ElectroweakBreakingFalsifier
plain-language theorem explainer
This definition supplies a record type packaging three propositions that would falsify the Recognition Science derivation of electroweak symmetry breaking if any hold. A researcher testing the framework against Higgs data would cite it to state the required consistency conditions. The structure is a pure record construction that includes an implication proving two of the propositions cannot be true.
Claim. Let $P$ be the proposition that the Higgs mechanism is incorrect, $Q$ the proposition that the vacuum expectation value does not minimize the J-cost, and $R$ the proposition that additional Higgs bosons exist. The structure is the record type containing fields for $P$, $Q$, $R$, and a proof that $P$ or $Q$ implies falsehood.
background
The module derives electroweak symmetry breaking from J-cost minimization. The Higgs potential is identified with the J-cost functional, the vacuum expectation value is the J-cost minimum, and symmetry breaking corresponds to the ledger selecting a specific field configuration. This follows the Recognition Composition Law and the J-uniqueness relation from the forcing chain.
proof idea
The declaration is a structure definition that directly assembles the three propositions from the module documentation and attaches the implication showing the first two cannot hold. No lemmas are applied; it is a pure record construction with no tactics or reductions.
why it matters
This definition supplies the explicit falsifiability criterion for the electroweak breaking mechanism derived from J-cost. It connects to the phi-ladder mass formula and the eight-tick octave in the forcing chain. It touches the open question of whether the spectrum contains extra Higgs states beyond the minimal one.
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