What question did this study set out to answer?

This research aims to derive the discrete gauge structure of the Standard Model from minimal inputs, exploring the limitations of the formulation.

June 13, 2026Open Access

The discrete skeleton of the Standard Model from a minimal subfactor: an economy result and the boundary where it stops

Key Points

This research aims to derive the discrete gauge structure of the Standard Model from minimal inputs, exploring the limitations of the formulation.
Utilized a minimality principle with an index-two subfactor.
Applied the Connes–Chamseddine noncommutative-geometry dictionary.
Incorporated empirical data on the chirality of weak interactions.
Derived the gauge algebra and fermion representations using three independent inputs.
Established a no-go theorem defining the boundary where the construction ceases.
Identified that continuous mixing parameters require a non-trivial modular flow absent in the minimal structure.

Abstract

The discrete gauge architecture of the Standard Model — the gauge algebra, the fermion representations, the hypercharge spectrum, and the generation count — is derived from a single structural input: the index-two subfactor, selected by a minimality principle. The derivation costs exactly three independent inputs: one minimality selection (the minimal Jones index, with the generating Ising fusion category following as a consequence by the A–D–E classification in the amenable setting), one imported translation (the Connes–Chamseddine noncommutative-geometry dictionary), and one empirical fact (the chirality of the weak interaction). A no-go theorem establishes the boundary where the construction stops: the discrete skeleton is the tracial (timeless) sector; masses, couplings, and continuous mixing parameters enter only with a non-trivial modular flow, which the minimal structure does not carry. This is companion paper I of a quartet; companion paper II (the bipartite hinge) develops the boundary; companion paper III (the closure vector) derives the forced mixing amplitudes; companion paper IV (the exhaustion theorem) proves the forced content is complete

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