q15 claim — reaching the aspect-ten cut

Status: residue at the midnight cutoff on 2026-09-12. No new bound. The SDP search did not run and no q15 certificate or verifier was produced. The certified leading coefficient remains 1.1005.

For the fermionic Coulomb Hamiltonian and critical electron count defined in PROBLEM.md, the target is

The prior certified notebook bound is q14's $N_c(Z)<1.1005Z+3.933Z^{1/3}$ for $Z\ge4$. The published comparison is Hundertmark–Pattakos–Schulz, arXiv:2504.18487v1, with leading coefficient 1.1185 and remainder coefficient 4 on the same range.

The proposed finite handle uses 40 rational bins covering $[1,10]$, with target $\varphi=2281/2500=0.9124$. A positive-semidefinite plus entrywise nonnegative decomposition would bound the compact radial quotient. After its reweighting error, the intended target is at least $10/11$. The existing mass-stationary argument gives $Q>10/11$ for larger used-support aspect. This would prove $\beta_3\ge10/11$; the HPS Section 7 calculation must then certify the displayed bound.

Certification would require separate rational matrix and Gram witnesses checked in Python and Rust. Numerical solver status is never a premise. The present run_all.sh returns 2 with an explicit missing-certificate message. It cannot report success for this unfinished claim. The target inequality above is not established.

Falsifier: a valid bound-state example violating the displayed inequality disproves it. An invalid matrix inequality, uncovered radial measure, incorrect compact-to-global passage, or failed outward scalar bound invalidates the certificate. Incomplete search is residue, not a new bound. Bounded excess remains open.