◉ Particles
Particles as geometric seats (torus knots / packages on S³). The public multiplet card separates what is core-ready from what is structural only — with explicit N/A and forbidden silent fills. Core narrative: v2.15 three books + dual generation tracks.
Writing rule
Keep columns separate: label · sector · dual · path · m_dyn · abs MeV · quantum numbers. Never paste the electron dual onto a hadron. Never sell pack units as MeV without an identity package. Continuum hold is not required for the electron row.
Generation & flavour (honesty)
- μ/τ: Route E Willmore ladder (ratios vs data) parallel to S⁷ Foot structure — Foot δ is [E INPUT] and Foot K/L is [E] algebra of that input.
- Not other torus knots for μ/τ; not proton = T(2,3) theorem.
- Quarks are SM lobe/channel labels — not free eᵢ. Heavy multiplet membership (FL-HEAVY) is parked after lab H1–H6.
- Equivalence is to measurements (charges, moments, spectra, scaling), not to three live quarks or virtual photons. A probe of an intact proton has not counted three quarks. See /framework.
v1 multiplet card (Q1b)
Modelled| Column | ElectronT(1,1) | Hadronic candidateT(2,3) |
|---|---|---|
| Sector | L0 leptonic ground | H programme |
| Dual pack | ≈(0.07, −0.65) force seat | N/A (no L0 paste) |
| m_dyn | pack units (not MeV alone) | N/A until O-H-pack |
| Abs MeV | lab check / m_Mach under P_EMC | N/A — not proton theorem |
| Q / j / FD | Q=±e, j=½, FD under packages | Q, j, FD open |
| Core-ready | Yes | No (structural) |
- Proton = T(2,3) theorem — forbidden
- μ/τ as other knots at the same bag — forbidden
- Route E Willmore ladder for charged-lepton ratios — the formula is Barut 1979; coefficient origin open
Core Concepts
Neutrino Coframe
The triad of bulk, neck, and fibre is packaging. The notice-pair Δm² figures are algebra. PMNS, including δ_CP, stays open. The absolute scale stays open.
Spin-½ from Topology
Exchanging two T(1,1) seats on the Hopf atlas picks up a phase of π. This is the topological origin of half-integer spin. Finkelstein–Rubinstein theorem applied.
Fermi–Dirac Statistics
Follows from the FR phase. Identical topological particles cannot occupy the same seat. The Pauli exclusion principle is a theorem, not a postulate.
The Electron
The electron is T(1,1) under named packages: spin type from cover geometry [E]; mass and charge are not a zero-parameter mint (α and a remain leftovers).
Antiparticles
An antiparticle is the topological mirror of its partner: T(p,q) ↔ T(q,p) with opposite orientation. The live pair vertex is the instantaneous placement, not a thermal bubble.
Spin–Statistics Theorem
Integer-spin particles commute (boson), half-integer anti-commute (fermion). Derived from the FR phase and Hopf atlas exchange.
Particle Spectrum Skeleton
The allowed T(p,q) with gcd(p,q)=1 give the particle spectrum. Mapping to known particles: T(2,3)=proton, T(3,2)=neutron, T(1,1)=electron.
Mass Hierarchy
Why is the muon 207× heavier than the electron? The mass hierarchy of leptons and quarks from torus knot geometry. Open investigation.
Quark Model
Quarks as fractional-winding knots confined by the knot lattice. Colour confinement from the topology of the S³ lattice.
The 24×24 Golden Torus Hadron Spectrum
Lifting ℤ[i] to the Clifford torus on S³ decomposes the 120-vertex 600-cell into 4 Golden Rays (φ⁰, φ¹, φ², ∞), organizing 102 hadrons with 2.57° median offset, eliminating 2D Fermat gaps via Lagrange's four-square theorem, and deriving √2 mass swings on diagonal seats. Banked under [M packaging].