IndisputableMonolith.Physics.HiggsBosonFromJCost
This module links the J-cost function to the Higgs boson by defining the recognition vacuum at J(1)=0 as the Higgs VEV at equilibrium. It supplies supporting declarations such as higgs_vacuum, higgs_mass_positive, and HiggsBosonCert that interpret the Cost module in physical terms. The module serves physicists working on Recognition Science derivations of particle masses. It contains no proofs and functions as a collection of definitions and certificates.
claimThe recognition vacuum is the equilibrium point satisfying $J(1)=0$, identified with the Higgs vacuum expectation value. Related declarations establish positivity of the associated mass and symmetry properties under the J-cost.
background
Recognition Science starts from the single functional equation whose solutions yield the J-cost, defined in the imported Cost module as $J(x)=(x+x^{-1})/2-1$. This module sits in the Physics domain and uses that J to interpret the vacuum. The supplied module doc-comment states the core identification: the recognition vacuum J(1)=0 corresponds to the Higgs VEV at equilibrium. Upstream results consist solely of the Cost module that supplies the J function and the Recognition Composition Law.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the Higgs sector entry point that later mass and symmetry results in the same file build upon. It directly implements the module doc-comment linking J-cost equilibrium to the Higgs VEV, placing the construction inside the Recognition Science derivation of particle properties from the forcing chain and phi-ladder. No downstream uses are recorded in the supplied graph.
scope and limits
- Does not derive the full Higgs potential or quartic term.
- Does not compute a numerical Higgs mass value.
- Does not address gauge boson masses or electroweak mixing.
- Does not connect to the eight-tick octave or spatial dimension D=3.