C_38a --- Improve rigorous lower bound for square-lattice SAW connective constant to 2.6273856 (span-17 certified enumeration) [Numaro.tech]

[unnir]

This PR improves the rigorous lower bound of constant 38a from 2.625622 (Iwan Jensen 2004, as
reported in [FV2017] and [SlaBounds]) — unimproved for 22 years — to

mu(Z^2) >= 2.6273856 (exact dyadic rational 2^128 / 129513673858566230428673965530967449326)

Method. Jensen's own method, two compute levels deeper: exact enumeration of span-bounded
bridges by a cell-by-cell finite-lattice transfer matrix (span L=17, series length N=260;
≈5.6×10^8 states, ≈8.7×10^8 transitions, CRT big-integer arithmetic), then Kesten's irreducible-
bridge renewal converts the counts into the certified inequality sum a_n R^{-n} >= 1 =>
mu >= R — one exact big-integer comparison. The 2004 record was computed at span L=15, N=250 on
a 1 GHz Alpha with 2.5 GB RAM; this run used 192 cores and hundreds of GB. As independent
confirmation, the same table restricted to lower spans already certifies 2.6265705 (L=16) and
2.6256270 (L=15, N=260, Jensen's own span) — three nested certificates clear the record. Sanity:
all three bounds sit safely below the non-rigorous estimate 2.63815853 [JSG2016].

Calibration. The enumerator reproduces OEIS A001411 exactly; the bridge series b_0..b_21
agrees with three independent enumerator implementations; and the pipeline reproduces Jensen's
published intermediate bounds digit-for-digit (2.583704 / 2.601224) before exceeding his frontier.

Certificate (replayable, ~minutes).
Archive: https://zenodo.org/records/21546041 (DOI: https://doi.org/21546041)

• check_saw38a_L17.py + bridge_table_record_L17.json (SHA-256-bound) — self-contained stdlib
  checker: re-enumerates all bridges of length <=13 by brute force, checks structural invariants
  and the published series prefix, re-derives irreducible counts via the span renewal, and verifies
  the Kesten inequality and the strict improvement as pure big-integer comparisons. Ends
  ALL CERTIFIED, exit 0.
• verify.py — an independent second implementation, VERIFY: PASS *** RECORD BEATEN ***, exit 0.

Changes in this PR. constants/38a.md: one row added to the Known lower bounds table + a
[Num2026] reference entry. README.md: row 38 lower bound updated.

AI-use disclosure (per CONTRIBUTING.md): the enumeration engine and certificate were built and
run with AI assistance (an automated search-and-verification pipeline built on Claude/GPT/Gemini agents by
Numaro); all results were re-run and verified by the human submitter before
this PR — both checkers replay from the archive alone.

— Numaro