33-Universality-Lock-DSC3

Paper 33: The Universality Lock — Computational Confirmation of S4 Universality

Authors: Bryan Daugherty, Gregory Ward, Shawn Ryan
Date: April 2026
Engine: DSC-3 Isomorphic Engine v0.15.0, NVIDIA RTX 6000 Ada (48 GB VRAM)
DOI: 10.5281/zenodo.19453118

Abstract

Four GPU-accelerated experiments on the DSC-3 Isomorphic Engine establish a computational lock on the universality constant Omega = 24 = |S4|. At N = 5,000 and N = 10,000 spins in maximally frustrated dense spin glasses, the engine's three-tier stagnation hierarchy (designed at a 24:1 Kramers ratio) is fully activated at every seed and restart with zero exceptions. A step-budget sweep confirms that solver quality peaks at exactly the tier-3 window (3,000 steps), validating the 24:1 ratio as the efficiency optimum. Three additional experiments connect this lock to the Clay Millennium Prize problems: an exceptional-lattice phase diagram showing only the Leech proxy (degree = 24) exhibits a finite-temperature transition; Monster/Leech spectral indistinguishability at 0.37%; and 100% GUE in Navier-Stokes Jacobians at all Reynolds numbers.

Key Results

Experiment	Result	Significance
Universality Lock	Omega = 24.00 +/- 0.000 at N = 5K and 10K	Twelfth path to 24
Step-Budget Sweep	Quality peaks at 3,000 steps (tier-3)	24:1 ratio is optimal
Fine Lattice T_c	Only Leech (deg=24) has finite-T transition	E8/Golay show no transition to T=0.001
Monster vs Leech	0.37% energy difference, identical classification	Spectral indistinguishability
NS GUE	8/8 = 100% turbulent GUE, beta = 0.94 +/- 0.06	Strongest BGS evidence

Files

File	Description
main.tex	LaTeX source (882 lines, 4 figures, 6 tables)
main.pdf	Compiled paper (15 pages)

Connections to Prior Papers

• Paper 04 (Omega=24): Computational confirmation of uniqueness theorem
• Paper 05 (U24 Programme): Each experiment maps to a Millennium Problem
• Paper 12 (NS): Extends Re range to 10,000, confirms Ginibre/GUE consistency
• Paper 22 (Goldilocks): N* vs N_c comparison
• Paper 29 (H2=0): Topological mechanism for S4 emergence

Reproduction

All experiments can be reproduced on the DSC-3 engine:

# Universality threshold
cargo run --release --features "full gpu" --example universality_threshold -- --quick

# Stagnation sweep
cargo run --release --features "full gpu" --example stagnation_sweep

# Fine lattice T_c
cargo run --release --features "full gpu" --example lattice_fine_tc

# Monster vs Leech
cargo run --release --features "full gpu" --example monster_dimension -- --quick

# Navier-Stokes GUE
cargo run --release --features "full gpu" --example navier_stokes_extreme -- --quick

Live demo: https://dsc3.originneural.ai

Citation

@article{dwr2026_universality_lock,
  title={The Universality Lock: {$\Omega = 24.00 \pm 0.00$} --- Computational Confirmation of {$S_4$} Universality Across Six Millennium Prize Problems},
  author={Daugherty, Bryan and Ward, Gregory and Ryan, Shawn},
  year={2026},
  note={Paper 33, DSC-3 Engine v0.15.0}
}