WordLength
The structure assigning a natural number length to each gauge skeleton and completion pair supports kernel specifications in mass modeling. Researchers in Recognition Science working on particle spectra would reference it for defining representation lengths. The declaration consists solely of a structure with one functional field and carries no additional proof obligations.
claimA word length structure consists of a map such that the output is a natural number for each gauge skeleton (with rational hypercharge, color representation boolean, and weak doublet boolean) and completion (with integers for the three multiplicity fields).
background
The module defines auxiliary structures for gauge representations in mass calculations. The gauge skeleton structure records the hypercharge as a rational number, a boolean flag for color representation, and a boolean indicating a weak doublet. The completion structure records three integer fields for multiplicities nY, n3, and n2.
proof idea
This is a structure definition introducing a single field that maps a gauge skeleton and a completion to a natural number. No lemmas or tactics are applied.
why it matters in Recognition Science
This structure supplies the type for length assignments in the kernel definitions of the masses module. It supports specification of lengths for mass formulas using the phi-ladder in the Recognition Science framework. With no recorded downstream theorems, it functions as a foundational type for mass kernel constructions.
scope and limits
- Does not provide any mechanism to compute specific length values from the inputs.
- Does not impose additional constraints or relations on the fields of the input structures.
- Does not reference the forcing chain or recognition composition law.
formal statement (Lean)
16structure WordLength where
17 len : GaugeSkeleton → Completion → Nat
18