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 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 = Wg/Nc for each SM fermion class is machine-checked (. ChargeTheorem: \charge\ₗeptons, zero, -lean) ; anomaly cancellation yields Wg = Nc (Nc-3) iff Nc=3, certifying colour rank (\cancellation\forces\Nc\₃). Braid winding pattern from Nc: the winding set \Nc-1, -1, 0, -Nc\ for the SM at Nc=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~.