Improve lower bound for the Gyarmati–Hennecart–Ruzsa sum-difference constant to 1.187326127925948 (base-89 capped digit construction, limit certificate)

[unnir]

This PR improves the lower bound of constant 3a from 1.1835129324 ([MI2026], PR #95) to

C_3a >= 1.187326127925948 (margin +0.0038132; safely below the 4/3 upper bound and the 5/4 digit-lemma ceiling)

Construction. A capped digit construction U_d over base B=89 with the sparse 29-letter alphabet
A = [0,8,9,12,16,17,18,20,21,24,25,26,27,28,29,30,32,33,34,35,36,37,38,39,40,41,42,43,44]
(max digit 44, cap ratio ~10.70). The GHR2007 lemma value theta(U_d) is a valid lower bound for
EVERY depth d; theta(U_d) increases to a large-deviation limit L(A), so C_3a >= L(A) the same
limit-as-lower-bound principle used by [Z2025] in the existing ladder. L(A) is certified with
interval arithmetic (entropy lower bound for the difference side, a dual upper bound for the sum
side, exact rational endpoints). Two notes the certificate makes explicit: [MI2026] certified only
their construction's finite d=420 value — the same limit principle applied to their own base-33
alphabet already yields 1.18552; and the method's structural ceiling is ~1.1875 (the lemma's d<q
hypothesis forces a*r < 1), which this construction essentially attains.

Certificate (replayable).
Archive: https://zenodo.org/records/21504058 (DOI: https://doi.org/21504058)

• verify.py + gsd_3a_cert.json — standalone checker: recomputes exact |U_d + U_d| and
  |U_d − U_d| by brute-force big-integer counting at several depths (calibrated against [MI2026]'s
  published d=120 value to 40 digits), confirms the per-depth values climb, and verifies the
  interval-arithmetic limit bound strictly exceeds the previous record. RESULT: ALL PASS, exit 0.

Changes in this PR. constants/3a.md: one row added to the lower-bounds table + a [Num2026]
reference entry. README.md: row 3a lower bound updated.

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