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theorem proved term proof

C_competing_gt_C_kernel

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formal statement (Lean)

 204theorem C_competing_gt_C_kernel :
 205    C_kernel < C_kernel_competing := by

proof body

Term-mode proof.

 206  unfold C_kernel C_kernel_competing
 207  -- phi^(-2) < phi^(-3/2) since phi > 1 and -2 < -3/2
 208  have hphi_gt_one : 1 < phi := one_lt_phi
 209  exact Real.rpow_lt_rpow_of_exponent_lt hphi_gt_one (by norm_num : (-(2 : ℝ)) < -(3/2 : ℝ))
 210
 211/-- The competing amplitude `C'` PLUS `J(φ)` exceeds the half-rung
 212    budget, violating the structural identity `J(φ) + C = 1/2`. -/

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