance-matching in quantum and neural systems.
• Identified a firing rate of approximately 0.1352 spikes/ms corresponding to resonant dynamics.
• Characterized a unique geometric window for preserving integrated information.