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 component, whose phase carries chirality—the observable signature of a dual-operator evolution , 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 ( .ChargeTheorem: \_charge\_leptons, zero , -lean); anomaly cancellation yields W_g = N_c(N_c-3) iff N_c=3, certifying colour rank ( \_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 ( .ChargeDerivation: \_winding\_numbers\_from\_Nc, \_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 ( .CompositeTriples, zero ). 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~.