Follow-up package (numerical, not certified). Period 40, density 1. Requires numpy, scipy; lp_twospecies.py also needs cvxpy (Clarabel).
offline_multi.py SOLFILE CASE   CASE = M1a | M1f | M2 | M3 | SAN : localised deep bound with several pairs (and a sanity check).
offline_multi2.py SOLFILE CASE  CASE = WM (several shallow pairs, certificate extension) | MIX (shallow + deep) | S3L1 (single pair, delta scan).
lp_twospecies.py B m ds         two-species LP with kernels uniform in delta in [0, ds] (real points + pairs); prints min w.
   out/lp2s_ds*.txt: B = 2 at ds = 0.001 (sanity), 0.02, 0.025, 0.03, 0.04, 0.05; out/lp2s_B3_ds0.05.txt: B = 3.
   The loss with ds follows (1 - beta_R - V)/2 + K(2 i ds)^2 - 1 (Poisson identity; see the comment).
cert_B2_m20_sol.npz: the certified certificate of post 73.
