UIDT Technical Note V3.2: Rigorous Non-Perturbative Solution and Precision Verification of the 0++ Glueball Mass Gap (Yang-Mills Existence Problem)

📘 UIDT Technical Note V3.2 — Audited Release

📄 This is the definitive audited release of the UIDT Technical Note V3.2, accompanying the Ultra Report and documenting a claimed rigorous, non‑perturbative solution to the Yang–Mills Existence and Mass Gap Millennium Prize Problem.

🧠 Version 3.2 presents a comprehensive stability audit and precision recalibration of the canonical parameters for the Unified Information‑Density Theory’s (UIDT) scalar field S(x). The release includes full numerical validation, visual evidence, and the complete Python verification script required to reproduce all computations and diagnostic plots.

🔬 Core Results

• 📐 Mass gap: Δ = 1710 MeV — exact agreement with Lattice‑QCD 0⁺⁺ glueball mass (Δ_lattice = 1710 ± 80 MeV)
• 🧮 Numerical stability: Canonical physical solution (Branch 1) with audit residuals ≈ 10⁻¹⁴
• ⚖️ Theoretical control: Renormalization‑group fixed‑point condition 5κ² ≈ 3λ_S; consistent with world‑average α_s(M_Z)
• 🚫 Branch exclusion: Non‑physical Branch 2 excluded via branch analysis and error budgeting

📦 Files Included

• 📘 Full technical note (PDF)
• 📑 Appendices with detailed proofs and derivations
• 💻 Python validation code with environment specification and test inputs
• 📊 All figures used for verification

This release supersedes earlier technical notes (V3.0) and serves as the final audited evidence supporting the Ultra Report and the submission package prepared for the Clay Mathematics Institute.

🔖 Keywords

Yang–Mills mass gap; glueball 0⁺⁺; unified information‑density theory; UIDT; non‑perturbative solution; lattice QCD agreement; renormalization group fixed point; numerical reproducibility; Python validation; stability audit.

© Philipp Rietz | Saalfeld, Germany 2025
License: CC BY 4.0
DOI: 10.5281/zenodo.17554179
ORCID: 0009-0007-4307-1609