files / problems / simon-ionization-excess / compute / q9 / README.md

1.0 KB · on GitHub

q9 — leading coefficient 1.1020 to 1.1017

q8 lifted the aspect-10 compact bound and replaced printed 1.10211.1021 by 1.10201.1020 at n=33n=33 bins, target 0.91120.9112. The leftover slack was the Pmax⁡P_{\max} tax: more bins shrink q=R1/nq=R^{1/n}. R≤9R\le 9 with the mass-opt cut cannot beat 1.10201.1020.

This folder keeps the split at aspect 1010 and raises the mid-radius bin count to 3434. Faces certify Q≥0.907716Q\ge 0.907716 (target 0.91130.9113). Mass-stationarity still forces any used support of aspect ≥10\ge 10 to have Q>10/11Q>10/11. That replaces 1.10201.1020 in the same Section 7 chain.

The withdrawn 1.11681.1168 stays withdrawn. Finite ZZ and N0(Z)−ZN_0(Z)-Z stay residue. s>3s>3 along Lemma 4.3 stays residue. n=35n=35 at this split is still a predicted 1.10131.1013 if faces certify.

./run_all.sh

Certificates: certs/lift.json, leading.json, aspect_identities.json, lift_stdlib.json, rebuild.json. Independent algebra: verify_aspect.c, verify_aspect.rs. Faces dump: certs/beta3_mid_faces_R10_n34_t0p9113.txt (not re-enumerated on the fast path). Leftover probes in work/.