Finite handles — Simon ionization excess

Created 2026-09-06 from PROBLEM.md and the existing computation notes. Historical statuses below report the notebook record; they are not new independent certifications by q14. One assigned leaf per campaign.

Leaf	Campaign	Status	Finite predicate / remaining work
HPS remainder on the Lieb ratio interval	q1	certified	Recorded $N_c<1.1185Z+3.9781Z^{1/3}$ for $Z\ge4$ .
Compact aspect-four bound and unrestricted lift	q2	residue	Compact certificate only; unrestricted $1.1168$ was withdrawn.
Aspect-twelve mass-stationary lift	q3	certified	Recorded leading $1.1118$ .
Aspect-ten, 26 bins	q4	certified	Recorded leading $1.1057$ .
Aspect-ten, 30 bins	q5	certified	Recorded leading $1.1035$ .
Aspect-ten, 32 bins	q6	certified	Recorded leading $1.1026$ .
Aspect-ten, 33 bins, target $0.9111$	q7	certified	Recorded leading $1.1021$ .
Aspect-ten, 33 bins, target $0.9112$	q8	certified	Recorded leading $1.1020$ .
Aspect-ten, 34 bins	q9	certified	Recorded leading $1.1017$ .
Aspect-ten, 35 bins	q10	certified	Recorded leading $1.1013$ .
Aspect-ten, 36 bins	q11	certified	Recorded leading $1.1010$ .
Aspect-ten, 37-bin mask enumeration	q12	residue	Incomplete enumeration; superseded by q13, never a bound by itself.
Aspect-ten, 37-bin Gray enumeration	q13	certified	Recorded $N_c<1.1006Z+3.933Z^{1/3}$ for $Z\ge4$ .
Exact copositivity certificate for a raised compact target	q14	certified	Target $0.912$ on 37 rational bins, two independently checked matrix witnesses; $N_c<1.1005Z+3.933Z^{1/3}$ for $Z\ge4$ . See CLAIM.md.
Refined compact partition reaching the aspect-ten cut	q15	residue	Stopped at midnight before SDP search; no certificate for the proposed 40-bin target $0.9124$ . Attempted leading $1.1$ is unproved; certified leading remains $1.1005$ . See CLAIM.md.
Sharper endpoint-moment cut	unassigned	open	Certify an improvement on $R/(R+1)$ and combine with a compact bound.
Further HPS remainder optimization	unassigned	open	Certify improved constants over the full stated $Z$ range.
Finite- $Z$ integer exclusion	unassigned	open	Exclude a previously allowed electron count; existing small- $Z$ probes did not improve Lieb.
Extend the same radialization to $s>3$	unassigned	blocked	Existing two-shell obstruction prevents this route without a different argument.