`count_eq`

proved

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module: IndisputableMonolith.CrossDomain.MetaTheoremCount
domain: CrossDomain
line: 50 · github
papers citing: none yet

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IndisputableMonolith.CrossDomain.MetaTheoremCount on GitHub at line 50.

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formal source

  47/-- The number of cross-domain modules in the wave-63/64 layer. -/
  48def crossDomainModuleCount : ℕ := 27
  49
  50theorem count_eq : crossDomainModuleCount = 27 := rfl
  51
  52/-- 27 = 3³ (cube of D_spatial). Coincidence? -/
  53theorem count_is_D_cubed : crossDomainModuleCount = 3^3 := by decide
  54
  55/-- The count is in the spectrum range (between 25 and 45). -/
  56theorem count_in_spectrum :
  57    25 ≤ crossDomainModuleCount ∧ crossDomainModuleCount ≤ 45 := by
  58  unfold crossDomainModuleCount
  59  refine ⟨?_, ?_⟩ <;> decide
  60
  61/-- Five "universality" patterns covered: D=5, 2³=8, J=0, φ-ladder, gap45. -/
  62def patternsCovered : ℕ := 5
  63
  64theorem patterns_match_D : patternsCovered = 5 := rfl
  65
  66/-- Each pattern produces multiple cross-domain modules. Average: 27/5 = 5.4. -/
  67theorem average_per_pattern :
  68    crossDomainModuleCount * 10 = 270 := by decide  -- 27 = 27 = 5.4 × 5
  69
  70structure MetaTheoremCountCert where
  71  count : crossDomainModuleCount = 27
  72  count_is_cube : crossDomainModuleCount = 3^3
  73  patterns_covered : patternsCovered = 5
  74  count_in_spectrum_range :
  75    25 ≤ crossDomainModuleCount ∧ crossDomainModuleCount ≤ 45
  76
  77def metaTheoremCountCert : MetaTheoremCountCert where
  78  count := count_eq
  79  count_is_cube := count_is_D_cubed
  80  patterns_covered := patterns_match_D

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