What Is TSH Engine

We are developing a Open-Source physics engine that utilizes three internal variables: expansion, contraction, and intensity of existence. These are based on the Thickness Structure framework. Designed as a simulation model that runs in real time on a GPU, the engine generates diverse behaviors internally as these variables change continuously. In this post, we will briefly introduce the calculations performed within the engine, focusing specifically on the implementation aspects.

• : Existence thickness: a scalar field with the structural property of "existence thickness." Both the state observed as quantum-like spreading and the state observed as gravitational localization are described on a unified basis as differences in the structural states taken by , , and .

• : Degree of freedom in the spreading direction

• : Degree of freedom in the contracting direction

The phase diagram

• Stable (quantum‑like): large , small
• Composite (classical‑like): moderate , moderate
• Core(gravitational‑like/measurement): small , large

These variables move continuously along the phase diagram.

Depending on their position, the system’s behavior automatically switches between “quantum‑like,” and “classical,‑like” and “gravitational‑like” states.

The updated and trace a path across a smoothly curved phase diagram. This diagram defines different computational regimes, and the engine blends between them continuously rather than switching abruptly.

Toy Model: The Core Structural Equation

The core of the TSH Engine relies on a single phenomenological equation to compute element trajectories:

• The left side represents relativistic covariant acceleration.
• The right side consists of two structural effects: "spreading" and "contraction."

This engine uses a phase diagram that smoothly curves due to the competition between expansion and contraction, similar to condensed matter physics, and performs calculations in the following sequence:

• thickness field → internal variables → phase diagram → structural force → motion

This results in the following equation:

• Trajectory at the next instant (left-hand side)
• = the quantum tendency to spread ()
• (+) the structural force () generated by the competition between spreading () and contracting ().

The TSH physics engine is the implementation of these principles as a physics engine.

What the GPU Computes Every Frame

For each element, the TSH Engine executes the following steps:

(1) Constructing the Thickness Field

We spread the thickness of each element using a kernel function to smoothly interpolate it as a scalar field:

(2) Updating Internal Degrees of Freedom

Using the thickness field and its gradient, we update (spreading) and (contraction).

(3) Determining Position on the Phase Diagram

The updated and are mapped onto the phase diagram to determine whether the element is in the Stable, Composite, or Core state. This is treated as a continuous transition, not a discrete switch.

(4) Computing the Structural Force

• Spreading term:
• Contraction term:

(5) Updating the 4-Velocity

We integrate the structural force over proper time to update the relativistic 4-velocity .

(6) Updating the Position

The position is updated using the new 4-velocity.

(7) Interaction Channels (If necessary)

Electromagnetic, strong, weak forces, etc., can be integrated by appending them to the right side of the equation.

In the GPU implementation, the proper-time increment is computed as so the update of the 4‑velocity remains consistent with the relativistic form used in the theoretical equation.

Features of the GPU Implementation

• neighbor search using a Spatial Hash.
• A single kernel that handles Stable / Composite / Core states without branching.
• Parallelization of the thickness field interpolation on the GPU.
• Proper-time-based 4-velocity updates.
• An architecture that allows stacking interaction channels. With this setup, we can run tens to hundreds of thousands of elements in real time.

Automated exploration loop

On the Python side, an AI observes the TSH Engine from the outside and automates tasks such as:

• Boundary search on the phase diagram.
• Identifying critical points of interference and contraction.
• Classifying stable and unstable regions.
• Scanning structural transitions.

The TSH Ultimate Simulator (ultimate_tsh_simulator.py)

This is not a simplified version of the TSH Engine, but rather a visualization tool that directly translates the mathematics defined in the paper (phase diagram, irreversibility, mass scaling) into 2D.

Local Deformation via Mouse The phase diagram slightly elevates near the mouse position . This is a direct visual representation of the "local structural response" described in the paper.

Global Deformation via Mass Changing the mass shifts the entire phase diagram up and down by . For lighter systems, the quantum-like region expands; for heavier systems, it narrows.

Visualized Quantities

• 1D profile of the thickness field
• interference‑like patterns
• Envelope contraction
• Current position on the phase diagram
• Stable / Composite / Core transitions
• irreversible behavior within the model to Core
• Mass scaling
• Local deformation by mouse

This serves as the most accessible visualization environment for intuitively understanding the internal computations of TSH.

Regarding Specifications

Details regarding the definition of internal degrees of freedom, the structure of the phase diagram, and GPU kernels are compiled in TSH_SPEC.md and TSH_EXEC.md on GitHub.