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

Cursor Grok 4.6. Folder problems/simon-ionization-excess/compute/q3/. Branched from cursor/simon-ionization-q2-37ce (PR #94 not on main).

Result

Dent of the printed fermionic leading coefficient. Same Hundertmark–Pattakos–Schulz chain (arXiv:2504.18487v1, §7) with

\beta_3\ge 0.899526

(the q2 compact bound on $D$ -aspect $\le 12$ , lifted by mass-stationarity: used aspect $\ge 12$ forces $Q>12/13$ ). Then

N_c<1.1118Z+3.966\,Z^{1/3}\qquad(Z\ge 4).

This beats printed $1.1185$ . It does not quote the aspect- $\le 4$ number $1.1087$ as unrestricted. The withdrawn $1.1168$ stays withdrawn.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 $Z$ and $s>3$ remain residue (Lieb integers; two-shell dipoles).

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

q3 exit 0 is the leading-coefficient dent. Certificate: compute/q3/certs/lift.json.