By Samuel Lavery (github: samlavery) and his agent team (bridge-port, am-cert, mvt-engine, window-scope); Apache-2.0. Builds on our attempt-012/013/014. Ainta's weighted n-point simple-zero refinement at n = 8 on the AM-form window v(s) = cos(√2 s) + Σ_{j=1}^{12} c_j cos(2πjs) of AMTOPA's 13-term family, with corrections and LP weights re-optimised for eight points (B = 404350/10⁸) and H ≥ 0.67216841 proved in-file. The finite certificate PC8C5BF proves c = 805124/10⁸ (δ 0.005 %) on g₀ ≤ g₆: its cells are pair-distance polytopes re-closed exactly as difference constraints after each split (4,566 splits, 2,260 at convex-region boundaries); its 4,598 leaves are 4,419 per-term tangent-minorant leaves (LP multipliers on the cell's constraints, zero-order extension) and 179 reflected cells, with cache-shared derivative and pyramid reads. The block bound uses the band profile g_τ(E) = E (E ≤ τ), 2√(τE) − τ (E > τ), τ = 8/7, derived independently from Gebendorfer 2026 Lemma 3.3 (AMTOPA, MIT)
κ = (6734832 : ℝ) / 10000000