total_terms
plain-language theorem explainer
The equality between the total count of Standard Model Lagrangian sectors and the main-term count plus one holds by direct evaluation of the fixed constants. Researchers deriving the SM structure from Recognition Science forcing chains would cite this to confirm the five-sector decomposition. The proof is a one-line decision procedure that checks the arithmetic identity on the predefined natural numbers.
Claim. In the Recognition Science model the total number of Standard Model Lagrangian sectors equals the number of principal terms plus one topological term: $5 = 4 + 1$.
background
The module decomposes the Standard Model Lagrangian into four main sectors (gauge kinetic terms for SU(3)×SU(2)×U(1), fermion kinetic terms for the Weyl fermions, Yukawa couplings, and Higgs potential) together with one QCD topological θ-term. This yields the relation 4 = 2^(D-1) for spatial dimension D, with the extra term bringing the total to five sectors. The upstream definitions fix mainTermCount at 4 and totalTermCount at 5.
proof idea
The proof is a one-line wrapper that applies the decide tactic to the numerical equality between the two constant definitions.
why it matters
The result supplies the total5 field inside smLagrangianCert, which certifies the overall SM Lagrangian structure. It closes the counting step that links the four main terms (2^2) to the Recognition Science eight-tick octave and the D = 3 spatial dimension derived from the forcing chain. No open scaffolding remains on this arithmetic identity.
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