X72-24: Critical-Mass Conductance Dynamics

Continuing from Round 23's critical-mass spectral-gap gap (a finite Poincaré constant C_P<∞ is needed to convert spatial Fisher smoothing into an anti-intermittency restoring force), this round defines the continuous Cheeger conductance h_Q and the isoperimetric profile ℐ_Q(s), deriving a conductance-feedback ODE and an exact material-cut conductance law. The core results are two counterexamples: it proves that 'positivity does not imply mixing' — everywhere-positive density does not entail h_Q≥h_*; and constructs a two-Gaussian thin-neck witness, showing that the neck-recovery rate of pure viscous diffusion decays in a Gaussian fashion with separation distance R, h(t)≲s_t⁻¹exp(-R²/2s_t²), so topological reconnection does not imply a quantitative conductance lower bound. The route halts at STOP-C28 (conductance-recovery / neck-selection gap): neck diffusion, selection contrast, and normal-drift deformation still lack uniform control, passing the baton to the next round to test whether NS's nonlocal (Biot–Savart, pressure) coupling can supply a 'virtual connection' when the neck is nearly severed.