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Tau Universe KK — DiscoverPhysics World

A pure geometric 5D Kaluza-Klein world on R² × S¹ (compact fifth dimension)

This repository contains a new world definition for the DiscoverPhysics benchmark. It implements the core mechanism of the Tau Universe Framework: a single compact fifth spatial dimension realized as a circle S¹.

What This World Tests

The force law is a pure image-sum over periodic copies of particles along the compact fifth dimension (Kaluza-Klein construction). No extra fields or ad-hoc potentials are used — only geometry.

The world is designed to test whether structured periodic motion, particularly harmonics in the 142857 / 1/7 family, emerges naturally from the compact S¹ geometry. This is directly motivated by the periodic signals observed in JWST JADES high-redshift galaxy data.

Key Features

Pure Kaluza-Klein image-sum force law
Velocity Verlet integrator (symplectic)
Support for coherent rotating initial conditions
Includes the Yuan 2n3m preprocessing filter for harmonic enhancement
Full spectral analysis tools (raw + filtered)
Honest testing notes from extensive 2D pure-dynamics runs

Quick Start

from python.tau_world_patch import tau_world_pairwise_force
import numpy as np

positions = np.random.randn(12, 2) * 0.6
masses = np.ones(12)
forces = tau_world_pairwise_force(positions, masses, tau=0.7)

See the full submission package for complete code, YAML definition, documentation, and analysis tools.

Current Testing Status (Honest)

Extensive pure-dynamics testing was performed using velocity Verlet (up to 16,384 steps) with both random and coherent rotating initial conditions.

Findings:

The KK image-sum reliably produces structured low-frequency periodicity across particles.
In raw 2D position time series, dominant power appears at low frequencies (~0.018). The precise 1/7 fundamental is subtle.
The Yuan 2n3m filter improves results when applied to appropriate derived signals (radial distance, local density estimators), but does not help when applied directly to raw Cartesian position series.
These results are consistent with the framework’s expectation that the clean 142857 harmonics strengthen with scale, dimensionality (3D), varied masses, and longer coherence times.

Full testing notes are included in the submission package.

Files

The complete submission package (code + YAML + documentation + testing notes) is available here:

GitHub: Tau_Universe_DiscoverPhysics_Submission.zip

Attribution

Developed as part of the Tau Universe Framework by Ernest C. Gatlin III (Clay Gatlin).

This world is submitted in the spirit of open, falsifiable testing of geometric unification ideas. We welcome rigorous external validation or refutation.

License: MIT

Last updated: May 2026

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