module module moderate

`IndisputableMonolith.StandardModel.ElectroweakBreaking`

Module defining the Higgs sector in Recognition Science units: the Mexican-hat potential, vacuum expectation value, and the resulting W/Z and Higgs masses. A Standard Model theorist would cite it for the RS-native vev and mass ladder. Definitions and a minimization claim for the J-cost of the Higgs field; no deep forcing proofs live here.

claimThe module packages the Higgs potential $V(H)$, the vacuum expectation value $v=\langle H\rangle$, the observed $v$, Higgs mass $m_H$, $W$ and $Z$ masses $m_W,m_Z$, the ratio $m_W/m_Z$, and the J-cost of the Higgs configuration, together with the claim that the vev minimizes that cost.

background

Recognition Science works in RS-native units with $c=1$ and a discrete ledger whose cost is the J-functional $J(x)=(x+x^{-1})/2-1$. The golden ratio $\phi$ is forced by self-similarity of that ledger (PhiForcing). Masses sit on a $\phi$-ladder relative to a yardstick.

This module sits in the Standard Model layer. It introduces the usual electroweak Higgs potential and the associated vacuum expectation value, then ties the Higgs configuration to the J-cost so that the physical vev can be read as a cost minimizer. Observed masses ($m_W$, $m_Z$, $m_H$, $v$) appear as named constants for comparison with the RS ladder.

Upstream material is thin: Constants supplies the RS time quantum; Cost supplies $J$; PhiForcing supplies the forced $\phi$. No full electroweak Lagrangian is reconstructed here.

proof idea

Primarily a definition module. It declares the Higgs potential, vev, mass parameters, and the J-cost of the Higgs field, then records a minimization statement that the physical vev minimizes that cost. No multi-step forcing chain or uniqueness argument is developed in-module; any nontrivial claim is a short algebraic or calculus check against the potential and $J$.

why it matters in Recognition Science

Gives the Standard Model electroweak breaking data a home inside the RS monolith so later mass-ladder and coupling work can cite a single vev and $W/Z$ ratio. Downstream use is not yet wired in the graph (no used_by edges). It does not itself force $D=3$, the eight-tick octave, or $\alpha$; those remain in the T0–T8 chain and related modules. The link of interest is whether the J-cost minimum recovers the observed vev scale on the $\phi$-ladder.

scope and limits

Does not derive the Higgs potential from the Recognition Composition Law or T0–T8.
Does not prove uniqueness of the electroweak vacuum beyond a local J-cost minimum claim.
Does not compute running couplings or full one-loop electroweak precision observables.
Does not force $m_W$, $m_Z$, or $m_H$ from $\phi$ alone without external yardstick input.
Does not include Yukawa sector or fermion mass generation.

depends on (3)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import
IndisputableMonolith.Foundation.PhiForcing module_import

declarations in this module (25)

def higgsPotential L51
def vev L55
def vev_observed L59
def higgsMass L62
def higgsMass_observed L66
def wBosonMass L73
def zBosonMass L78
def wZRatio L83
def mW_observed L89
def mZ_observed L90
def jcostHiggs L101
theorem vev_minimizes_jcost L109
theorem symmetry_breaking_from_jcost L125
theorem vev_higgs_ratio L138
theorem vev_higgs_ratio_not_one L146
theorem hierarchy_problem L162
theorem rs_hierarchy L179
def goldstoneBosons L196
theorem photon_massless L203
theorem observed_wz_mass_hierarchy L208
def higgsDiscovery L225
def higgsFermionCoupling L235
def higgsGaugeCoupling L236
def summary L248
structure ElectroweakBreakingFalsifier L262