Thickness Structure Hypothesis Dynamics - Consistent Dynamical Equation

Description A Compact Structural Simulator Based on the Thickness Structure Hypothesis (TSH) This repository provides an executable model based on the structural dynamics suggested by the Thickness Structure Hypothesis (TSH). The simulator implements a compact dynamical equation derived from a covariant action involving the structural quantities p(x), Δf, and γT, and explores the possibility of organizing quantum‑like, classical‑like, and gravitational‑like behaviors within a common structural framework. The implementation numerically reproduces key structural components of the TSH formulation, including: the Δf–γT phase diagram the structural potential Φstruct the structural force Fμ=−∇μΦstruct(Δf,γT) mass‑dependent boundary behavior irreversible transitions across phase boundaries the evolution of the thickness‑field p(x) The simulator directly integrates the dynamical terms appearing in the compact covariant action, providing a computational environment for examining the structural behavior encoded in the TSH framework. Interpretation of the Dynamics The dynamical equation implemented here can be viewed operationally as: **“Next‑step trajectory = spreading tendency from −∇μln⁡p structural force determined by Δf and γT.”** −∇μln⁡p: spreading tendency (Bohm‑type behavior) Δf: structural degree of freedom associated with interference and nonlocality γT: structural degree of freedom associated with contraction and localization Fμ: structural force determined by the Δf–γT phase diagram Through this balance, the simulator produces behaviors that may resemble: quantum‑like spreading (Stable region) classical‑like trajectories (Composite region) gravitational‑ or measurement‑like localization (Core region) What the Simulator Computes The code performs the structural feedback cycle: (p(x),Δf,γT)t→Fμ→uμ(t+δt)→(p(x),Δf,γT)t+δt This realizes the loop: phase → structural force → motion → update → phase as suggested by the structural formulation. Characteristics of the Implementation uses the structural potential defined in the TSH formulation reproduces the three structural regions from the same phase diagram exhibits irreversible transitions when crossing structural boundaries visualizes interference‑like, classical‑like, and collapse‑like behavior follows the compact covariant action used in the theoretical formulation The simulator is intended as a computational tool for exploring the structural dynamics implied by the TSH framework. TSH Physics Engine (Structural Interaction Framework) The repository includes a structural physics engine capable of handling a variety of behaviors—quantum‑like, classical‑like, relativistic, and interaction‑related—within a single structural field p(x) and the associated structural variables Δf and γT. Because the structural action depends only on these internal variables, standard interaction tensors can be incorporated in a compatible way without modifying the structural equations. This allows the engine to accommodate: Standard Model–type sectors GUT‑like sectors effective string‑theoretic fields fluid or condensed‑matter tensors within the same structural framework. Computational Properties The structural formulation reduces the need for multiple PDE solvers and enables efficient GPU execution: single O(N) update loop no Navier–Stokes, Schrödinger, or GR field equations phase‑diagram‑based force evaluation real‑time simulation for large systems These properties allow the simulator to explore regimes that are typically difficult to compute within conventional formulations. Physics Engine (simulation, games, research) & AI Physics Engine (learning, optimization, universe editing)https://github.com/ababphysics/TSH/ xhttps://x.com/abab162535