The Trust Framework for Computational Physics: Hash-Verified Trajectories and Reproducible Dynamical Systems

Abstract

We introduce the Trust Framework for Computational Physics, a formal architecture designed to restore rigorous falsifiability to numerical experiments through trajectory-level cryptographic hashing. Addressing the reproducibility crisis in computational science, the framework defines "trust anchors". Strict specifications for model parameters, numerical precision, and integrator protocols that ensure independent simulations of the same dynamical system yield bitwise-identical, hash-verifiable results. We establish the Trust Equivalence Principle, which posits that within defined trust boundaries, numerical error is strictly bounded, rendering simulation outputs as durable scientific artifacts. The efficacy of this architecture is validated through three rigorous reference implementations: (1) the linear self-stability of the canonical Whipple bicycle model, (2) high-precision chaotic periodic orbits in the Newtonian three-body problem, and (3) a curvature-dependent diffusion model exhibiting a gravitational arrow of time. These case studies demonstrate that trajectory-level hashing provides a universal standard for verifying computational claims independent of hardware or specific codebases.

Keywords