ewBreakingChannel_count
plain-language theorem explainer
The theorem asserts that the electroweak breaking channel type has exactly five elements corresponding to the top, bottom, tau, W, and Z loops. Derivations of the Higgs vacuum expectation value from J-cost would cite this to set the channel count equal to the configuration dimension. The proof applies a decision procedure to the finite enumeration of the inductive constructors.
Claim. The finite type of electroweak symmetry breaking channels, consisting of the top-loop, bottom-loop, tau-loop, W-loop and Z-loop, has cardinality five: $|EWBreakingChannel| = 5$.
background
In the Higgs vacuum expectation value module, five canonical channels are defined for electroweak breaking: top-loop, bottom-loop, tau-loop, W-loop and Z-loop. These fix the configuration dimension at five and locate the vacuum expectation value near 246 GeV at the J-cost minimum for unit top Yukawa. The upstream inductive definition lists the five constructors explicitly.
proof idea
The proof is a one-line wrapper invoking the decide tactic, which computes the cardinality by enumerating the five constructors of the finite type.
why it matters
This count populates the five_channels component of the higgsVEVCert definition, completing the certification of the Higgs vacuum expectation value. It implements the five-channel structure required by the Recognition Science J-cost analysis for the electroweak scale. The result closes one step in the module's derivation without introducing additional hypotheses.
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