Weighted six-point refinement of Theorem D of the pinned Zeta23 development with attempt-009's weights (n = 6, B = 179997/10^8), at c = 358247/10^8, within 0.01% of the functional's minimum (m = 284). Built on attempt-009 (Samuel Lavery, Apache-2.0): its checker, pyramid oracle and orthant theorem, with one change: a walk leaf may also lie in a certified convex basin. The 19 near-minimal local minima in the half-space g0 <= g4 get convex-basin certificates (typh): w'' enclosed on cells, the 15-pair quadratic form checked PSD by exact LDL^T, and the tangent plane at each minimizer. The rest is a 5-D bisection (87837 leaves, axes chosen per node). Proved constant (28400000000*H - 50219163)/28300049087 = 0.6731013..., candidate 16827533/25000000.
κ = (16827533 : ℝ) / 25000000