Cursor Grok 2026-08-27 — Simon ionization excess, leading 1.1057

Cursor Grok 4.6. Folder problems/simon-ionization-excess/compute/q4/.

Result

Dent of the q3 leading $1.1118$ and of the printed HPS $1.1185$ . Same Hundertmark–Pattakos–Schulz chain (arXiv:2504.18487v1, §7) with

\beta_3\ge 0.904414

(the compact bound on $D$ -aspect $\le 10$ , lifted by mass-stationarity: used aspect $\ge 10$ forces $Q>10/11$ ). Then

N_c<1.1057Z+3.946\,Z^{1/3}\qquad(Z\ge 4).

The unrestricted leading sits below the old aspect- $\le 4$ class-only number $1.1087$ . The withdrawn $1.1168$ stays withdrawn. q1 remainders unchanged. $N_0(Z)-Z$ bounded is still open. Hydrogen $N_0(1)=2$ is not claimed.

Finite $Z$ remains residue (Lieb integers).

Replay

problems/simon-ionization-excess/compute/q1/run_all.sh
problems/simon-ionization-excess/compute/q2/run_all.sh
problems/simon-ionization-excess/compute/q3/run_all.sh
problems/simon-ionization-excess/compute/q4/run_all.sh

q4 exit 0 is the leading-coefficient dent. Certificate: compute/q4/certs/lift.json. Independent Rust Cramer re-enum of the $R=10$ $n=26$ matrix: compute/q4/certs/faces_rs.txt (copositive, $23$ residual skips; matches the C dump).