q3 — alternative handles versus CCR 1.44655

Replay:

cd problems/simon-lieb-thirring/compute/q3
./run_all.sh

Carvalho Corso–Ried, arXiv:2403.04347v2, Corollary 1.7, is the published later record

from $M_3=0.371185695$. That value is the method ceiling of the Frank–Hundertmark–Jex–Nam / Hundertmark–Kunstmann–Ried–Vugalter variational problem (solved in closed form as a Clausen series in arXiv:2407.10117v2). A new FHJN trial pair cannot go below it. This folder tries other published conversions and a 1D test-potential search.

What ran:

1. Weidl’s real interpolation between the sharp $\gamma=\tfrac12$ (Hundertmark–Lieb–Thomas $L_{1/2,1}=\tfrac12$) and $\gamma=\tfrac32$ (Laptev–Weidl $3/16$), independently in Python and rustc. The Ky-Fan factor forces $C(\tfrac12)>2$, so the converted ratio is about $3.84$.
2. Seiringer–Solovej remainder absorption (arXiv:2303.04504v2) at $d=1$, with the Airy zero enclosed by a power series. $R_1\approx 0.132$, ratio about $2.75$.
3. Weidl’s Neumann covering, now scored at $\gamma=1$. A constant well already gives local ratio $1/\sqrt{3}$ over classical $\approx 2.72$.
4. A Dirichlet-grid search over square wells, two-sech wells, Gaussian sums, and histograms, looking for a test potential whose ratio exceeds the one-bound-state value $2/\sqrt{3}$.
5. Empirical $T/\int\rho^3$ on Hermite and finite-well blocks (not a bound).

None of these beat $1.44655$. The q2 Clausen envelope is replayed at the end of run_all.sh so the published record is still independently enclosed.

Certificates live in certs/. Summary of the leftover: certs/leftover.json.