Cursor Grok 2026-08-28 — Simon ionization excess, n=36

Cursor Grok 4.6. Folder problems/simon-ionization-excess/compute/q11/.

Result

Dent of the q10 printed leading $1.1013$ . Same Hundertmark–Pattakos–Schulz chain (arXiv:2504.18487v1, §7). q10 stays frozen: aspect $10$ , $n=35$ , $\varphi=0.9115$ , $1/\gamma=1.10129973$ prints as $1.1013$ . Those faces were not re-enumerated.

At $n=36$ mid-radius bins, target $\varphi=0.9117$ , faces $68{,}719{,}476{,}735$ are copositive, $\min m^\top Mm>6\cdot 10^{-4}$ , $\min\varphi=0.911885$ . Compact $\gamma=0.9083146735963096$ , $1/\gamma=1.100940$ prints as $1.1010$ . Cut $10/11>\gamma$ .

N<1.1010Z+3.849\,Z^{1/3}+0.01320+0.1827\,Z^{-1/3}+0.019490\,Z^{-2/3} \qquad(Z\ge 4),

N_c<1.1010Z+3.934\,Z^{1/3}\qquad(Z\ge 4).

$R\le 9$ with the mass-opt cut cannot beat $1.1013$ . The withdrawn $1.1168$ stays withdrawn.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).

Replay

problems/simon-ionization-excess/compute/q11/run_all.sh

Certificate: compute/q11/certs/lift.json.