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theorem proved term proof

alphaInv_seed_ratio

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formal statement (Lean)

  80theorem alphaInv_seed_ratio :
  81    alphaInv / alpha_seed = Real.exp (-(f_gap / alpha_seed)) := by

proof body

Term-mode proof.

  82  unfold alphaInv
  83  field_simp
  84
  85/-! ## Part 2: The Logarithmic Structure
  86
  87Taking the natural log of α⁻¹/α_seed gives:
  88    ln(α⁻¹/α_seed) = -f_gap/α_seed
  89
  90This is the defining relation of the exponential form in log coordinates.
  91It says that the logarithm of the coupling ratio is LINEAR in f_gap with
  92slope -1/α_seed.
  93-/
  94
  95/-- The log of the ratio alphaInv/alpha_seed equals -f_gap/alpha_seed. -/

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