A certified n=17 lower bound for the Fourier Entropy-Influence constant

This record is a self-contained certificate archive for the Mosaic Intelligence lower-bound contribution C_71 ≥ 6.514326913930565372 (full floor truncation: 6.51432691393056537265062517595609726535914349523745739524537) for the Fourier Entropy-Influence constant (problem 71a of teorth/optimizationproblems): an explicit balanced, logic-monotone Boolean function on n = 17 variables, amplified by the O'Donnell–Tan rule (arXiv:1304.1347, Lemma 5.1). Exact influence I = 261/128; spectral entropy certified by interval arithmetic with enclosure width < 1e-100; all verdicts are exact rational comparisons of interval endpoints. It supersedes our n = 14 certificate (C_71 ≥ 6.4901128435233943, DOI 10.5281/zenodo.20794146, merged as PR #94) and improves the published record C ≥ beta(1/2) > 6.4547837 (Hod 2017, arXiv:1711.00762, Thm 4.4). Because the function is logic-monotone, the bound holds even restricted to monotone functions. Files: check_c71_n17.py (single-file verifier, Python 3.9+ and mpmath only, truth table inlined and SHA-256-bound to the certificate; runs in seconds, exit 0 iff certified — also included standalone on this record for one-command replay) and fei_c71_n17_bundle.zip (certificate, companion truth table, from-scratch 18-check adversarial audit with run log, README with replay instructions). Verify: pip install mpmath; python3 check_c71_n17.py — expected output ends in ALL CERTIFIED. Deep check: python3 audit_ridge_fourthline_n17.py certs/ridge_n17_g4_best2_iter14.json (expect exit 0, ALL 18 CHECKS PASSED). Fully AI-derived: the construction was found and certified by Mosaic Intelligence's automated search-and-verification system; all results were independently re-run and verified before release. Contact and updates: Mosaic Intelligence — https://x.com/111111 · https://github.com/463464q435q43