files / problems / long-gap-dilate / compute / q1 / README.md

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q1 — rising factorials, a SAT push past 71, and more families

The 2026-08-17 start left no compute/qN/. This folder is the first named search. Shakan’s universal 2 is still the published record.

What was tried

  1. Rebuild the homogeneous Rédei slice and Wronskian on every stored SAT witness, and expand the unused rising-factorial polynomial w(d,t) = d ∏_a (t+da+1)_m far enough to read the actual Alon degrees of u,v. The extra Stirling terms do not cut those degrees below the wall k = nm-p+1. At the scales C = 2.5 and C = 3 one has k ≥ p, so the middle-coefficient list is empty.
  2. Downward SAT for G(p, round √p) on the next primes after 71, with a hard process kill. Cadical proves T=24 unsat at p=73 in 165s and Glucose4 supplies a hitting set at T=25, so G(73,9)=24 exactly (also written into ../certs/sat_G.jsonl). Upper bounds G(79,9)≤26, G(83,9)≤27, G(89,9)≤30 timed out on the next smaller T. A timeout is an incomplete search, not a lower bound.
  3. More families (quadratic rulers, Paley prefixes, cyclotomic cosets, Singer orbits including the (73,9,1) set {2^k} in F_73, and a longer anneal) through p = 200. No infinite family with max_d g ≤ (2+ε)√p.

Replay

cd problems/long-gap-dilate/compute/q1
./run_all.sh

Parent replay is unchanged:

cd problems/long-gap-dilate
sh compute/run_all.sh

Does not claim a universal C>2.