A conditional route to 76.7% simple zeros of the Riemann zeta function via twisted dispersion

Assuming the Riemann Hypothesis, Bui and Heath-Brown proved that at least 19/27 ≈ 70.37% of the nontrivial zeros of ζ(s) are simple. Their method, following Conrey, Ghosh and Gonek, yields the proportion 1-(1+θ)-3 for a mollifier of length Tθ, and the proof is limited to θ ≤ 1/2. We isolate the single estimate that blocks θ > 1/2: a power saving, at level θ, for the bilinear sum Σh,k≤y (b(h)b(k)/k) Σn c(n) e(-hn/k), where c = Λ*log*log and y = Tθ, which is a Bombieri-Vinogradov type statement beyond the square-root barrier with an additive twist averaged over a moving residue. We state this as a conjecture and record the conditional consequences: level 4/7 gives 74.230%, level 153/256 gives 75.478%, level 3/5 gives 75.586%, and level 66/107 gives 76.340%. At level 5/8, the level of distribution for primes with triply well-factorable weights recently proved unconditionally by Pascadi, the conjecture would give 1-(13/8)-3 = 76.695%. We identify three concrete ingredients that would suffice, present numerical computations of the required cancellation (near-orthogonality of order k-1/2, off-diagonal cancellation fitting y-1.00, and exact recovery of the template saving), and describe three obstructions that any proof must overcome. Nothing beyond 19/27 is proved here. All proportions above 19/27 in this note are conditional on Conjecture 2.1.