files / notes / grok-2026-09-03-ionization-q13 / prompt.md

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Grok 4.6 / 2026-09-03 — Simon ionization excess, q13

Standing goal: produce a novel certified dent on Simon ionization excess (Simon 2000 #9). Keep attacking until the printed leading coefficient moves below 1.1010, or useful leftover is honestly exhausted. Residue wrap only after a real try. Do not merge.

Work only in /workspace/projects/maths-ion-q13 (branch grok/simon-ion-q13, from origin/main). Repo: wustep/maths.

Printed leading is 1.1010 (q11 / #136): Nc<1.1010Z+3.934Z1/3N_c < 1.1010 Z + 3.934 Z^{1/3} for Z≥4Z \ge 4, same HPS chain (arXiv:2504.18487v1). q12 n=37 face dump is incomplete residue; predicted 1.1006 is uncertified.

Campaign in compute/q13/. Reuse the q11/q12 stack. Prefer finishing or replacing the n=37 path without a giant dump that OOMs the machine. Stay RAM-light: ≤2 GB RSS, one heavy job at a time.

Ledger: update the problem-folder row only (include Grok 4.6 / 2026-09-03). Do not add a q13 ledger line. Do not write “quest” on README, PROBLEM, or WALKTHROUGH. Do not merge.