q13 — mid-radius bins at the proven aspect-10 split

Same HPS §7 / arXiv:2504.18487v1 chain as q1–q12. The published record is still v1 only. q11 (#136 / 9d99070) certified printed leading 1.1010 at aspect 10, $n=36$, target $\varphi=0.9117$. That cert stays frozen. q12 started $n=37$ with the naive mask dump and stopped incomplete. Those four shards stay leftover, not a bound.

This folder certifies printed leading 1.1006 at the same split with $n=37$, target $\varphi=0.9119$: compact $\gamma=0.9086061090539742$, $1/\gamma=1.1005869210379662$, cut $10/11>\gamma$. Faces $137{,}438{,}953{,}471$, copositive, $0$ residual skips, $\min m^\top Mm>6\cdot 10^{-4}$, $\min\varphi=0.912085$. The dump is a Gray-code walk of $M_S$ (verify_gray.c), one thread, about 2 MB RSS, not a four-shard Gauss-Jordan dump.

$R\le 9$ with $Q>R/(R+1)$ cannot beat 1.1010. Finite-$Z$ integers (Lieb), $N_0(Z)-Z$ bounded, and $s>3$ along Lemma 4.3 stay leftover. The withdrawn $1.1168$ stays withdrawn.

Replay

problems/simon-ionization-excess/compute/q13/run_all.sh

Exit 0 is the leading-coefficient lift of q11's 1.1010. Certificate: certs/lift.json.

Fast path, once the Gray dump is stored:

python3 write_raise.py && python3 verify_lift.py && python3 lift_cert.py

write_raise.py, verify_lift.py, and verify_rebuild.py are stdlib. verify_aspect.c / .rs replay the mass-opt identities. tighten_leading.py is the interval §7 printer (ceil_dec). Set PYTHON to a venv with mpmath if the system Python lacks it.