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Bio-salted hash is the intrinsic Lyapunov function of identity dynamics. Hardness and stability are dual.Let \mathcal{B} be biometric manifold, \sigma: \mathcal{B} \times \mathcal{R} \to \mathcal{H} satisfy collision resistance and continuity. Define V(x, h) = \| \sigma(x, r^*) - h \|^2 + \lambda \text{Ent}(x).For \dot{x}=f(x,u), \dot{V} \le -\gamma V + \beta \mathbf{1}_{\text{spoof}}.Duality: Collision resistance \iff V>0; Salt uniqueness \iff isolated equilibrium; ZK \iff \dot{V}<0 invariant. Breaking hash \equiv \dot{V}>0 escape. Security is stability. Gödelian self-reference: verification certifies its own well-posedness.Do \pi_1(\mathcal{B}) obstructions bound \gamma? Minimal salt entropy for global V?
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