Particles: Kinks, Fields, Masses
How the abstract algebraic substrate becomes the particle zoo. The Φ_MDL field, BPS kinks as particles, quantum numbers from winding, and nine fermion masses at 0.295% RMS — derived, not fitted.
What you'll understand after this path
What Φ_MDL is — a Z₇-symmetric Klein-Gordon quantum field — and how it relates to the CMCA certificate. The field is the universe; the CMCA certifies it.
Why stable topological defects in Φ_MDL are exactly the Standard Model particles. No point particles inserted by hand — they are forced by the topology of Z₇.
How the GTE orbit's N-values {73, 42, 275} map to the electron, muon, and tau masses through the InformationMassTransformer — zero free parameters.
This path assumes you know what the polynomial p(L,C,R) = C+R−CR−LCR does
(L03), what MDL selection means (L02, L08), what GTE orbits are (L06), and the four
levels of the theory (L11). If any of those are unfamiliar,
start with Path 1 or
Path 2.
Lessons
The Φ_MDL Field
What is Φ_MDL? A Z₇-symmetric Klein-Gordon quantum field — the continuum substrate that the CMCA certificate specifies. The blueprint vs. the building.
The Three-Tape CMCA
From 1+1D to 3+1D: three CMCA tapes sharing a common clock τ_c. Why three tapes, what the Dimensional Protocol Principle forces, and how 3+1D spacetime geometry emerges.
Particles as Topological Kinks
A kink is a stable domain wall between two degenerate minima of V(Φ). Z₇ has seven minima → seven winding sectors → seven particle families. The particle spectrum is topological, not dynamical.
Standard Model Quantum Numbers
Where do electric charge, color, and weak isospin come from? All emerge from the Z₇ winding structure. The SM gauge group is the unique PSC-consistent gauge group — derived, not assumed.
Masses from Arithmetic
The InformationMassTransformer: N-values {73, 42, 275} from the GTE orbit → electron, muon, tau masses. Nine charged fermion masses at 0.295% RMS. The 1000-permutation null test confirms this is not numerology.
The GTE–Wolfram Bridge
How GTE relates to the Wolfram Physics programme. Where they agree (both: local rules, universal computation), where they differ (GTE adds the selection principle that Wolfram Physics lacks).