We establish a structural decomposition — the "vine theorem" — for the curvature remainder of the D-sequence derived from the Stieltjes moments of the completed Riemann xi function. On the ordered ratio chamber q₁ ≥ q₂ ≥. . . > 0, the remainder R = B − Bgeo decomposes as a sum of gap-weighted positive strands: R = Σ aᵢ · Pᵢ, where each Pᵢ has all nonnegative coefficients. This provides a constructive, sequentially verifiable certificate that all 2×2 Turán minors Mₖ = Dₖ² − Dₖ₋₁Dₖ₊₁ are nonnegative. The strand cardinalities are r-invariant (independent of the finite-difference order) and follow a universal pattern across k = 3, 4, 5. The structure extends to 3×3 subdiscriminant Hankel minors (2-gap case) with an invariant 57/12 strand split. Six exact theorems are formulated: Cauchy factorization, parity law, vine decomposition, universal strand structure, geometric zero, and island diagnosis. The vine theorem is a genuine mathematical result within its domain (n=0 Jensen slice, ordered chamber, 2×2 and 3×3 2-gap conditions) but does not bridge to Jensen hyperbolicity or the Riemann Hypothesis. RH is NOT proved.
Sterling Dudley Hayden (Mon,) studied this question.