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Critical-Line Proportion Ladder

Critical-Line Proportion Ladder (CPL)

This line is built on a real, published Anthropic paper — Claude, "More Than Two Thirds of the Zeros of the Riemann Zeta Function Lie on the Critical Line" (2026-08-10, official Lean companion repo). The paper unconditionally pushes the lower bound on the proportion of critical-line zeros from 41.6% (Pratt–Robles–Zaharescu–Zeindler) to 67.25%, the largest single-step jump known in this direction — but the paper itself, and subsequent coverage, both state plainly: this does not resolve the Riemann Hypothesis, makes no claim about the remaining 32.8% of zeros, and has no directional bearing on RH itself.

Neo.K's CPL research is the follow-on exploration: can a constant the paper itself leaves unaddressed (the 68.185% certificate ceiling) be independently reconstructed? Can 67.25% be pushed to 70%, 80%, 90%, or even approaching 100%? Every step strictly distinguishes "proven," "conditionally provable," "open," and "extrapolation forbidden" — engineering progress is never swapped in for a mathematical theorem.

A single relay-style research line — v1 through v11 (15 documents) are all now live as pages — first reconstructing the 68.185% ceiling, then attacking the support axis, and finally translating support requirements into arithmetic-input requirements and auditing the literature. v11's MMIP is an as-yet-unopened research proposal, not a closed conclusion; later versions await a new package from Neo.K.

This is the same mathematical object as the Riemann Hypothesis case (Chinese) (zeros of the Riemann zeta function), but a different kind of research — not an attempt to prove or disprove RH, but an extension of an already-published, already-verified external result.