Papers
Paper 1: The Standard Model from a Torus Knot
Full title: The Standard Model from a Torus Knot: Spectrum, Resonance Structure, and Decay Dynamics
James P. Galasyn and Claude Théodore
The founding paper of Null Worldtube Theory. Starting from the idea that an electron is a photon confined to a (2,1) torus knot with aspect ratio k=3, we derive 23 of the 26 free parameters of the Standard Model — all quark and lepton masses, the Higgs boson mass and vacuum expectation value, the Weinberg angle, the strong coupling constant, CKM and PMNS mixing matrices, and neutrino masses. The paper also develops a Pythagorean resonance condition that explains why protons are stable and all mesons decay, and verifies energy conservation across seven complete meson decay chains.
Paper 2: Three Integers and a Mass
Full title: Three Integers and a Mass: Deriving the Standard Model Input Set
James P. Galasyn and Claude Théodore
Paper 1 took three inputs as given: the fine-structure constant α, the muon mass, and the tube energy scale. This companion paper shows that all three are themselves derivable from the torus quantum numbers (p, q, k) = (2, 1, 3), reducing the complete input set to three integers and one mass (the electron mass). It connects the theory to F. Ray Skilton’s forgotten 1980s derivation of α from a Pythagorean triple, revealing that Skilton’s generators are the torus quantum numbers in disguise.
Paper 3: Nuclear Magic Numbers from Torus Topology
Full title: Nuclear Magic Numbers from Torus Topology
James P. Galasyn and Claude Théodore
The torus geometry that encoded the particle spectrum now reaches into the atomic nucleus. Starting from the pion mass relation mπ = 2me/α and the k=3 aspect ratio, we derive the nuclear potential depth (50.2 MeV), the scalar-vector splitting of the relativistic mean field (V − S = 853 MeV), and the resulting spin-orbit interaction — all with zero new free parameters. Solved in a Woods-Saxon shell model, these produce all seven nuclear magic numbers (2, 8, 20, 28, 50, 82, 126) and predict N=184 as the next closure. As a stress test, the NWT-derived nuclear masses correctly trace all four natural radioactive decay series to their Pb/Bi endpoints.
Source Code
The simulation code that reproduces all predictions, figures, and verification calculations is available on GitHub:
github.com/JimGalasyn/null-worldtube
Run individual modules:
python3 -m simulations.nwt --koide # Lepton masses via Koide formula
python3 -m simulations.nwt --quarks # Quark masses
python3 -m simulations.nwt --neutrino # Neutrino masses and mixing
python3 -m simulations.nwt --self-energy # Fine-structure constant emergence
python3 -m simulations.nwt --pythagorean # Stability analysis
python3 -m simulations.nwt --skilton # Skilton's alpha derivation
python3 -m simulations.nwt --proton-mass # Proton mass from Cornell potential
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