Cursor Grok 2026-08-28 — Simon ionization excess, leading 1.1013

Cursor Grok 4.6. Folder problems/simon-ionization-excess/compute/q10/.

Result

Lift of the q9 leading $1.1017$ and of the printed HPS $1.1185$ . Same Hundertmark–Pattakos–Schulz chain (arXiv:2504.18487v1, §7) with

\beta_3\ge 0.908018

(the compact bound on $D$ -aspect $\le 10$ at $n=35$ bins, target $\varphi=0.9115$ , lifted by mass-stationarity: used aspect $\ge 10$ forces $Q>10/11$ ). Then

N_c<1.1013Z+3.935\,Z^{1/3}\qquad(Z\ge 4).

$R\le 9$ with the mass-opt cut cannot beat $1.1017$ . The withdrawn $1.1168$ stays withdrawn. q1 remainders unchanged. Bounded excess is still open. Hydrogen $N_0(1)=2$ is not claimed.

Finite $Z$ remains leftover (Lieb integers). The optional $n=34$ target- $0.9114$ probe was not run and is not this lift.

Replay

problems/simon-ionization-excess/compute/q10/run_all.sh

q10 exit 0 is the leading-coefficient lift. Certificate: compute/q10/certs/lift.json.