IndisputableMonolith.StandardModel.ElectroweakBreaking
The module assembles definitions for the Higgs potential, vacuum expectation value, and associated boson masses in the Standard Model using J-cost minimization. Physicists constructing electroweak symmetry breaking from discrete self-similar ledgers would cite these objects. It consists of a collection of definitions and one-line lemmas that link the phi-ladder to observed vev and mass ratios.
claimThe Higgs potential is realized as the J-cost function $J_{ m Higgs}( u)$ on the vacuum expectation value $ u$, with $ u$ minimizing $J_{ m Higgs}$ and yielding $m_W$, $m_Z$, and $m_H$ via the phi-ladder scaling.
background
The module imports the RS time quantum $ au_0 = 1$ tick from Constants, the J-cost structure from Cost, and the forcing of $\phi$ by self-similarity in a discrete ledger from PhiForcing. PhiForcing states that $oldsymbol{ ext{This module proves that }oldsymbol{ ext{φ is forced by self-similarity in a discrete ledger with J-cost}}}$. Sibling declarations introduce higgsPotential, vev, jcostHiggs, and vev_minimizes_jcost, all expressed in RS-native units where $c=1$, $ar h=oldsymbol{ ext{φ}}^{-5}$.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the electroweak-breaking layer that connects T5 J-uniqueness and T6 phi fixed point to the Standard Model Higgs sector. It prepares the ground for mass formulas of the form yardstick $ imesoldsymbol{ ext{φ}}^{rung-8+gap(Z)}$ and for the alpha band constraint. No downstream theorems are recorded in the supplied graph.
scope and limits
- Does not derive the full SU(2)$\times$U(1) gauge Lagrangian.
- Does not compute running couplings or loop corrections.
- Does not address fermion mass generation or Yukawa sector.
- Does not prove stability of the potential beyond the listed minimizer.
depends on (3)
declarations in this module (25)
-
def
higgsPotential -
def
vev -
def
vev_observed -
def
higgsMass -
def
higgsMass_observed -
def
wBosonMass -
def
zBosonMass -
def
wZRatio -
def
mW_observed -
def
mZ_observed -
def
jcostHiggs -
theorem
vev_minimizes_jcost -
theorem
symmetry_breaking_from_jcost -
theorem
vev_higgs_ratio -
theorem
vev_higgs_ratio_not_one -
theorem
hierarchy_problem -
theorem
rs_hierarchy -
def
goldstoneBosons -
theorem
photon_massless -
theorem
observed_wz_mass_hierarchy -
def
higgsDiscovery -
def
higgsFermionCoupling -
def
higgsGaugeCoupling -
def
summary -
structure
ElectroweakBreakingFalsifier