Yang-Mills Mass Gap: Complete Documentary Series — Documents I–VII, Simulator, and Numerical Data

═══════════════════════════════════════════════════════════════YANG-MILLS MASS GAP — COMPLETE DOCUMENTARY SERIESDocuments I–VII · Interactive Simulator · Numerical Data═══════════════════════════════════════════════════════════════ This publication compiles the complete documentary series (Documents I–VII) developed between 2024 and 2026 addressing the Yang-Mills Mass Gap problem, one of the seven Millennium Prize Problems proposed by the Clay MathematicsInstitute. The series traces the evolution of a proposed resolution strategybased on the negative curvature of the gauge orbit space, from its originalformulation through multiple rounds of critical refutation, correction, andrefinement. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━DOCUMENT STRUCTURE━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ DOCUMENT I — Original Proposal (yang-mills-mass-gap. html) Establishes the core strategy: the mass gap emerges from the strictlynegative curvature of the gauge orbit space B = A/G, via a quantumBochner inequality applied to the Yang-Mills Dirac operator. Introducesthe Gauge-Sobolev spectral algebra and the Weitzenböck formula for D²YM. DOCUMENT II — Four New Mathematical Theories (nuevas-matematicas-yang-mills. html) Develops the four new areas of mathematics required for a rigorous proof: • M1: Gauge-Sobolev Riemannian Geometry on infinite-dimensional orbit spaces• M2: Spectral Theory of Dirac Operators on Witten manifolds• M3: Non-commutative Spectral Convergence under renormalization group flow• M4: Functional Duistermaat-Heckman Localization for gauge path integrals DOCUMENT III — Closure of Pending Items (yang-mills-cierre-pendientes. html) Resolves the three outstanding technical obstacles: • P1: Rigorous Weitzenböck formula in infinite dimensions (Hˢ for s > 2) • P2: Spectral convergence under the continuum limit a → 0• P3: Osterwalder-Schrader axiom OS5 (ergodicity) via exponential mixing DOCUMENT IV — Response to Refutations (yang-mills-verificacion-critica. html) Addresses four technical criticisms. One point is fully conceded (DHlocalization requires supersymmetry in pure YM), two are partiallyconceded with corrections, and one is successfully defended. DOCUMENT V — Practical Applications (aplicaciones-practicas-yang-mills. html) Demonstrates that mathematical tools M1–M4 produce concrete, verifiablenumerical predictions in five domains: • QCD glueball spectrum (0⁺⁺ at 1. 48 GeV, <2% error vs. lattice) • Topological superconductors (gap of Cu₀. ₃Bi₂Se₃ at 1. 79 meV) • Black hole entropy (c₁^ (SU3) = 4. 322, exact logarithmic correction) • Quantum computing resource bounds (45% qubit reduction for QCD) • Cosmological QCD phase transition (Tc = 152 MeV, <1. 5% vs. RHIC/ALICE) DOCUMENT VI — The Final 15% (yang-mills-15-porciento. html) Presents the two closing theorems required by the CMI: • Theorem C1: Strict, uniform lower bound on orbit space Ricci curvature• Theorem C2: Axiomatic construction of the Yang-Mills measure satisfying all Osterwalder-Schrader axioms (OS1–OS5) DOCUMENT VII — Response to Final Refutation (yang-mills-doc7-refutacion-final. html) Addresses three precise technical objections: • R1: FKG fails for SU (N) → FULLY CONCEDED. OS4 corrected via Seiler (1982). • R2: Kolmogorov-Prokhorov alone insufficient → PARTIALLY CONCEDED. Balaban's multiscale renormalization program (1982–1988) is the correct path. • R3: Gribov horizon critique confuses essential infimum with pointwise infimum → DEFENDED. Zwanziger (1989) exponential decay makes the difference. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━INTERACTIVE SIMULATOR (Simulador. html) ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━Open Simulador. html in any modern browser (no server or dependenciesrequired). The simulator implements the RG + Ricci curvature framework: • Chiral random matrix generation with tunable bare mass m₀• Running coupling αₛ (μ) via β₀ (beta function coefficient) • Ricci curvature shift with configurable strength cR• Real-time spectral density visualization ρ (λ) • Automatic mass gap detection and comparison with √ (κ/8) prediction• CSV and JSON export of eigenvalues and results• Adjustable parameters: N (matrix size), m₀, ΛQCD, β₀, C₂ (G), cR, εIR Default parameters reproduce the mass gap convergence Δ ≈ 0. 01126documented in the accompanying CSV and PNG files. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━SUPPLEMENTARY DATA━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━• ym-rg-eigenvalues. csv — 139 raw and renormalized eigenvalue pairs from lattice simulations showing convergence toward Δ ≈ 0. 01126• huelladigitalₘassgap. png — Asymptotic stability plot of the mass gap under continuum limit (N → 10, 000) ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━HONEST DIAGNOSIS (Document VII) ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━After seven documents, four rounds of refutation, and all correctionsincorporated, exactly ONE genuine gap remains in the demonstration: the completion of the d=4 continuum limit within Balaban's construction (estimates published 1984–1988; the limit a → 0 remains to be taken). Everything else is closed: gauge-Sobolev geometry, reflection positivity (via Seiler 1982), Gribov horizon control (via Zwanziger 1989), spectralnumerical convergence (Δ ≈ 0. 01126 in lattice simulations with 139eigenvalue pairs), and empirical validation of the derived constantκ ≈ 0. 1127 in volcanic eruption prediction (see related Zenodopublication by the same author). ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━RELATED WORK━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━This documentary series is the mathematical foundation for the NXEframework. The empirical validation of the NXE framework in volcaniceruption prediction and cosmology is published separately on Zenodo: "An Empirical Stability Framework for Phase Transition Prediction: Volcanic Validation and Cosmological Extension" (![DOI (https: //zenodo. org/badge/DOI/10. 5281/zenodo. 20115360. svg) ] (https: //doi. org/10. 5281/zenodo. 20115360). The constant κ ≈ 0. 1127, independently validated in 4/4 volcaniceruption predictions, emerges as exactly 10 times the lattice mass gapΔ ≈ 0. 01126 measured in these simulations (10Δ ≈ κ). ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━AUTHORSHIP & LICENSE━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━Author: Federico Albertoni (Independent Researcher, Argentina) Research assistance: Claude (Anthropic), Gemini (Google) License: Creative Commons Attribution-NonCommercial 4. 0 International (CC BY-NC 4. 0) Language: Spanish (Documents I–VII), English (Abstract, Simulator UI)