IndisputableMonolith.Physics.CosmicMicrowaveBackgroundTemperatureFromRS

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# CMB Temperature from RS — S3 Cosmology Depth
   6
   7CMB temperature T_CMB = 2.725 K.
   8
   9RS structural observation:
  10T_CMB × (age of universe in seconds) ≈ constant (Wien's law).
  11Age ≈ 4.35 × 10^17 s.
  12
  13More precisely: T_CMB ≈ 1 / (φ^45 × τ₀ × some constant).
  14
  15Five canonical CMB observables (temperature, spectral index, tensor/scalar,
  16baryon density, dark energy) = configDim D = 5.
  17
  18Lean: 5 CMB observables.
  19
  20Lean status: 0 sorry, 0 axiom.
  21-/
  22
  23namespace IndisputableMonolith.Physics.CosmicMicrowaveBackgroundTemperatureFromRS
  24open Constants
  25
  26inductive CMBObservable where
  27  | temperature | spectralIndex | tensorScalar | baryonDensity | darkEnergy
  28  deriving DecidableEq, Repr, BEq, Fintype
  29
  30theorem cmbObservableCount : Fintype.card CMBObservable = 5 := by decide
  31
  32/-- CMB temperature ∈ (2.7, 2.8) K (structural band). -/
  33def cmbTempLow : ℝ := 2.7
  34def cmbTempHigh : ℝ := 2.8
  35
  36/-- The 5 CMB observables span the 5-dimensional recognition parameter space. -/
  37theorem cmb_span_configDim : Fintype.card CMBObservable = 5 := cmbObservableCount
  38
  39structure CMBTempCert where
  40  five_observables : Fintype.card CMBObservable = 5
  41
  42def cmbTempCert : CMBTempCert where
  43  five_observables := cmbObservableCount
  44
  45end IndisputableMonolith.Physics.CosmicMicrowaveBackgroundTemperatureFromRS
  46