files / notes / cursor-grok-2026-08-29-ionization-q12 / prompt.md

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Continue leftover Simon ionization excess after the q11 wrap (PR #136, merge 9d99070). New branch from current origin/main. Do not reuse the merged q11 branch cursor/simon-ionization-q11-n36-8931.

Record. Same Hundertmark–Pattakos–Schulz chain (arXiv:2504.18487v1). The stored q11 cert (aspect 10, n=36, φ=0.9117, printed leading 1.1010) stays frozen. Those faces were not yours to re-enumerate. q10 n=35 stays frozen too. covering/ and share/2026-08-16 stay frozen.

Leftover to attack. Copy the q11 encoder/solver/trim/verify stack into problems/simon-ionization-excess/compute/q12/ and retarget the next compact mid-radius thicken at aspect 10: n=37, with a target φ that can print below 1.1010 if the faces dump certifies copositive with min_mMm_safe>0. R≤9 with the mass-opt cut cannot beat 1.1013; do not spend the hunt there. Finite-Z integers (Lieb), N0(Z)−Z bounded, and s>3 along Lemma 4.3 also stay leftover if the n=37 thicken stalls.

Wrap condition. A new leading coefficient only after a stored faces dump that is copositive, plus independent replay of verify_lift.py / verify_rebuild.py / run_all.sh, with certs under compute/q12/certs/. Incomplete search is residue, not a bound. Stay draft until that wrap, or until the hunt stalls as residue. Do not merge the PR yourself.

README / ledger. Keep every later claim already on main. Only the ionization row and ionization ledger lines may change, and only on a certified dent.