DOI: 10.5281/zenodo.17652927
title: Curvature-Dependent Arrow-of-Time Trust Dataset v1.0: Hash-Verified Diffusion in an Asymmetric Gravitational Potential

description: 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.