arXiv AI October 31, 2026 By Pratik Jawahar, Riccardo Maggioni, Jonas Petersen, Matteo Cozzi, Gian-Alessandro Lombardi, Marek Gajewski, Camilla Mazzoleni, Federico Martelli

Certified Access: Test-Time Compute on Conservative Physics-Structured AI Memory

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The paper introduces a theoretical and empirical framework for test‑time compute on a Latent Dynamics Model used as memory. It shows that mechanisms such as retries, confidence‑based escalation, and non‑local routing can be formally analyzed using a damped symplectic step of a learned Hamiltonian, yielding exact phase‑volume Jacobians, bounded energy changes, and latch‑transport laws. The authors verify a certificate stack on an analytic testbed, demonstrating how escape failures are resolved by a Lorentz squeeze and reach failures by a gated canonical translation, and evaluate scaling limits against a physics‑free baseline.

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