The Topology of the Standard Model from First Principles: A Derivation of the Canonical Braid Atlas

The quantum numbers of the Standard Model (spin, charge, family) are experimentally verified but theoretically unexplained. We present a theory that derives these properties from a deeper, information-theoretic foundation: the Universal Generative Principle (UGP). We model fundamental particles as topologically stable, braided worldlines on a discrete substrate. A consistent description ties the UGP arithmetic identifiers (GTE triples) to an effectively complex-valued c component, whose phase carries chirality—the observable signature of a dual-operator evolution \T, T^ for matter versus antimatter, with chirality as a dynamical, path-dependent property. This framework yields a kinematic dictionary—the GTE Rosetta Stone—mapping braid "phenotype" (writhe, strand count, crossing number) to the complex triple "genotype," fixed by Lorentz, SU(3), and SU(2) symmetry with an explicit pipeline in Appendix B. The Canonical Braid Atlas v2.0 summarizes derived topological fingerprints for all fundamental fermions, extended here to composite hadrons and massive electroweak bosons. Electric charge (Theorem C-W): Q = W_g/N_c for each SM fermion class is machine-checked (BraidAtlas.ChargeTheorem: sm\_charge\_leptons, zero sorry, ugp-lean); anomaly cancellation yields W_g = N_c(N_c-3) iff N_c=3, certifying colour rank (anomaly\_cancellation\_forces\_Nc\_3). Braid winding pattern from N_c: the winding set \N_c-1,-1,0,-N_c for the SM at N_c=3 is derived algebraically (BraidAtlas.ChargeDerivation: sm\_winding\_numbers\_from\_Nc, y\_ql\_unifies\_vv\_and\_winding), closing the kinematic consistency between hypercharge bookkeeping and braid charges. Nine light-baryon (a,b,c;g) triples are Lean-certified (BraidAtlas.CompositeTriples, zero sorry). Companion results on gauge-sector rigidity and RCC closure over all compact simple groups appear in PSC and deeper-theory manuscripts; see the companion formalization paper .