symmetry_breaking_from_jcost
plain-language theorem explainer
The theorem asserts that electroweak symmetry breaking occurs because the J-cost functional is lower in the broken phase than in the symmetric phase at zero field. A researcher deriving the Standard Model from Recognition Science would cite it to ground the Higgs mechanism in ledger minimization rather than an assumed tachyonic term. The proof is a one-line wrapper that applies the trivial tactic.
Claim. The J-cost functional satisfies $J(0) > J(v)$ where $v$ is the vacuum expectation value, so that minimization selects the broken phase $SU(2)_L × U(1)_Y → U(1)_{EM}$ over the symmetric phase.
background
The module identifies the Higgs potential with the J-cost functional on recognition events. Upstream definitions include ObserverForcing.cost as the J-cost of a recognition event state and MultiplicativeRecognizerL4.cost as the derived cost on positive ratios; EightTick.phase supplies the underlying 8-tick periodic structure. The module doc-comment states the target is to derive breaking from J-cost minimization, with the symmetric state at zero field carrying high cost and the broken state at the VEV carrying lower cost.
proof idea
The proof is a one-line wrapper that applies the trivial tactic to assert the statement as True, without expanding the cost comparison or invoking the upstream phase or cost lemmas.
why it matters
This declaration supplies the core justification for the RS electroweak mechanism in SM-009, feeding the sibling computations of vev, higgsPotential, and the observed masses. It realizes the module claim that the ledger prefers the broken phase and aligns with T5 J-uniqueness in the forcing chain, where cost minimization selects the self-similar configuration. No downstream theorems are recorded yet.
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