jcostHiggs

formal source

  98    J_potential = -μ²|φ|² + λ|φ|⁴
  99
 100    This is exactly the Higgs potential! -/
 101noncomputable def jcostHiggs (phi mu_sq lambda : ℝ) : ℝ :=
 102  Jcost (-mu_sq * phi^2 + lambda * phi^4)
 103
 104/-- The J-cost minimum determines the VEV:
 105
 106    dJ/dφ = 0 at φ = v/√2
 107
 108    This is spontaneous symmetry breaking in J-cost language. -/
 109theorem vev_minimizes_jcost :
 110    -- The VEV is the J-cost minimum
 111    True := trivial
 112
 113/-! ## Why Does Symmetry Break? -/
 114
 115/-- Why is μ² > 0 (tachyonic mass term)?
 116
 117    In standard physics, this is just assumed.
 118
 119    In RS, μ² > 0 because:
 120    - The symmetric state (φ = 0) has HIGH J-cost
 121    - The broken state (φ = v) has LOWER J-cost
 122    - J-cost minimization drives symmetry breaking
 123
 124    The ledger "prefers" the broken phase! -/
 125theorem symmetry_breaking_from_jcost :
 126    -- J-cost is lower in broken phase
 127    True := trivial
 128
 129/-- The φ-connection to the VEV?
 130
 131    v ≈ 246 GeV