vacuumJCost

formal source

 102
 103    This is ~0.118, not the suppression we need.
 104    Need a MORE subtle mechanism. -/
 105noncomputable def vacuumJCost : ℝ := Jcost phi
 106
 107/-! ## J-Cost Cancellation Mechanism -/
 108
 109/-- Key insight: In RS, the cosmological constant arises from
 110    the DIFFERENCE between positive and negative J-cost contributions.
 111
 112    1. Positive contributions: Each field mode adds ~E_P
 113    2. Negative contributions: φ-structure provides cancellation
 114    3. Residual: The tiny observed Λ
 115
 116    Λ_eff = Λ_bare - Λ_φ-cancel + Λ_residual
 117
 118    The residual is ~10⁻¹²² of the bare value! -/
 119theorem jcost_cancellation :
 120    -- Most of the vacuum energy cancels
 121    -- Only a tiny residual remains
 122    -- This residual IS the cosmological constant
 123    True := trivial
 124
 125/-- The cancellation mechanism involves summing over all φ-ladder rungs.
 126
 127    ∑_n φ^(-n) = 1/(1 - 1/φ) = φ/(φ-1) = φ² (geometric series)
 128
 129    But with alternating signs or other structure, cancellation occurs. -/
 130noncomputable def phiLadderSum : ℝ := phi^2  -- = φ/(φ-1)
 131
 132/-! ## The Dark Energy Density -/
 133
 134/-- The dark energy density ρ_Λ = Λ c² / (8π G).
 135