photonicCodeRate

formal source

  48  unfold languageModelAlignmentFraction; norm_num
  49
  50/-- Photonic code rate: 7/8. -/
  51def photonicCodeRate : ℚ := 7/8
  52def photonic_code_rate_rfl : photonicCodeRate = 7/8 := rfl
  53
  54/-- 7/8 = (2³ - 1)/2³ (flip variants / total). -/
  55theorem seven_eighths_from_F2_cube :
  56    languageModelAlignmentFraction = (2^3 - 1 : ℚ) / 2^3 := by
  57  unfold languageModelAlignmentFraction; norm_num
  58
  59structure ThreeSubstrateCert where
  60  three_substrates : Fintype.card ValidationSubstrate = 3
  61  fixed_point : Jcost 1 = 0
  62  descent : ∀ {r : ℝ}, 0 < r → r ≠ 1 → 0 < Jcost r
  63  symmetry : ∀ {r : ℝ}, 0 < r → Jcost r = Jcost r⁻¹
  64  lm_alignment : languageModelAlignmentFraction = 7/8
  65  photonic_rate : photonicCodeRate = 7 / 8
  66  f2_cube_connection : languageModelAlignmentFraction = (2^3 - 1 : ℚ) / 2^3
  67
  68def threeSubstrateCert : ThreeSubstrateCert where
  69  three_substrates := validationSubstrateCount
  70  fixed_point := shared_fixed_point
  71  descent := shared_descent
  72  symmetry := shared_symmetry
  73  lm_alignment := lm_fraction_eq
  74  photonic_rate := photonic_code_rate_rfl
  75  f2_cube_connection := seven_eighths_from_F2_cube
  76
  77end IndisputableMonolith.Foundation.ThreeSubstrateValidationCert