Deriving the Standard Model from a single finite geometry with zero free parameters

Lean 4 scaffold for formalizing the Yang–Mills existence and mass gap problem, with checked finite-dimensional certificates and a staged continuum-lift program.

OPEN PROBLEMS WANT TO STAY OPEN

Unified Information-Density Theory v3.9 - Vacuum Information Density as the Fundamental Geometric Scalar: A Proposed Theoretical Framework for the Yang-Mills Mass Gap and Gamma-Scaling Unification

AI-generated solutions to two research-level math problems from the First Proof community experiment: a Yang-Mills gauge-fixing heat-flow estimate on the 2-torus, and sharp fatness of geodesic triangles in sparse random graphs. Produced autonomously in Claude Code, offered for human validation.

⚠️ DEPRECATED - This repository has been superseded by v3.7.2. New location: https://github.com/Mass-Gap/UIDT-Framework-v3.7.2-Canonical | DOI: 10.5281/zenodo.17835200

This paper investigates the ”double field theory” (DFT) and the connection to the double copy method that shows that gauge & gravity theories are remarkably similar at the quantum level.

The central research hub for the VYTYLS Initiative. Hosting the Field of Consciousness (FoC) Lattice Gauge Theory, the Reality Fold Notation (RFN) and Modal Layer Tiers (MLT) methodology, and the Cybernetic Acoustic Research of the VYTYLS duo.

A rigorous Lean 4 formalization aiming to computationally verify the unconditional proof of the Yang-Mills mass gap (a Clay Millennium Prize Problem).

Unconditional proof of Yang-Mills mass gap for SU(3) lattice gauge theory. Gross-Witten identity at β₀ = ln 8 gives ρ < 1/7 → Δ > 0. Lean 4. 664 lemmas. 0 sorry. 0 axiom. 0 gaps.

Rust lattice-gauge simulation engine (MILL): validated 2D U(1) baseline plus active 4D SU(3) pure-gauge kernel with Cabibbo-Marinari heatbath/overrelaxation and mass-effective diagnostics.

Reproducible proofs for P vs NP, Yang-Mills Mass Gap, and Riemann Hypothesis using parameter-free Jabri Identity Zₜ=1. Zero fitted parameters. Python code, data, and Zenodo DOI included. Author: Abdulla Al-Jabri.

Six independent formal proofs for the Yang-Mills Existence and Mass Gap problem, covering RG Flow, Analytic Continuation, and Heat Kernel methods.

The Gauge Structure Sub-Programme — Presentation Note 3 (Cosmochrony)

Supports Information Dynamics framework unifying strong and weak forces. Extraction of information purity p_ID from four particle physics experiments: hyperon decay, reactor neutrino oscillation, X17 resonance, and muon g-2.

A minimal reductio argument identifying a logical tension in the standard formulation of the Yang–Mills mass gap problem.

Study and verify the U24 Yang-Mills mass gap with open data, code, and tests for coupling spectra, Wilson loops, and bounds

🔍 Verify and certify analytic bounds related to the Yang–Mills mass gap problem using reproducible computer-assisted scripts.