DUT Universal Simulator v2.2: Advanced Cosmic Dynamics & Meta-Checks

Physical Model for Gravitational Potential

The gravitational potential within the core is described by the equation:

V(r,t) = V₀·e^-α·r · cos(ω·r + $\phi_0$(t)) + β·(1 - e^-r)·r^-1

Where: $V_0$ = oscillation amplitude, $\alpha$ = exponential decay rate, $\omega$ = angular frequency, $\phi_0$(t) = animation phase (time-dependent), $\beta$ = central potential coefficient (singularity-free), r = normalized radial distance. This model inherently avoids singularities at the origin.

Dynamic Entropic Gradient and Information Gravity

The entropic gradient ∇S(r,t) is conceptually derived from the potential and local density:

∇S(r,t) ≈ - (dV/dr) · $\rho$(r,t)

Where: dV/dr is the derivative of the gravitational potential, and $\rho$(r,t) is the local density, assumed to decay exponentially with radial distance and time for illustrative purposes. A "causal boundary" is shown where $\rho$(r) becomes negligible. **Thermodynamic information gravity** is modeled by coupling the entropy gradient with metric deformations: $\delta G_{\mu\nu} \sim \nabla_\mu S \nabla_\nu S$.

Quantum Metric Regularization & Theory of Everything (TOE) Precursor

This simulator conceptually integrates components for the dynamic metric tensor ($g_{\mu\nu}(r,t)$), including quantum vacuum pressure and entropic stratification, towards a unified stress-energy tensor. This aims to explore scenarios where singularities are avoided through thermodynamically consistent formulations. The conceptual Einstein Field Equation is:

G_μν + Λg_μν = 8πG (T_μν^matter + T_μν^vacuum + T_μν^entropy)

A conceptual **quantum decoherence rate** is also calculated, simulating the loss of quantum coherence near the core due to gravitational interactions and thermal dissipation. The **total DUT Hamiltonian** is conceptually represented by the sum of energies associated with gravity, quantum fields, and entropy: $H_{total} = H_{GR} + H_{QG} + H_{entropy}$.

Note on Advanced Simulations

For full resolution of dynamic tensor equations and 3D/4D rendering with spatial voxelization at high fidelity, migration to cloud supercomputing platforms using technologies such as WebAssembly (WASM), CUDA, JAX, or PyTorch would be necessary. The current implementation focuses on conceptual models and enhanced 1D visualizations in a browser environment.