IndisputableMonolith.Physics.HiggsBosonFromJCost
The module establishes the recognition vacuum J(1) = 0 as the Higgs vacuum expectation value at equilibrium. It imports the Cost module to ground Higgs-related definitions in the J-cost framework. Physicists deriving particle properties from recognition principles cite this for the vacuum state. The module structure is definitional with no internal proofs.
claimThe recognition vacuum satisfies $J(1) = 0$, identified with the Higgs vacuum expectation value at equilibrium.
background
Recognition Science derives physics from the J-cost function satisfying the Recognition Composition Law. The upstream Cost module defines $J(x) = (x + x^{-1})/2 - 1$ and supplies the zero at argument 1. This module applies that zero-cost point to the Higgs field in the forcing chain setting from T0 to T8, with D = 3 dimensions and phi-ladder mass scaling.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the vacuum condition that feeds HiggsBosonCert and sibling results such as higgs_vacuum and higgs_mass_positive. It realizes the link from J-cost to the Higgs boson, consistent with the mass formula yardstick * phi^(rung - 8 + gap(Z)) and constants G = phi^5 / pi.
scope and limits
- Does not derive numerical values for the Higgs mass.
- Does not address gauge interactions or decays.
- Does not incorporate quantum corrections or renormalization.