Certificate archive: improved lower bound C_71 > 6.521845710923046575 for the Fourier Entropy-Influence constant (n = 18 explicit construction)

This record is a self-contained certificate archive for an improved lower-bound contribution

**C_71 > 6.521845710923046575** (full floor truncation: 6.521845710923046575658143972948578468366...)

for the Fourier Entropy-Influence constant (problem 71a of teorth/optimizationproblems): an explicit balanced, logic-monotone Boolean function on **n = 18** variables, amplified by the O'Donnell–Tan rule (arXiv:1304.1347). Exact influence I = 261/128; spectral entropy certified by interval arithmetic; every verdict is an exact rational comparison of interval endpoints, and the strict-improvement comparison is made against the previous record's certified **upper** endpoint, so the gain — exactly 1/133 — is itself certified rather than implied by truncations.

Construction: the previous record function (n = 17, C_71 > 6.514326913930565372, merged as teorth/optimizationproblems PR #124) is a perturbed-majority-of-9 core with eight auxiliary variables acting on the majority boundary; one auxiliary there acts on four core cells while all others act on two — a resource-shortage artifact of n = 17. Adding an 18th variable and rehosting two of those four cells onto it makes the auxiliary action uniform (nine auxiliaries, two cells each); halving the moved coefficient magnitudes raises spectral entropy by exactly twice the moved weight at identical total influence. Because the resulting function is logic-monotone (exhaustively verified), the bound holds even restricted to monotone functions. Supporting analysis (included in the archive README): a core-size scan m = 5..13 recovering the O'Donnell–Tan m = 5 example exactly as an external anchor and showing m = 9 is the sweet spot, and a two-level spectral decomposition showing 2-cell uniform hosting is optimal within its structure class — the construction sits at a measured structure-class optimum.

**AI disclosure:** the construction was found and certified with AI assistance; all results were independently re-run and verified by the human contributor before release, per the repository's AI-use policy.

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