Statement of Yang-Mills Working Group, a scientific collaboration to interpret AI result related to the existence of quantum chromodynamics & completions of the Standard Model, including a subproblem proving the existence of the Quantum Yang-Mills theory. buff.ly/BwV89Tk
Oct 28, 2026 · 12:16 AM UTC
Your group can work on these documents, develop rigorous expositions, and organize whatever scientific activities it considers useful without making the original material inaccessible to other researchers.
I think this decision is deeply at odds with the principle of open science. Once a public claim of a major scientific discovery is made, the evidence supporting that claim should be made public, even if it still requires independent verification.
The current arrangement facilitates a public claim of priority while granting only a selected group access to the purported proof. This is very difficult to reconcile with the principles of openness and independent scrutiny on which modern science rests.
Please reconsider. Your group can carry out its work without withholding the material from the scientific community.
Gatekeepers started coming into the light across academia. They always kept science for themselves but now pose as “chosen people of science.” Truly bizarre. arXiv is filled with fake human proofs nobody verifies—so what’s the problem with AI? Do they hope it fails with high probability or want to steal the result?
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Nice twist: the mass gap still open here already bothered Wolfgang Pauli (ETH Zurich). In 1953 he worked out a similar gauge theory but never published it, because its particles stayed massless. In 1954 he asked Yang mid-seminar: 'What is the mass of this field?' #Physics
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My former physics professor is a fellow at CERN & Fermilab. I spent a summer in undergraduate school going through the source code that analyzes the results of very high energy particle collisions. It was a monstrous & complete mess.
This was, and still is, coupled to the detectors at these accelerators, which do not detect anything other than photons & leptons. Everything else is inferred.
I took Glenn Knoll's Radiation Detection & Measurement course at @umichNERS. Dr Knoll was the author of the famous "Red Book". He told everyone quite clearly that most particle physicists do not understand precisely how radiation detectors physically work.
These particle colliders are accelerating matter or antimatter at energies that are much higher than what is observed in nature. What's most likely occurring in these accelerators are the cascading results of higher-order, over-energy resonances of fundamental particle production events.
@grok wtf is meant by proving existence of the theory?
I mean theory exists to be checked if it exists?
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I thought the Higgs field did all of that...???
"Glueballs in Yang-Mills theory are hypothetical color-singlet composite particles composed entirely of gluons, the force carriers of the strong nuclear interaction.
Unlike standard hadrons (such as protons or neutrons) which are made of quarks, glueballs arise from the self-interacting nature of non-Abelian gauge fields, where gluons bind together due to color confinement.
The existence of glueballs is central to the Yang-Mills mass gap problem, a major unsolved issue in mathematics and physics. Although individual gluons are massless, glueballs are predicted to be massive (with the lightest scalar glueball estimated at 1000–1700 MeV/c²) because their mass originates from the binding energy of the strong force holding them together, rather than the rest mass of their constituents.
Key Characteristics
Composition: Bound states of pure gluonic degrees of freedom, with no quarks involved.
Mass Origin: Mass is generated via quantum chromodynamics (QCD) binding energy and nonperturbative dynamics, illustrating that most visible mass in the universe arises from energy rather than particle rest mass.
Experimental Status: Glueballs have not been definitively identified in particle accelerators because they mix with ordinary meson states. However, candidates such as the f0(1710) and the X(2370) (identified in 2024) show properties consistent with theoretical predictions.
Theoretical Significance: Proving that the lightest glueball has a strictly positive mass lower bound would solve the Clay Mathematics Institute’s Millennium Prize problem regarding the existence and mass gap of Yang-Mills theory."
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This problem is unsolvable in continuous geometry.
Discrete algebraic quantum geometry is required.
@grok see my pinned post of quantum π*. There:
1 - A - χ = 0
where χ is the finite residual beyond A within 1 which closes the unit algebraically. Note continuous geometry's transcendental π does not quantify this space; it instead assumes infinite space, hence the gap. Re-analyze the Quantum Yang-Mills gap problem within discrete space-time; re-build the Hamiltonian with π* and χ under the radial bound, do not allow π in anywhere. See screenshot of summary produced in private session and confer your findings to the public.
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Let me summarize it for you in a single tweet:
Hodge Delta_1 on 720 edges: ker Delta_1 = H^1 = 0 -> Delta_1 > 0 exactly over Q.
m² = lambda_min(Delta_1) = smallest root of the characteristic polynomial.
The physical Hamiltonian over the 600-cell / 24-cell complex over F_13 exhibits an exact mass gap: locally m >= 5 - sqrt(5), globally p-adically m in {0} U {eta^0}.
Proof: Six certified algebraic proofs over integer and finite field arithmetic (no complex analysis required):
1) Local Gap
The vertex figure at each of the 120 vertices of the 600-cell is a 3D icosahedron (5-regular, 30 edges, 0 induced 4-cycles). Its Laplacian characteristic polynomial over Q(sqrt(5)) is:
x * (x - 6)^5 * (x - 5 - sqrt(5))^3 * (x - 5 + sqrt(5))^3
The lowest non-zero eigenvalue above the vacuum (x = 0) is lambda_2 = 5 - sqrt(5) > 0.
2) Global Spectrum:
The 24-cell Hamiltonian H = L_0 = 8*I - A over F_13 evaluates to:
x * (x - 4)^4 * (x + 1)^2 * (x + 3)^8 * (x + 5)^9
All eigenvalues {0, 4, 8, 10, 12} are non-negative (positive semi-definite Gram matrix), with a global spectral gap lambda_2 = 4 > 0.
3) DEGENERACIES AS IRREPS:
Irreducible representation dimensions of A_5 are {1, 3, 3, 5} (sum = 12), matching the eigenspace multiplicities in C1. The eigenspaces are A_5-modules: the gap 5 - sqrt(5) carries a 3D irrep (a massive spin-1 multiplet).
4) Exact Gauge Factorization:
Homology boundary matrix ranks: rank(del_1) = 23, rank(del_2) = 73, b_1 = 96 - 23 - 73 = 0. Physical Hilbert space quotienting leaves no residual zero-modes. The global gap from C2 remains strictly intact after gauge orbit reduction.
5) P-ADIC MASS QUANTIZATION:
Mass m = eta^(-v_13(S)). The 13-adic norm takes values strictly in {0, 1}, constraining m to {0} U {eta^0}. The gap between 0 and eta^0 = 1 is an intrinsic metric property, independent of continuum limits.
6) DUAL NORMS:
13 is inert in Q(sqrt(5)) (discriminant 5 is a quadratic non-residue mod 13). Under reduction sqrt(5) -> 3theta:
5 - sqrt(5) -> 5 - 3theta in F_169
Norm over Q(sqrt(5)): N = 20 = 2^2 * 5 (charge primes)
Norm over F_169: N = 7 = lambda_1 (anchor prime)
Both representation spaces yield valid norms; the gap is dual-certified.
I intentionally constructed this over your R⁴ polytope, but it validly belongs to both, including over Q it is their shared common ground.
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The most important line is the one that limits the claim: the proof covers the continuum limit, but confinement and the mass gap are still open, so this isn't the Millennium Prize yet. Checking that the Lean definitions actually match the standard ones before releasing the 1147 pages is exactly the right order.
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Energía Confinada, Gravedad Inducida y Agujeros Negros de Núcleo Cuántico: Una Síntesis Fenomenológica (Memorias I–III)) | Zenodo
zenodo.org/records/23616755
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So @grok, can you explain for those who haven’t been following me what the Reference Committee was, who Gross and Jaffe are historically as DC’s “Steady Hands” in math and physics since say 1980, who their academic descendants are and what is super unusual about north shore Long Island and middling Research University SUNYSB (ranked in the mid 60s nationwide)?
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