Improve lower bound for the Fourier Entropy-Influence constant to 6.521845710923046575 (n=18 certified construction)

[unnir]

This PR improves the lower bound of constant 71a from 6.514326913930565372 ([MI2026b], PR #124) to

C_71 > 6.521845710923046575 (full certified floor: 6.5218457109230465756581439729485784683666...)

Construction. The [MI2026b] n=17 record function 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. We add an 18th variable and
rehost two of those four cells onto it, making 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 (I = 261/128), for a certified gain of exactly 1/133
via the O'Donnell–Tan amplification rule C >= H/(I-1). The function is balanced and logic-monotone
(exhaustively verified), so the bound holds even restricted to monotone functions.

Certificate (replayable in ~60 seconds).
Archive: https://zenodo.org/records/21497769 (DOI: https://doi.org/10.5281/zenodo.21497769)

• check_c71_n18.py — single-file verifier (Python 3.9+, mpmath only; truth table inlined and
  SHA-256-bound). python3 check_c71_n18.py -> ends ALL CERTIFIED, exit 0. Every verdict is an
  exact rational comparison of interval endpoints; the strict-improvement comparison is made
  against the previous record's certified upper endpoint, so the gain is itself certified.
• verify.py + fei_c71_n18_artifact.json — independent second verifier (from-scratch numpy
  Walsh–Hadamard transform, exact-Fraction influence). python3 verify.py fei_c71_n18_artifact.json
  -> RESULT: PASS, exit 0.

Changes in this PR. constants/71a.md: description-paragraph record value, best-established
range line, one row added to the Known lower bounds table, and a [Num2026] reference entry
(mirroring the existing entry format). README.md: row 71 lower bound updated (note: supersedes
the pending update in PR #128).

AI-use disclosure (per CONTRIBUTING.md): the construction was found and certified with AI
assistance (an automated search-and-verification pipeline built on AI agents by
Numaro); all results were re-run and verified by the human submitter before
this PR — both verifiers replay from the Zenodo archive alone.

Here is the our report: https://numaro.tech/research/fourier-entropy-influence-2026/

— Numaro