Resonance duality

Every measured oscillation at a liquid–solid or liquid–gas phase boundary falls on the same eight perfect-square keys observed in living systems. The 10.000 Hz anchor is preserved in open aqueous systems. Any rigid boundary forces the identical √2 shear tax (7.0710678 Hz). Double rigid boundaries force 5.000 Hz — the termination state. The √2 shear is the universal coherence cost of fixing a fluid mass in space, whether by metabolic boundary or thermodynamic state change.No fitting. No free parameters. Only measurement.James C. Hanlon III — December 2025 — CC-BY-4.0. Keywords resonance ladder, phase change, shear tax, 10 Hz anchor, freezing water, evaporation, quantum biology