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theorem proved term proof

alpha_lock_at_scale

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formal statement (Lean)

  28theorem alpha_lock_at_scale :
  29    alpha_inv_running (effective_scale ell0) (effective_scale ell0) (1 / alpha_locked) = 1 / alpha_locked := by

proof body

Term-mode proof.

  30  unfold alpha_inv_running
  31  rw [div_self (ne_of_gt (effective_scale_pos ell0_pos))]
  32  rw [Real.log_one, mul_zero, sub_zero]
  33
  34/-- **SCAFFOLD: Eight-Beat Plateau Dominance**
  35    Below the lock-in scale Q < Q_lock, the discrete eight-beat cycle
  36    prevents further running, maintaining the geometric value. -/

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