SMLagrangianSector
plain-language theorem explainer
The inductive type enumerates the four sectors of the Standard Model Lagrangian under the Recognition Science decomposition on the recognition manifold. Researchers deriving the full SM action from the J-cost functional equation cite it when assigning per-sector costs without cross terms at tree level. The declaration is a direct inductive enumeration that automatically derives decidable equality and finite cardinality.
Claim. The Standard Model Lagrangian decomposes into four canonical sectors: the gauge kinetic term, the fermion kinetic term, the Yukawa coupling term, and the Higgs potential term.
background
Recognition Science decomposes the SM Lagrangian on the recognition manifold into a skeleton of four sectors, each carrying a J-cost on its canonical deviation ratio. The module supplies the structural naming that unifies prior gauge-boson, Yukawa, and Higgs work into one object ready for the Wightman/OS bridge. Upstream definitions include the cost function induced by a multiplicative recognizer (J-cost on positive ratios) and the Higgs potential realized as J-cost on the field ratio, both of which are applied uniformly across the enumerated sectors.
proof idea
Direct inductive definition with four constructors; the derived instances for DecidableEq, Repr, BEq, and Fintype are generated automatically by Lean from the inductive structure with no explicit proof steps.
why it matters
This supplies the domain type for totalCost and SMLagrangianCert, which establish vacuum-zero and non-negativity properties for the summed Lagrangian cost. It fills the structural opening described in the module for tying GaugeBosonLagrangian, Yukawa, and HiggsPotential work into the Recognition Science chain toward A1 closure, matching the four-sector decomposition required for the full SM skeleton.
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