The 70%/80%/90%/99% Target Ladder

Builds a target table: P_2/3 and P_67.25 are unconditionally proved (Claude's Theorem B/D); P_68.185 is only a certificate ceiling statement, not an “achieved proportion”; P_70/80/90 have rough support-requirement estimates (σ≈1.04/1.26/1.70); the paper gives no finite support threshold for P_99, and this document explicitly forbids linearly extrapolating from the first three points. It introduces a coordinate for comparing different certificates: if the corresponding horizontal/symmetric-diagonal count satisfies H(T)≤(C+o(1))N(T), the simple-critical proportion has lower bound 2-C, which converts the targets into C≤1.30/1.20/1.10/1.01 (100% density corresponds to C→1). It proposes that the real research plane is the two-dimensional coordinate (σ,k) — σ being the controllable pair-correlation Fourier support/bandwidth, k being the reliably attainable spectral-moment order — split into three axes: Axis A Support expansion, Axis B Moment expansion, and Axis C Certificate enrichment (adding constraints such as zero-side block geometry rather than more support/moments — currently the least understood axis). P_70 is the first real breakthrough point, with three routes listed (Support; Fourth Moment, which can reach 13/18≈72.22%; and a broader bandwidth-one certificate). P_99 sets the strictest research discipline of all: don't guess σ_99 — the real first question is “what information suffices to derive P_99,” not curve-fitting.