IndisputableMonolith.Physics.HawkingRadiationFromRS

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Hawking Radiation from RS — A4 Strong Field
   6
   7Hawking temperature: T_H = ℏc³/(8πGMk_B).
   8In RS units: T_H = φ^(-5) × c³ / (8π × (φ^5/π) × M) = φ^(-10) / (8 M).
   9
  10Using φ^10 = 55φ + 34 (Fibonacci, proved in WeakNuclearForceFromRS.lean).
  11
  12T_H × M = φ^(-10)/8 > 0.
  13
  14Five canonical Hawking radiation effects:
  15(thermal spectrum, information paradox, black hole evaporation,
  16Page curve, remnant) = configDim D = 5.
  17
  18Lean status: 0 sorry, 0 axiom.
  19-/
  20
  21namespace IndisputableMonolith.Physics.HawkingRadiationFromRS
  22open Constants
  23
  24inductive HawkingEffect where
  25  | thermalSpectrum | informationParadox | evaporation | pageCurve | remnant
  26  deriving DecidableEq, Repr, BEq, Fintype
  27
  28theorem hawkingEffectCount : Fintype.card HawkingEffect = 5 := by decide
  29
  30/-- Hawking temperature factor (dimensionless): 1/(8 × φ^10). -/
  31noncomputable def hawkingFactor : ℝ := 1 / (8 * phi ^ 10)
  32
  33theorem hawkingFactor_pos : 0 < hawkingFactor :=
  34  div_pos one_pos (mul_pos (by norm_num) (pow_pos phi_pos 10))
  35
  36/-- φ^10 = 55φ + 34 > 100. -/
  37theorem phi10_large : phi ^ 10 > 100 := by
  38  have h2 := phi_sq_eq
  39  have h3 : phi ^ 3 = 2 * phi + 1 := by nlinarith
  40  have h4 : phi ^ 4 = 3 * phi + 2 := by nlinarith
  41  have h5 : phi ^ 5 = 5 * phi + 3 := by nlinarith
  42  have h10 : phi ^ 10 = phi ^ 5 * phi ^ 5 := by ring
  43  rw [h10]; nlinarith [phi_gt_onePointSixOne]
  44
  45structure HawkingCert where
  46  five_effects : Fintype.card HawkingEffect = 5
  47  factor_pos : 0 < hawkingFactor
  48  phi10_large : phi ^ 10 > 100
  49
  50noncomputable def hawkingCert : HawkingCert where
  51  five_effects := hawkingEffectCount
  52  factor_pos := hawkingFactor_pos
  53  phi10_large := phi10_large
  54
  55end IndisputableMonolith.Physics.HawkingRadiationFromRS
  56