What question did this study set out to answer?

To explain the theoretical underpinnings of the Standard Model's quantum numbers using an information-theoretic approach.

June 11, 2026Open Access

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

Key Points

To explain the theoretical underpinnings of the Standard Model's quantum numbers using an information-theoretic approach.
Developed a model of fundamental particles as topologically stable, braided worldlines on a discrete substrate.
Used the Universal Generative Principle to derive particle properties, establishing a kinematic dictionary linking braid characteristics to particle identities.
Presented findings through the Canonical Braid Atlas summarizing topological signatures of fundamental fermions and composite hadrons.
Demonstrated that electric charge can be defined as Q = W_g/N_c for each SM fermion class, with anomaly cancellation confirming color rank.
Derived braid winding patterns algebraically for N_c=3, establishing a consistency between hypercharge bookkeeping and braid charges.
Validated nine light-baryon triples through Lean certification, contributing to a systematic theory of gauge-sector rigidity and structure.

Abstract

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~.

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