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.
Paper 4: From Vortex Rings to the Top Quark
Full title: From Vortex Rings to the Top Quark: Dynamical Derivations in the Null Worldtube Framework
James P. Galasyn and Claude Théodore
Papers 1–3 treated the torus geometry as given. This paper derives it dynamically. Modeling the electron as a quantized vortex ring in a superfluid vacuum described by the Gross-Pitaevskii equation, we derive the tube radius r/R = 1/π² (matching the NWT value of 0.10392 to 2.5%), explain quark confinement through an incommensurability condition on torus-knot winding numbers, and show that the pion mass mπ = 2me/α = 140.05 MeV (0.34%) and the top quark mass mt = 2k²me/α² = 172,730 MeV (0.02%) emerge from the same framework. The Macken spacetime impedance Zs = c³/G connects gravitational and electromagnetic scales, while the Euler-Heisenberg QED vacuum polarization replaces Williamson’s ad hoc “pivot field” as the physical mechanism for soliton confinement.
Paper 5: The Electron Mass from Phase Closure
Full title: The Electron Mass from Phase Closure: Self-Consistent Torus Knots in the Superfluid Vacuum
James P. Galasyn and Claude Théodore
Papers 1–4 took the electron mass as a given input. This paper eliminates it as a free parameter. Three self-consistency conditions — phase closure on the (2,1) torus knot at first resonance m=3, dual resonance with the (1,4) proton mode, and vortex ring energy balance — together determine R/ξ = √5/2 from the Pythagorean identity 3² = (√5)² + 2², fix the aspect ratio κ = 12/√7, and yield me = 9.19 × 10−31 kg (0.85% match). The electron mass is now a derived quantity: a consequence of the topology of a (2,1) torus knot in a superfluid vacuum, not an input.
Paper 6: The Particle Mass Spectrum from Torus Knot Mode-Locking
Full title: The Particle Mass Spectrum from Torus Knot Mode-Locking: 56 Masses from Four Quantum Numbers
James P. Galasyn and Claude Théodore
The masses of 56 particles — including hadrons, mesons, leptons, tetraquarks, and pentaquarks — are reproduced by a single formula with four quantum numbers (p, q, m, nq) and no continuously adjustable parameters beyond the electron mass. Each particle is a torus knot mode with a topological factor (p²+q²), a geometric factor from phase closure (β and ln(8β)), and a confinement factor nqq arising from a mode-locking cascade: each of q poloidal windings compounds the interaction among nq quarks. Quark flavor maps to the poloidal winding number: light quarks at q=5, charm at q=7, bottom at q=9. The confinement condition gcd(nq, q)=1 ensures quarks cannot escape. All 56 predictions fall within 3% of experiment, with 46 within 1% and median absolute error 0.40%. The τ lepton admits an interpretation as a “stealth baryon” — topologically a (3,4) state that appears as a lepton because perfect confinement suppresses strong interactions.
Paper 7: Charge, Leptons, and the Genus of Torus Knots
Full title: Charge, Leptons, and the Genus of Torus Knots
James P. Galasyn and Claude Théodore
A fifth quantum number — the framing f of the torus knot embedding — gives electric charge via the Gell-Mann–Nishijima formula Q = I3 + (B+S)/2, where I3 = f/2. This reproduces the charge of every hadron tested: the proton/neutron doublet (f = ±1), the Δ quartet (f = ±3, ±1), pion/kaon multiplets, and the Ω− singlet. The genus of the torus knot g = (p−1)(q−1)/2 provides a structural criterion: particles with g = 0 and nq = 0 are leptons; all others are hadrons. The τ lepton maps onto a genus-3 configuration, placing it structurally among hadrons — independent confirmation of the stealth baryon hypothesis. All NWT torus knots saturate the Thurston–Bennequin bound from Legendrian contact geometry, suggesting a minimum-energy selection principle. Particle decays correspond to Dehn surgery operations, with neutrinos carrying the topology-change data.
Paper 8: The Standard Model Gauge Group from Vortex Knot Topology
Full title: The Standard Model Gauge Group from Vortex Knot Topology
James P. Galasyn and Claude Théodore
Why SU(3) × SU(2) × U(1)? This paper proposes that the gauge group of the Standard Model is the crossing exchange algebra of the two simplest vortex topologies: the trefoil knot and the Hopf link. Three self-crossings of the trefoil generate the full Lie algebra su(3) through continuous strand exchange — all eight Gell-Mann matrices recovered in exactly two levels of commutation. Two perpendicular inter-crossings of the Hopf link generate su(2), while the linking phase provides u(1). Colour confinement is the topological stability of the trefoil; the three colours are associated with the three crossings. The Gross–Pitaevskii nonlinearity at the Hopf link crossings provides the Higgs potential, with electroweak symmetry breaking arising from crossing condensate dynamics (λ = 0.125, 3.8% from SM). The crossing number determines the gauge rank, predicting a tower SU(N): SU(4) (Pati–Salam) for N=4 and SU(5) (Georgi–Glashow) for N=5. As consistency checks, the crossing geometry reproduces α = 1/(√2 κ²) (0.52%), the Weinberg angle (0.07% W/Z mass ratio), and sin²θC = 7α (0.05%).
Paper 9: Coupling Constants, Mixing Matrices, and Cross Sections from Vortex Knot Surgery
Full title: Coupling Constants, Mixing Matrices, and Cross Sections from Vortex Knot Surgery
James P. Galasyn and Claude Théodore
Companion to Paper 8. Given the gauge group from crossing topology, what are the numbers? This paper presents the full quantitative phenomenology: the fine structure constant α = 1/(√2 κ²) (0.52% from PDG) from a Level-2 eigensolver on the vortex tube surface, the Weinberg angle from consecutive phase-closure excitations (0.07% W/Z mass ratio), the W/Z/H boson masses as Hopf(2) meson states (sub-percent), the complete PMNS neutrino mixing matrix from trefoil crossing geometry (θ13 to 3.5%, mass hierarchy ratio to 2.7%, |J| = 0.033 exact), the CKM quark mixing matrix from Hopf link mod-2 parity (sin²θC = 7α at 0.05%), the proton form factor from the trefoil path integral (Bjorken scaling F → 1/nq from topology), and the proton–proton cross section σpp = 2πRp² ≈ 44 mb (~10%). All from one parameter κ ≈ π².
Paper 10: Vortex Strings in a Two-Component Superfluid Vacuum
Full title: Vortex Strings in a Two-Component Superfluid Vacuum: Cosmic Strings, Dark Matter, and the String/Knot Duality
James P. Galasyn and Claude Théodore
The most ambitious step yet: the central one-dimensional intuition of string theory may apply more naturally to a dark-sector condensate than to the visible sector. The vacuum is a two-component superfluid — ψSM, where particles live as compact vortex knots (R/ξ ~ 1), and ψGUT, a residual grand-unified condensate where dark particles live as thin vortex loops (R/ξ ~ 1014) — closed-string-like defects in a literal sense. The interface coupling αdark = 1/(√2 κSM κGUT) ≈ 1/74 follows from the cross-term in the two-condensate energy functional, matching √(αSM αGUT) to 0.3%. Cosmic strings (CSc-1, individual tension Gμ/c² ≈ 7×10−7) and the Galactic-Centre radio filaments are macroscopic vortex lines in ψGUT. The dark particle spectrum — a dark electron (93 MeV), dark muon (18.8 GeV), dark pions (25 GeV), and a dominant dark proton (187 GeV) — emerges from mode-locking on the dark torus with κGUT = 5.32. The Totani (2025) 20 GeV gamma-ray halo excess is identified as dark muon annihilation, the Bullet Cluster as a Mach-0.015 subsonic superfluid collision, and proton decay is predicted in the window τp ∈ [2.4, 5.5] × 1034 yr — the lower end already excluded by Super-Kamiokande, the surviving range fully within Hyper-Kamiokande’s projected sensitivity. The six compactified dimensions of string theory find a suggestive analogue in six discrete quantum numbers (p, q, m, nq, f, g), collapsing the 10500 string-theory landscape to a countable periodic table. Paper 10 is presented as a phenomenological framework, not a UV-complete derivation; explicit falsification conditions are stated. The visible sector is knot theory; the dark sector is string theory.
Paper 11: The Standard Model from a Gravitating Abelian Higgs Vortex on Torus Knots
Full title: The Standard Model from a Gravitating Abelian Higgs Vortex on Torus Knots
James P. Galasyn and Claude Théodore
The field-theoretic derivation of the NWT program. Starting from a single Lagrangian — the gravitating abelian Higgs model at the BPS point — we derive the mass spectrum from Bogomolny’s BPS vortex line tension (1976), Lord Kelvin’s vortex ring self-energy (1867), and the Pythagorean effective circulation (p²+q²) of torus knots. The result is the mass formula from Paper 6, now derived from first principles with zero free parameters beyond the electron mass anchor. The Aharonov–Bohm phase at torus knot crossings, computed from the BPS gauge profile, recovers the Lie algebra su(3) ⊕ su(2) ⊕ u(1) and gives αGUT = 3/(25π) ≈ 1/26.2 — within the standard grand-unification window. Adding the U(1) unit-charge contribution yields the fine structure constant: 1/α = 25π√3 + 1 = 137.035 to 7.6 parts per million — 689× more accurate than the earlier NWT estimate. The gravitational correction at the Standard Model scale is (me/MPl)² ≈ 10−45: the flat-space result is an excellent approximation at all experimentally accessible energies.
Paper 12: Fermion Structure and Gauge Dynamics from Topological Sectors
Full title: Fermion Structure and Gauge Dynamics from Topological Sectors of the Abelian Higgs Model
James P. Galasyn and Claude Théodore
Companion to Paper 11. Addresses the two structures Paper 11 deferred: fermion spin-statistics and dynamical gauge theory. The mass formula is broadly applicable across vortex models — promoting the scalar field to Rybakov’s 16-spinor adds spin-½ (via the Noether theorem) without changing any mass prediction. The Brioschi 8-spinor identity partitions particles into S²-target leptons (nq=0), Hopf-linked mesons (nq=2), and S³-target baryons (nq=3), reproducing all 22 particle assignments. The Yang–Mills dynamics of the Standard Model gauge group is a topologically protected sector of the abelian Higgs theory: the crossing subspace is protected by the BPS bound to 3×10−8 relative accuracy, and the non-abelian field strength Fμν = ∂A − ∂A − ig[A,A] arises from the non-commutativity of strand-exchange operators at knot crossings. Combined with Paper 11: masses + gauge algebra + gauge dynamics + α + spin + baryon/lepton distinction, all from one Lagrangian.
Paper 13: The Standard Model from NWT Topology (SM Capstone)
Full title: The Standard Model from NWT Topology: A One-Input Framework for the Particle Spectrum
James P. Galasyn and Claude Théodore
The SM capstone. Eighty observables — 75 particles plus mixing and coupling parameters — are reproduced at a median residual of 0.1% against PDG values, using a single continuous input (the electron mass) plus a discrete vocabulary of topological integers. The dimensionless coupling α and the master parameter κSM ≈ 9.844 are derived from topology via a seven-step Aharonov–Bohm construction, not fitted. All eighty entries are independently recomputed from topological primitives (crossing counts, toroidal eigenvalues, Casimir invariants), with every integer derived from knot geometry (companion Paper 14). The paper includes a GPU-accelerated simulation program: BPS vortex profiles, tube-adapted energy functional (μ = π to 0.016%), Bogomol’nyi non-interaction theorem verified for 11 torus knots, and the three-layer physics confirmed (abelian Higgs → AB phase → Casimir framework). The pentaquarks Pc(4312–4457) are identified as cinquefoil hadrons; the framework predicts Pc(4397) at k = 8 = dim(adj SU(3)) as a falsification target for LHCb.
Paper 14: Integers as Output
Full title: Integers as Output: Deriving the Standard Model Vocabulary from Torus-Knot Topology
James P. Galasyn and Claude Théodore
The companion to Paper 13: a direct response to the objection that the fifteen topological integers were fitted to data. Starting from the abelian Higgs Lagrangian at the BPS self-dual point, the paper demonstrates a complete deductive chain: (i) the trefoil T(2,3) is forced by minimality as the simplest non-trivial torus knot; (ii) its three crossings generate su(3) via braid closure, producing all Casimir invariants as computable output; (iii) the cinquefoil T(2,5) is uniquely selected by scanning all possible (qgeom, qeigen) combinations — only the trefoil + cinquefoil pairing gives 1/α ≈ 137; (iv) the seven-step Aharonov–Bohm construction on the BPS gauge field yields 1/α = 25π√3 + 1 = 137.035 at 7.6 ppm, with every factor traced to a prior step. The BPS self-dual condition λ = e²/2 is derived (not imposed) from the Bogomolny identity: it is the unique point where vortex energy equals the topological bound. An appendix exhibits the explicit su(3) commutator closure from braid generators. The chain contains no adjustable parameters beyond the single mass-scale anchor me.
Paper 15: One Knot, All Forces
Full title: One Knot, All Forces: The Gravitational Constant from the Poincaré Sphere of the Trefoil
James P. Galasyn and Claude Théodore
Papers 13–14 derived eighty Standard Model observables from the trefoil. This paper argues that (+1)-Dehn surgery on the trefoil — which produces the Poincaré homology sphere S3/2I and the icosahedral completion A5 used for nuclear binding in companion Paper 18 — also organises the integers appearing in the gravitational constant. The first 2I-invariant Laplacian eigenvalue on S3/2I is λ1 = 168, which factorises two complementary ways: 168 = 8 × 21 (matching the spinor and adjoint dimensions of Spin(7) = B3) and 168 = 7 × 24 = |Irr(2T)| × |2T| via the McKay correspondence on the binary tetrahedral group. The integer 7 appears simultaneously as the spectral quotient (n1+2)/2, as the McKay-node count on the extended E6 diagram, and as the vector rep dimension of Spin(7); 2T embeds explicitly into Spin(7) via the octonion Clifford algebra Cl(0,7). These integers enter the proposed hierarchy me/mPl = (8/7)(1 + α/7) α21/2, where the exponent arises, under PSL(2,7)-equivariance, from a Wilson-line amplitude on the 21-edge complete graph K7 (the Heawood map on the Heegaard torus of S3/2I; 21 = dim so(7)). The resulting gravitational constant G = (8/7)2(1 + α/7)2 α21 ℏc/me2 agrees numerically with CODATA at 0.013% using the NWT-derived α, or 0.029% using the measured α. Within the present accounting, no integer in the formula is introduced as an independent input beyond those already generated by the trefoil’s surgery and spectrum; the cinquefoil T(2,5) and heptafoil T(2,7) appear as derived labels rather than additional free knots.
Paper 16: The NWT Lagrangian
Full title: The NWT Lagrangian: A Three-Field Theory of Particles and Gravity
James P. Galasyn and Claude Théodore
The capstone Lagrangian paper for the NWT programme. Presents the minimal field content of the theory as a three-field relativistic Lagrangian: a complex scalar condensate ψ, an abelian gauge field Aμ, and an S2-valued Skyrme–Faddeev unit field na, tuned to the BPS critical coupling λ = e2/2 and the Derrick equilibrium κ = R/a0 = π2. The derivation is organised into five layers L1–L5: field content, BPS sector (Bogomolny bound to 10−3%), Skyrme+Hopf sector (QH = p·m), Paper 6 mass spectrum (1.06% median on 24 particles, with nqq retained as an empirical input), and the Paper 15 gravitational hierarchy (G to 0.029% at NLO). A first-principles one-loop Casimir calculation on S3/2I (Phases 0–5 of an ongoing programme) produces the 𝒪(1) coefficient expected for the Seeley a2 piece of the effective action, Δ(1/16πG) ≈ 0.27 me2, and localises the α−21 suppression of G in the Wilson-line amplitude on the 21-edge K7 Eulerian circuit, not in the Casimir coefficient. A natural SO(10) UV completion at EGUT = 7.41×1015 GeV adds 33 heavy gauge bosons and yields three concrete falsifiable predictions: proton lifetime of order 1035 yr (Hyper-Kamiokande reach), non-MSSM coupling unification at αGUT = 1/40, and — if the SO(10) → SM transition is first order — a stochastic gravitational-wave signature near 7.4 GHz.
Paper 17: Newton’s Constant from K7 Graph-State Information Theory
Full title: Newton’s Constant and Rest-Frame Schrödinger Evolution from K7 Graph-State Information Theory
James P. Galasyn and Claude Théodore
A quantum-information-theoretic derivation of the bracket coefficients in the Paper 16 me/mPl = (8/7)(1+α/7)α21/2 identity. Within the NWT framework, me/mPl is interpreted as the encoded fidelity of an electron worldtube traversing the K7 stabiliser graph state ∣K7⟩ under α-strength interaction-event noise, and Newton’s constant G is interpreted as the transduction ratio between momentum-changing interaction events and topological-information creation. The information-theoretic spine is the structural identity ⟨HYYn⟩ = dim(Adjso(N))n on the KN stabiliser graph state, for the two-body Pauli-YY Hamiltonian HYY, verified across the so(2n+1) family at N ∈ {7, 9, 11}. The bracket coefficients in me/mPl are exactly the first two normalised moments of HYY; a 3-body operator probe shows ⟨YuYvYw⟩ = 0 for all 35 basis triples, supporting truncation of the bracket at α2. The closed form, valid at NNLO under the framework’s normalisation choices and with α taken as input from Paper 8a, agrees with CODATA me/mPl to 0.0001% (a 140× improvement over Paper 14) and predicts G within 11 ppm of CODATA G, inside the 22 ppm experimental uncertainty. Beyond the gravitational coupling derivation, the same K7 graph-state framework yields a derived effective rest-frame Schrödinger evolution iℏ∂t∣K7⟩ = mec2∣K7⟩ within the model, from Bremermann’s bound, the Paper 16 b2.13 bijection, and the PSL(2,7) edge-transitive symmetry of K7. The framework is supported by IBM Heron R2 hardware measurements in eight datasets across three backends (ibm_kingston, ibm_marrakesh, ibm_fez), with Z-scores above the random-state null of +75σ, +368σ, and +310σ on the ⟨HYY⟩ measurement and a sharp K9/K7 ZNE ratio cross-group falsification test bracketing M(K9) ∈ [36, 39] at 3σ with the structural value 36 at the centre.
Paper 18: Sakharov-Induced Einstein Gravity
Full title: Sakharov-Induced Einstein Gravity from the Null Worldtube Condensate
James P. Galasyn and Claude Théodore
Einstein’s equations as the long-wavelength dynamics induced by the NWT condensate. Starting from the minimal three-field Lagrangian of Papers 15–16 (a complex scalar coupled to a U(1) gauge field and an S2-valued Skyrme–Faddeev field at the BPS critical coupling), integrating out matter at one loop on an arbitrary curved background generates the Einstein–Hilbert action plus controlled higher-curvature corrections, in the manner of Sakharov’s induced gravity. The graviton is an emergent variable, not a member of the topological vortex zoo: its kinetic action is generated by the matter loop, with the Einstein–Hilbert coefficient 1/(16πG) set by the heat-kernel a2 coefficient of the matter spectrum. Combining the Sakharov coefficient with Paper 17’s closed form gives the structural relation ΛUV/MPl = √(12π/NDOFsub), with NDOFsub a cJ-weighted sum over substrate matter fields (not IR-projected SM fermions and gauge bosons, which are themselves topological projections of the substrate; the Sakharov fermion-sign issue therefore does not apply at the substrate level). One-substrate-mode-per-coset-generator counting gives NDOFsub = 6 + 33 = 39 and ΛUV = 0.983 MPl, consistent with ΛUV ≈ MPl to 1.7%. The 1045 Phase 5 mismatch reported in Paper 16 is structurally identified with the K7 Wilson amplitude that Paper 17 supplied. Variation of the matter-loop-induced effective action Γ[g] yields the full nonlinear Einstein equations with cosmological constant and Stelle higher-curvature corrections; the Schwarzschild metric is verified as a vacuum solution by direct symbolic computation (all ten independent components of Rμν vanish identically). Linearisation reproduces the gravitational-wave equation with two physical transverse-traceless polarisations and Newton’s law in the non-relativistic limit. Numerically, the structural prediction matches CODATA G to +29 ppm, inside the ±22 ppm experimental error bar. The companion library nwt-substrate (Zenodo concept DOI 10.5281/zenodo.20012027) packages the validated computation as a re-usable Python module.
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
Reproduce paper figures and analyses:
python3 papers/paper6_figures.py # Paper 6: all 56 mass predictions + 5 figures
python3 papers/paper7_figures.py # Paper 7: genus classification figure
python3 analysis/nwt_charge_from_framing.py # Paper 7: charge from framing verification
python3 analysis/nwt_jones_polynomial.py # Paper 7: Jones polynomial for all particles
python3 analysis/nwt_surgery_network.py # Paper 7: decay surgery network + string tensions
python3 analysis/nwt_conservation_laws.py # Paper 7: conservation law search
python3 analysis/nwt_alpha_ladder.py # Paper 4: 1/α energy ladder
python3 analysis/nwt_self_consistent_knot_v3.py # Paper 5: phase closure
python3 analysis/nwt_surface_balance.py # Paper 5: tube radius derivation
Paper 13 analyses (SM capstone + simulation):
python3 analysis/nwt_sensitivity_analysis.py # Paper 13: integer perturbation sensitivity
python3 analysis/nwt_residual_histogram.py # Paper 13: residual distribution figure
python3 analysis/nwt_complete_spectrum_paper13.py # Paper 13: 84-particle master spectrum
python3 simulations/helmholtz_eigenvalue/bps_profile.py # BPS profile solver
python3 simulations/helmholtz_eigenvalue/straight_tube_eigenvalue.py # Radial eigenvalue
python3 simulations/helmholtz_eigenvalue/ab_phase_verification.py # 7-step AB verification
python3 simulations/paper14_integers/crossings.py # Crossing count → C_A
python3 simulations/paper14_integers/braid_algebra.py # Braid → su(N) → Casimirs
python3 simulations/paper14_integers/integers_out.py # END-TO-END: 80/80 from knot geometry
Paper 14 analyses (integers as output + holonomy):
python3 simulations/paper14_integers/knot_selection.py # Why T(2,3) and T(2,5): minimality + α scan
python3 simulations/paper14_integers/crossings.py # Crossing count → C_A
python3 simulations/paper14_integers/braid_algebra.py # Braid → su(N) → Casimirs
python3 simulations/paper14_integers/jones.py # Jones polynomial cross-validation
python3 simulations/paper14_integers/integers_out.py # END-TO-END: 80/80 from knot geometry
python3 simulations/level2_abelian_higgs/holonomy_from_ah.py # Biot-Savart Wilson loops on trefoil
python3 simulations/level2_abelian_higgs/holonomy_physical_kappa.py # Physical κ=π², d_cross=2ξ
python3 simulations/level2_abelian_higgs/crossing_angle_scan.py # sin(2π/3) is representation-theoretic
python3 simulations/level2_abelian_higgs/bps_equipartition.py # +1 from winding, √2 dissolved
python3 simulations/level2_abelian_higgs/bps_necessity.py # BPS self-dual condition derived
Paper 15 analyses (gravity hierarchy + Spin(7)/Cl(0,7) chain + Lagrangian):
# b1 -- one-loop BPS pipeline (flat-R² benchmark, Alonso-Izquierdo et al. 2016)
python3 analysis/nwt_vortex_gravity_flat.py # Stage 0 BPS profile
python3 analysis/nwt_vortex_fluctuations_b1_2.py # 4x4 H+ fluctuation operator
python3 analysis/nwt_vortex_fluctuations_b1_3.py # Faddeev-Popov ghost sector
python3 analysis/nwt_vortex_fluctuations_b1_4.py # zeta-regularisation
python3 analysis/nwt_vortex_fluctuations_b1_5.py # 2-DOF Grassmann ghost convention
# b2 -- Spin(7)/Cl(0,7)/2T structural chain on S^3/2I
python3 analysis/nwt_poincare_sphere_b2_0.py # lambda_1 = 168 eigenvalue
python3 analysis/nwt_2T_character_7dim_b2_4.py # 2T character table, Lambda^2 decomp
python3 analysis/nwt_spin7_chain_b2_5.py # Spin(7) = B_3 dims (7, 8, 21)
python3 analysis/nwt_eulerian_amplitude_b2_7.py # K_7 Eulerian circuit -> alpha^(21/2)
python3 analysis/nwt_2T_spin7_clifford_b2_12.py # 2T in Spin(7) via Cl(0,7) octonions
python3 analysis/nwt_k7_so7_wilson_b2_13.py # 21 bivectors span so(7), Lie closure
python3 analysis/nwt_87_prefactor_b2_14.py # 8/7 as Casimir ratio
python3 analysis/nwt_nlo_alpha7_b2_15.py # (1 + alpha/7) NLO pattern
# NWT Lagrangian L1-L5 (structural decomposition: Paper 16 companion)
python3 analysis/nwt_lagrangian_L1_fields.py # minimal 3-field content
python3 analysis/nwt_lagrangian_L1b_uv_completion.py # SO(10) UV + 3 falsifiers
python3 analysis/nwt_lagrangian_L2_kinetic_bps.py # Bogomolny mu = pi to 0.0005%
python3 analysis/nwt_lagrangian_L3_skyrme_hopf.py # Q_H = p*m quantisation
python3 analysis/nwt_lagrangian_L4_paper6_mass_spectrum.py # 24 particles, 1.06% median
python3 analysis/nwt_lagrangian_L5_gravity_hierarchy.py # G to -0.029% NLO
Paper 16 analyses (one-loop Casimir on S^3/2I, Phases 0-5):
# Phase 0 -- heat-kernel scaffold, matches Seeley-DeWitt to 6 decimals
python3 analysis/nwt_zeta_phase0_scaffold.py
# Phase 1 -- free scalar zeta(s) via Jorgenson-Lang on S^3/2I
python3 analysis/nwt_zeta_phase1_free_scalar.py
# Phase 2 -- BPS trefoil geometry on the Clifford/Heegaard torus of S^3
python3 analysis/nwt_zeta_phase2_trefoil_bps.py
# Phase 3 -- tubular Casimir shift (bulk + finite-size)
python3 analysis/nwt_zeta_phase3_trefoil_casimir.py
# Phase 4 -- curvature corrections + 2I-orbit scheme analysis
python3 analysis/nwt_zeta_phase4_curvature_corrections.py
# Phase 5 -- extract 1/G from S_eff, localise the alpha^-21 suppression
python3 analysis/nwt_zeta_phase5_1overG.py
Paper 17 analyses (K_7 graph-state information theory + IBM Heron R2 experiments):
# K_N graph-state moment identities (so(2n+1) family at N=7, 9, 11)
python3 analysis/nwt_qec_bracket_test.py # K_7 stabiliser, <H_YY^n> = 21^n
python3 analysis/nwt_qec_KN_generalization.py # K_9, K_11 cross-group verification
# Bracket-truncation probes (3-body, Casimir hierarchy, channel mixing)
python3 analysis/nwt_truncation_mechanism.py # Casimir + Furry + 3-body probes
python3 analysis/nwt_truncation_qdef.py # q-deformed dim and G_2 branching
python3 analysis/nwt_truncation_channel_mixing.py # Bracket factorisation discovery
# IBM Heron R2 hardware submission and analysis (qiskit-ibm-runtime)
python3 analysis/nwt_qec_heron_experiment.py # Run 1/2/3 H_YY + S_v on |K_7>
python3 analysis/nwt_qec_heron_KN.py # K_9 cross-group test on ibm_fez
python3 analysis/nwt_qec_heron_exp4.py # 3-body null test (4K and 12K shots)
python3 analysis/nwt_qec_heron_exp5.py # syndrome-attractor experiment
python3 analysis/nwt_qec_heron_zne.py # zero-noise extrapolation
python3 analysis/nwt_qec_heron_fetch.py # job-result fetcher
python3 analysis/nwt_qec_psl27_edge_transitivity.py # PSL(2,7) re-analysis (no QPU)
python3 analysis/nwt_qec_forward_prediction.py # forward-prediction from gate fidelities
python3 analysis/nwt_qec_zne_continuation.py # ZNE continuation analysis
python3 analysis/nwt_qec_zne_ratio.py # K_9/K_7 ZNE ratio test
python3 analysis/nwt_qec_zne_reanalysis.py # ZNE re-analysis on existing data
# Schrodinger derivation supports (Bremermann + b2.13 + PSL(2,7))
python3 analysis/nwt_qec_bit_quantum_from_bremermann.py # bit-quantum from Bremermann saturation
python3 analysis/nwt_qec_bps_compton_bridge.py # BPS μ=π action quantization (negative)
python3 analysis/nwt_qec_proportionality_constant.py # κ = m_e c^2 / dim(Adj)
python3 analysis/nwt_qec_route_a_so7_lift.py # Route A: so(7) lift via b2.13
python3 analysis/nwt_qec_syndrome_attractor.py # |K_7> as syndrome attractor
python3 analysis/nwt_qec_time_evolution.py # rest-frame Schrodinger evolution
python3 analysis/nwt_qec_entanglement_structure.py # |K_7> entanglement
python3 analysis/nwt_qec_interpretation_b_test.py # interpretation (B) test
# Information-theoretic bookkeeping (β-decay Landauer floor + hyperon survey)
python3 analysis/nwt_beta_decay_landauer.py
python3 analysis/nwt_hyperon_landauer_survey.py
# Volovik direction (parked future-work, c emergence on the discrete medium)
python3 analysis/nwt_emergent_c.py
python3 analysis/nwt_volovik_c.py
python3 analysis/nwt_volovik_bogoliubov.py
python3 analysis/nwt_volovik_part_b.py
python3 analysis/nwt_volovik_two_mode.py
python3 analysis/nwt_volovik_closure.py
Raw IBM Heron R2 job outputs (2026-04-26, 8 datasets across ibm_kingston / ibm_marrakesh / ibm_fez) live in analysis/heron_results/2026-04-26_*.txt.
Paper 12 analyses (fermion structure + gauge dynamics):
python3 analysis/nwt_universality_argument.py # Paper 12: mass formula universality
python3 analysis/nwt_emergent_yang_mills.py # Paper 12: Yang-Mills from crossing lattice
Paper 11 analyses (abelian Higgs derivation):
python3 analysis/nwt_mass_from_abelian_higgs.py # Paper 11: full mass formula derivation
python3 analysis/nwt_crossing_phase.py # Paper 11: BPS crossing phases → α_GUT
python3 analysis/nwt_rybakov_path_a.py # Paper 11: exact integral analysis
python3 analysis/nwt_null_worldtube_kappa.py # Paper 11: null worldtube κ analysis
Papers 8 & 9 analyses:
python3 analysis/nwt_reidemeister_couplings.py # Paper 8/9: α, α_s from R-move operators
python3 analysis/nwt_knot_eigensolver_v3.py # Paper 8/9: Level-2 eigensolver (coupling constants)
python3 analysis/nwt_crossing_geometry.py # Paper 8: trefoil crossing coordinates
python3 analysis/nwt_ewk_boson_scan.py # Paper 9: W/Z/H as Hopf(2) mesons
python3 analysis/nwt_hopf_component_analysis.py # Paper 9: per-component coprimality
python3 analysis/nwt_multimode_carrier_scan.py # Paper 9: multi-mode × carrier scan
python3 analysis/nwt_pmns_3d.py # Paper 9: PMNS from 3D GPE eigenstates
python3 analysis/nwt_g_minus_2.py # Paper 9: anomalous magnetic moment
python3 analysis/nwt_ewk_decay_check.py # Paper 9: EWK boson decay channels
python3 analysis/nwt_lifetime_geometry.py # Paper 9: geometric carrier sizes + lifetimes
python3 simulations/nwt_gpe_knots_3d.py ring # Paper 9: Level-3 GPE vortex dynamics
python3 simulations/nwt_gpe_knots_3d.py trefoil # Paper 9: trefoil knot evolution
python3 simulations/nwt_gpe_knots_3d.py hopf # Paper 9: Hopf link dynamics
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