Retention You Can Predict, Scope and Delete:\\ a $(\mu,\gamma,T)$ Law and a Structural Deletion Guarantee\\ for a Physics-Structured Memory Store

Existing memory systems enforce retention via explicit bookkeeping policies. Forgetting or deletion thereby relies on methods like decay factors, expiry timestamps, or learned forget gates, which dictate when a specific entry expires. However, these programmatic rules do not specify the physical rate of value degradation, the continuous dynamical effect of tuning retention parameters, or the exact residual state of the network following an item's removal. In this work, we resolve these ambiguities by formalizing forgetting as a dynamical property of a memory store constructed as a Latent Dynamics Model: specifically, one produced by a damped symplectic step of a learned Hamiltonian. Our retention policy is defined by a computable physical budget parameterized by three variables: the stored direction's spectral mass $\mu$, the damping $\gamma$, and the temperature $T$. We demonstrate three core properties of this architecture. First, the retention dial possesses a computable critical point: retention half-life is non-monotonic in friction, forming a V-curve minimized at $\gamma_{\rm crit}=2\varepsilon\mu$. This curve spans approximately 11 orders of magnitude in $\mu^2$ and holds across both designed and emergent (learned-MLP) units. Second, retention is rigorously scopeable: at $T>0$, friction preserves memory while temperature erases it. A localized friction hole thus acts as a memory vault, demonstrating a $107.77\pm4.78\times$ retention factor on designed architectures. Finally, removal is purely structural: under canonical \citet{blelloch_strongly_2007} placement, store-level deletion is exact. Post-deletion, the store is byte-identical to a state that never held the item, governed by defined operational conditions, on a designed, non-learned 3-dimensional datastore at capacities 8--64.