Curvature-Dependent Arrow-of-Time Trust Dataset v1.0: Hash-Verified Diffusion in an Asymmetric Gravitational Potential

This record provides a curvature-dependent, hash-anchored toy model of the gravitational arrow of time, constructed as a one-dimensional diffusion process in an asymmetric effective potential. The accompanying Jupyter notebook, `curvature_arrow_of_time_trust_dataset_v1.ipynb`, defines a fully deterministic 1D curvature-dependent diffusion model. The system evolves a probability density ρ(x, t) on a finite spatial interval with periodic boundary conditions, subject to: • An asymmetric double-well effective potential V(x) that breaks left–right symmetry. • A curvature-dependent diffusion coefficient D(x) = D0 (1 + α |V''(x)|) that strengthens diffusion where the effective gravitational curvature is larger. • A drift term driven by the gradient of V(x), producing relaxation toward a biased equilibrium. The evolution equation is discretized using a fixed explicit finite-difference scheme with: • A fixed spatial grid (N points, spacing dx) on [-L, L]. • A fixed time step dt and total integration time T. • Periodic boundary conditions and explicit mass renormalization to control numerical drift. From this setup, the notebook produces: 1. `curvature_arrow_of_time_trajectory.json` A canonical JSON serialization of the full trajectory: - `times`: sample times t_k - `x`: spatial grid points x_i - `rho`: probability density snapshots ρ(x_i, t_k) 2. `curvature_arrow_of_time_summary.json` A compact summary including: - Model parameters (L, N, dx, dt, D0, α, potential tilt) - Diagnostics (mass range, entropy range over time) - The SHA-256 hash of the full trajectory payload. 3. The notebook `curvature_arrow_of_time_trust_dataset_v1.ipynb` A fully reproducible implementation of the model and the trust framework steps: - Deterministic integration with fixed precision. - Canonical JSON serialization of the trajectory. - SHA-256 hashing of the trajectory payload. - Summary JSON for quick verification. This record is explicitly positioned as a **trust dataset** for arrow-of-time / anti-time discussions rather than a novelty claim. It is designed to: • Provide a transparent, falsifiable reference implementation of a curvature-dependent arrow-of-time toy model. • Serve as a benchmark for numerical integrators, discretization schemes, and reproducibility pipelines in simple non-equilibrium systems. • Demonstrate how trajectory-level hashing and canonical serialization can be applied beyond purely mechanical systems, complementing trust datasets for bicycle self-stability and three-body periodic orbits. Related records: – High-precision replication of the Meijaard et al. (2007) benchmark self-stable bicycle model: Zenodo DOI 10.5281/zenodo.17634914– Three-Body Trust Catalog v1.0: Hash-Verified High-Precision Periodic Orbits: Zenodo DOI 10.5281/zenodo.17635887 – Hernandez, A. X., & Martinez, J. (2024) Gravitational asymmetry and the arrow of time: Zenodo DOI10.5281/zenodo.12224027 Together, these three records illustrate the generality of the emerging **Trust Framework for Computational Physics**, spanning linear mechanical stability, nonlinear gravitational dynamics, and curvature-dependent arrow-of-time toy models.