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theorem proved term proof

etaBAt_adjacent_ratio

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formal statement (Lean)

  71theorem etaBAt_adjacent_ratio (N : ℕ) :
  72    etaBAt (N + 1) / etaBAt N = phi⁻¹ := by

proof body

Term-mode proof.

  73  rw [etaBAt_succ_ratio]
  74  have hpos : 0 < etaBAt N := etaBAt_pos N
  75  field_simp [hpos.ne']
  76
  77/-- η_B falls below the empirical band (≈ 6 × 10⁻¹⁰) after a finite
  78e-fold count: `etaBAt 44 = phi^(-44)` matches the existing equilibrium
  79identity at the present epoch. -/

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