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

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YANG-MILLS MASS GAP — COMPLETE DOCUMENTARY SERIES
Documents I–VII · Interactive Simulator · Numerical Data
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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 Mathematics
Institute. The series traces the evolution of a proposed resolution strategy
based on the negative curvature of the gauge orbit space, from its original
formulation through multiple rounds of critical refutation, correction, and
refinement.

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DOCUMENT STRUCTURE
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DOCUMENT I — Original Proposal (yang-mills-mass-gap.html)
Establishes the core strategy: the mass gap emerges from the strictly
negative curvature of the gauge orbit space B = A/G, via a quantum
Bochner inequality applied to the Yang-Mills Dirac operator. Introduces
the 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 (DH
localization requires supersymmetry in pure YM), two are partially
conceded with corrections, and one is successfully defended.

DOCUMENT V — Practical Applications (aplicaciones-practicas-yang-mills.html)
Demonstrates that mathematical tools M1–M4 produce concrete, verifiable
numerical 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.

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INTERACTIVE SIMULATOR (Simulador.html)
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Open Simulador.html in any modern browser (no server or dependencies
required). 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 ≈ 0.01126
documented in the accompanying CSV and PNG files.

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SUPPLEMENTARY DATA
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• 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)

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HONEST DIAGNOSIS (Document VII)
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After seven documents, four rounds of refutation, and all corrections
incorporated, 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), spectral
numerical convergence (Δ ≈ 0.01126 in lattice simulations with 139
eigenvalue pairs), and empirical validation of the derived constant
κ ≈ 0.1127 in volcanic eruption prediction (see related Zenodo
publication by the same author).

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RELATED WORK
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This documentary series is the mathematical foundation for the NXE
framework. The empirical validation of the NXE framework in volcanic
eruption 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 volcanic
eruption predictions, emerges as exactly 10 times the lattice mass gap
Δ ≈ 0.01126 measured in these simulations (10Δ ≈ κ).

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AUTHORSHIP & LICENSE
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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)