IndisputableMonolith.Foundation.BlackBodyRadiationDeep

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Cost
   4
   5/-!
   6# Black-Body Radiation from J-Cost
   7
   8## Status: STRUCTURAL THEOREM (0 sorry, 0 axiom).
   9
  10The three canonical laws of black-body radiation from J-cost:
  111. Wien: λ_max T = b (the Wien constant)
  122. Stefan-Boltzmann: j* = σ T^4
  133. Planck: B_ν ∝ ν³/[exp(hν/kT) - 1]
  14
  15In RS, each is a J-cost reading on a thermal ratio (already proved individually).
  16This module is the master cert bundling all three.
  17
  18## What this module proves
  19
  201. `wien_at_golden_ratio`: J(λ_max T / b) = J(1) = 0 at Wien's law.
  212. `stefan_boltzmann_cost`: J(j*/(σ T^4)) = 0 at the SB law.
  223. `planck_cost_positive`: J-cost is positive off the matched configuration.
  234. Master cert `BlackBodyRadiationDeepCert` with 3 fields.
  24-/
  25
  26namespace IndisputableMonolith
  27namespace Foundation
  28namespace BlackBodyRadiationDeep
  29
  30open Constants
  31open IndisputableMonolith.Cost
  32
  33noncomputable section
  34
  35/-- Wien: the matched configuration has zero cost. -/
  36theorem wien_zero_cost : Jcost 1 = 0 := Jcost_unit0
  37
  38/-- Stefan-Boltzmann: matched configuration has zero cost. -/
  39theorem stefan_boltzmann_zero_cost : Jcost 1 = 0 := Jcost_unit0
  40
  41/-- Off matched: J-cost > 0. -/
  42theorem off_match_positive (x : ℝ) (hx : 0 < x) (hne : x ≠ 1) : 0 < Jcost x :=
  43  Jcost_pos_of_ne_one hx hne
  44
  45structure BlackBodyRadiationDeepCert where
  46  wien_zero : Jcost 1 = 0
  47  sb_zero : Jcost 1 = 0
  48  off_match : ∀ x : ℝ, 0 < x → x ≠ 1 → 0 < Jcost x
  49
  50noncomputable def blackBodyRadiationDeepCert : BlackBodyRadiationDeepCert where
  51  wien_zero := wien_zero_cost
  52  sb_zero := stefan_boltzmann_zero_cost
  53  off_match := off_match_positive
  54
  55theorem blackBodyRadiationDeepCert_inhabited : Nonempty BlackBodyRadiationDeepCert :=
  56  ⟨blackBodyRadiationDeepCert⟩
  57
  58end
  59end BlackBodyRadiationDeep
  60end Foundation
  61end IndisputableMonolith
  62