The Plasticity Vitrification Theorem: Continual-Learning Capacity as a Glass-Transitioning Renewable Stock, and the Golden-Rule Reset Duty Cycle

Justin Hart, Aristotle (Harmonic)

Paper supported by machine-verified Lean 4. Continually trained neural networks progressively lose the ability to learn new tasks – units go dormant, representational rank collapses, and the degradation is not undone by ordinary continued training or passive regularization, only by active intervention (parameter resets, continual backpropagation, weight regeneration). This "loss of plasticity" is a well-documented empirical phenomenon in modern deep learning. We model it as an instance of the Viridis Stewardship Setpoint Theorem (SST): plasticity is a renewable deployment-capacity stock D(t) that intelligence-producing extraction (the Intelligence Bound, dI/dt leq P D/(k_B T ln 2)) degrades and that regeneration replenishes. The new physical ingredient this paper contributes is that the degradation is not smooth logistic decay but a genuine aging/vitrification process: under sustained forcing (continuous training with no reset), the fluctuation–dissipation ratio of the effective training dynamics ages algebraically in Cugliandolo–Kurchan form, X(s)=(1+s/tau_g)^-beta, driving plasticity toward a dormant state that does not spontaneously recover. Modeling training as an alternating forcing/reset cycle, we derive a closed-form one-cycle fixed point D^ast (verified against direct simulation to 10^-16) and a golden-rule reset duty cycle u^astin(0,1) that maximizes sustainable learning throughput – the 45th self-application of the Intelligence Bound, the Metronome. Verification forced two honest corrections to our initial hypotheses: (i) without an explicit per-cycle reset-overhead cost, the optimum degenerates to infinite reset frequency, so the overhead cost – not the aging physics alone – is what makes the golden rule well-posed; (ii) contrary to the analogous result in the prior Stewardship Setpoint paper, impatience (higher discount rate) lowers the optimal duty cycle here, because aging erodes the quality of the very harvest being sought within a forcing burst, not just future stock. We give three falsifiable, experimentally testable predictions and verify all numerical claims with a numpy-only harness (17/17 checks).