Critical-Line Proportion Ladder: Starting from Claude's 67.25%

Starting from Claude's unconditional 67.25% result of 2026-08-10, this page studies the conditions needed to reach 70%/80%/90%/99%. The first order of business is a semantic lock: the percentages in this project are not a measure of how much of the Riemann Hypothesis is proved — P_q is defined as the liminf lower limit of the proportion of zeros that are simple and on the critical line, so even reaching P₁ (density one) still would not equal the pointwise, universally-quantified statement of RH. The core proof structure compresses to: Weil explicit formula → finite Gabor compression → zero-side inertia → prime-side traces → rank-trace certificate. The baseline flat-window certificate gives H(1)=2/3 at λ=1; after window optimisation in §7.1, this improves to c₁*=0.753296…, corresponding to 2-1/c₁*=0.672500…, i.e. 67.25%. It draws a sharp distinction between two ceilings that must not be conflated: 67.25% is the extremal value of the window-optimisation/two-trace subframework (the paper states outright that no window does better); 68.185% is the broader bandwidth-one-class upper bound given by Remark 1.1, but this batch has not yet found a complete derivation sufficient to independently reconstruct that constant, and it is flagged OPEN-RECONSTRUCTION-01. The page closes with a P0–P6 priority research list and points to Anthropic's official Lean companion repo (github.com/anthropics/zeta-23-lean).