⚠️ PRIORITY NOTICE — Please read NOTICE before using, forking, or adapting this work.
A constructive proof framework for the Yang-Mills Existence and Mass Gap (Clay Millennium Problem #4), developed by Lluis Eriksson between December 2025 and February 2026, comprising 68 publicly timestamped papers and this open-source mechanical verification tool.
Balaban RG Bridge (29 lemmas)
→ Kotecký-Preiss Polymer Convergence
→ Osterwalder-Schrader Axiom Verification (Mechanical Audit)
→ Wightman Reconstruction (Mass Gap Δ > 0)
| Resource | Link |
|---|---|
| 68 Papers (timestamped) | ai.vixra.org/author/lluis_eriksson |
| Zenodo DOI #1 | 10.5281/zenodo.18799942 |
| Zenodo DOI #2 | 10.5281/zenodo.18800920 |
| This Repository | github.com/lluiseriksson/ym-audit |
The full list of all 68 papers with viXra IDs, submission dates, and titles is available in the NOTICE file (Section 2).
Date range: December 16, 2025 — February 27, 2026
Key papers in the constructive pipeline:
| # | Date | viXra ID | Title |
|---|---|---|---|
| 68 | 2026-02-27 | 2602.0117 | Mechanical Audit Experiments and Reproducibility Appendix |
| 67 | 2026-02-20 | 2602.0096 | The Master Map: Audit-First Navigation Guide to the Yang-Mills Solution |
| 66 | 2026-02-19 | 2602.0092 | Rotational Symmetry Restoration and the Wightman Axioms |
| 65 | 2026-02-19 | 2602.0091 | Closing the Last Gap: Verified Terminal KP Bound and Clay Checklist |
| 64 | 2026-02-18 | 2602.0089 | Spectral Gap and Thermodynamic Limit via Log-Sobolev Inequalities |
| 63 | 2026-02-19 | 2602.0088 | Exponential Clustering and Mass Gap via Balaban's RG |
| 62 | 2026-02-19 | 2602.0087 | Irrelevant Operators and Anisotropy Bounds in Balaban's RG |
| 55 | 2026-02-14 | 2602.0069 | The Balaban-Dimock Structural Package |
| 54 | 2026-02-14 | 2602.0063 | Conditional Continuum Limit via Two-Layer Architecture |
| 45 | 2026-02-12 | 2602.0041 | Uniform Log-Sobolev Inequality and Mass Gap |
| 40 | 2026-02-08 | 2602.0033 | The Yang-Mills Mass Gap on the Lattice: a Self-Contained Proof |
| 1 | 2025-12-17 | 2512.0060 | Clustering, Recovery, and Locality in Algebraic QFT |
Cryptographic hashes of all 68 paper PDFs are published in this repository: eriksson_programme_sha256_hashes.txt
These hashes provide tamper-proof verification that the paper contents have not been modified after their public timestamp dates.
ym-audit/
├── LICENSE # AGPL-3.0
├── NOTICE # Priority declaration & attribution terms
├── README.md # This file
├── eriksson_programme_sha256_hashes.txt # SHA-256 hashes of all 68 papers
├── src/ # Core audit modules
│ ├── balaban_rg/ # Balaban RG lemma verification
│ ├── kotecky_preiss/ # Polymer expansion convergence
│ ├── os_axioms/ # Osterwalder-Schrader verification
│ └── wightman/ # Reconstruction theorem checks
├── tests/ # Automated test suites
└── docs/ # Technical documentation
git clone https://github.com/lluiseriksson/ym-audit.git
cd ym-audit
pip install -r requirements.txt
# Run the full mechanical audit pipeline
python -m src.audit --full
# Verify individual steps
python -m src.balaban_rg --verify
python -m src.kotecky_preiss --convergence-check
python -m src.os_axioms --reflection-positivity
python -m src.wightman --reconstruction
If you use this code, reference the architectural pipeline, or build upon The Eriksson Programme in any way, please cite:
@misc{eriksson2026yangmills,
author = {Eriksson, Lluis},
title = {The Eriksson Programme: Constructive Yang-Mills Mass Gap
via Mechanical Lemma-Audit},
year = {2025--2026},
howpublished = {viXra preprint series},
url = {https://ai.vixra.org/author/lluis_eriksson},
doi = {10.5281/zenodo.18799942},
note = {68 papers, Dec 2025 -- Feb 2026}
}
Any reimplementation of the architectural pipeline described above — in any programming language — must provide explicit attribution to Lluis Eriksson and The Eriksson Programme.
This includes but is not limited to:
- Academic papers that follow the same proof architecture
- Software that implements the same algorithmic audit logic
- Blog posts, presentations, or educational materials derived from this framework
- Translations of the code into other programming languages (Rust, OCaml, Haskell, Julia, Lean, C++, etc.)
Full attribution terms are specified in the NOTICE file under AGPL-3.0 Section 7(b).
Failure to attribute constitutes both academic misconduct and a violation of the AGPL-3.0 license terms.
The priority of The Eriksson Programme can be independently verified via:
| Source | What it proves |
|---|---|
| viXra submission metadata | Paper content + upload dates |
| Zenodo DOI records | Immutable DOI timestamps |
| GitHub commit history | Code development timeline |
| Wayback Machine | Third-party independent snapshots |
| SHA-256 hashes (this repo) | Cryptographic content integrity |
Copyright (C) 2025-2026 Lluis Eriksson
This program is free software: you can redistribute it and/or modify it under the terms of the GNU Affero General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Affero General Public License for more details.
See LICENSE for the full license text. See NOTICE for priority declaration and attribution requirements.
Mechanical audit experiments for a companion-paper programme on 4D SU(N) Yang–Mills existence and mass gap.
Papers archived at ai.vixra.org/author/lluis_eriksson.
git clone https://github.com/lluiseriksson/ym-audit.git && cd ym-audit
pip install -r requirements.txt
python run_audit.pyRuns 29 deterministic audit tests verifying load-bearing claims from the companion-paper programme (Papers 86–90, infrastructure, gauge proxies, UV-flow, non-triviality, toy model, and AQFT consequences). All 29 tests pass in ~70 s on a Colab CPU.
ANISO.Thm3.6.W4_Sym— W4 invariance of anisotropic harmonicANISO.h_aniso.Harmonicity— Laplacian harmonicity at c=3/2KP.Lem6.2.AnimalBound— Lattice-animal series convergenceMG.Prop6.1.Telescoping— Law of total covarianceOS1.LemB.Discretization_Oeta2— O(η²) finite difference errorP86.Prop4.1.CouplingControl_worstcase— RG coupling controlP87.Thm5.4.AnisotropyScaling_from_samples— Anisotropy scalingP90.Lem6.4.Superpoly_from_c_over_g2— Super-polynomial suppressionP90.Lem8.1.TriangularMixingLock_d4_exact— Triangular mixing lock
P89.Thm1.1.TerminalKP_geometric_series— Terminal KP convergenceP89.Lem6.1.ExpInequality— Elementary exponential inequalityP86.Thm6.3.UVSuppression_geometric— UV suppression geometric sumP87.Thm3.6.OneDimAniso_symbolic— 1D anisotropic sectorP87.Thm5.4.CauchyBound_perPolymer— Cauchy bound on polymer jetsP88.Thm4.2.VanishingRate_eta2log— OS1 vanishing rateP88.Lem4.4.LieAlgAnnihilation_SO4— Lie algebra annihilation ⇒ SO(4)P90.Lem6.2.KPMargin_explicit— KP margin sensitivity
GAUGE.Th4.1.PlaquetteExpansion_SU2— Strong-coupling Bessel expansionGAUGE.Prop4.3.PolyakovLoop_CenterSymmetry— Polyakov loop (exact Bessel)GAUGE.Sec5.CreutzRatio_Confinement— Creutz ratio ⇒ string tension
INFRA.RicciSUN.BakryEmery_N2_N3— Bakry–Émery Ric = N/4 for SU(2), SU(3)INFRA.B6.ScaleCancellation_d4— 2^{4k} cancellation in d=4INFRA.Flow.ColumnBound_d4— Heat-kernel ℓ² column bound
UVFLOW.Cor3.3.ParsevalIdentity— Parseval identity on d=4 torusUVFLOW.Cor3.3.DiagonalDecaySlope_d4— Diagonal decay exponent ≈ 2UVFLOW.Prop1.3.ReflectionCommutation— Flow–reflection commutation
P86.Thm8.7.NonTriviality_S4c— Haar MC on SU(2), SU(3): kurtosis ≠ 3TOY.2DYM.MassGap_SU2— 2D SU(2) YM exact mass gap (rel_err = 0)
AQFT.PetzRecovery.FidelityClustering_bound— Petz recovery fidelity bound
After running python run_audit.py:
| File | Description |
|---|---|
results.json |
Structured test results (status, timing, message) |
results.csv |
Tabular summary |
summary.md |
Human-readable Markdown report |
audit_figures.pdf |
Four-panel diagnostic figure |
audit_artifacts.zip |
Flat archive of all artifacts |
python export_overleaf_bundle.pyGenerates overleaf_bundle.zip containing LaTeX table fragments, provenance manifest, and data files for direct upload to Overleaf.
ym-audit/
run_audit.py # Single entry point: runs all 29 tests
export_overleaf_bundle.py # Generates LaTeX fragments + flat zip
requirements.txt # numpy, sympy, matplotlib, scipy
audit/
tests/
test_original_9.py # 9 original tests
test_core_chain.py # 8 core chain tests (P86–P90)
test_gauge.py # 3 gauge proxy tests
test_infrastructure.py # 3 infrastructure tests
test_uvflow.py # 3 UV-flow proxy tests
test_nontriviality_impl.py # Non-triviality (Haar MC)
test_toy_2dym.py # 2D YM toy model
test_aqft_petz.py # AQFT Petz recovery
- Python 3.8+
- numpy, sympy, matplotlib, scipy
AGPL-3.0 license