GOLS Lab 10 — Coupled Order Lattice System (COLS) Project Series

GOLS Lab 10 Beta — Coupled Order Lattice System (COLS) Project Series
This release presents GOLS Lab 10, an interactive environment derived from the Coupled Order Lattice System (COLS) — a new mathematical framework that unifies discrete modular arithmetic and continuous geometric order. Within COLS, the GOLS triangle is the geometric embodiment of modular relationships: each integer exponent n becomes a resonance point where number theory unfolds into geometry (A(n), hₚ, h_q, E_uni, E_bi). The Lab visualizes symmetry breaking and mixed-torus equidistribution in real time, bridging discrete residues and continuous harmonic patterns

COLS_Lab10_User_Manual_V2025

COLS_paper_V8_FINAL

Contents: papers (COLS_paper_V8_FINAL.pdf, COLS_additional_proofs_FINAL.pdf), user manual, and self-contained HTML labs (COLS_Lab10.html, COLS_Torus_M275_Smooth_V28.html) fully self-contained, (no external dependencies).

COLS_Lab10

. Runs locally in any modern browser, deterministic and reproducible.

Live interactive demo: https://ericpouhier-netizen.github.io/GOLS-Lab10/

Keywords: COLS, GOLS, modular geometry, discrete–continuous bridge, number theory visualization, CRT, resonance, symmetry breaking.