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 D²_YM. 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 (H^s 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 α_s(μ) via β₀ (beta function coefficient)• Ricci curvature shift with configurable strength c_R• 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, Λ_QCD, β₀, C₂(G), c_R, ε_IR 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• huella_digital_mass_gap.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" ([](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)