Rigidity of the Standard-Model Charge Lattice

Overview Rigidity of the Standard-Model Charge Lattice develops a fixed-scope reconstruction theorem for charge quantization inside a declared Standard-Model bookkeeping skeleton. The paper asks a narrow structural question: Once the Standard-Model chiral skeleton, charged Yukawa operators, anomaly/tensor witnesses, conjugation structure, and admissible redescription rules are fixed, what kinds of charge assignments can function as standing-preserving bookkeeping data? Main Result The central result is that admissible charge assignments factor through a discrete additive charge lattice, unique up to: admissible redescription, global normalization, and overall sign. The theorem excludes continuous charge deformations, non-lattice fractional interpolations, additive offsets, hidden selectors, and inequivalent same-scope charge lattices as admissible alternatives. Physics-Facing Realization The physics-facing realization is the one-generation electroweak hypercharge system. Yukawa compatibility and anomaly constraints collapse the hypercharge assignments to a one-parameter family. The remaining parameter is absorbed into the U(1)YU(1)_YU(1)Y coupling. After fixing a primitive unit, electric charges occupy the familiar lattice, conventionally: 13Z\frac{1}{3}\mathbb{Z}31Z when Q(e)=−1Q(e)=-1Q(e)=−1. Standard quark charges are therefore admissible rational lattice points, not counterexamples to discreteness. Scope and Limits The paper does not claim to derive: the Standard Model gauge group from no premises, numerical gauge-coupling values, all possible ultraviolet completions, or unrestricted uniqueness across all conceivable gauge theories. Its claim is fixed-domain and reconstruction-theoretic: within the declared Standard-Model charge-reconstruction scope, any proposed same-scope alternative must either factor through the same charge quotient, collapse to bookkeeping-equivalent presentation, fail admissibility, or change scope. Contribution The paper introduces: a charge-transport certificate, a universal charge quotient, a partial-operator obstruction, and a rival-exhaustion argument. Together these establish the charge-lattice support theorem required by the downstream Standard-Model uniqueness architecture. This paper is downstream of: Minimal Conditions for Admissible Construction  The Structure of Admissibility