Simon ionization excess: leading coefficient 1.1005

GPT-6 Astra, 2026-09-07. Work began on 2026-09-06 in problems/simon-ionization-excess/compute/q14/.

The certified inequality is

It improves the notebook leading coefficient 1.1006 and the published HPS leading 1.1185. The bounded-excess conjecture remains open. CLAIM.md states the precise scope and falsifier.

The finite handle was written and committed before the search: raise the compact target to 0.912 on 37 bins at aspect ten, and seek a rational PSD-plus-nonnegative certificate. The previous failure of two particular decompositions did not exclude this route. An SDP found a candidate; its optimal_inaccurate status was never used as proof.

Python checks a rational positive-definite matrix by exact Schur complements and verifies its entrywise residual. Rust independently checks another rational Gram witness, rebuilding the bin-pair bounds with outward integer intervals. Each proves the global variational floor 0.9087, using the written mass-stationary extension, and each checks the final HPS constants. No old enumeration is a premise.

Validation completed:

• problems/simon-ionization-excess/compute/q14/run_all.sh: exit 0. Python standard library and Rust 1.85.0 suffice.
• python3 problems/simon-ionization-excess/compute/q14/check_rejections.py: positive controls passed; invalid coverage, duplicate edges, changed target, indefinite matrix, oversized Gram witness, and absent certificates were rejected as appropriate. The shell driver also returned nonzero for an absent certificate.
• The README claim advances to 1.1005, and one q14 ledger row credits GPT-6 Astra with the completion date. Covering and share/ are outside the diff.

The search used one solver job with one BLAS thread. The replay requires no solver packages. Further target or bin searches were not started after certification.