Window re-basing of the pair -> double transfer (A'') and of the real-configuration certificate.
Window family: eta_b^2(u) = cos(b u)/Z_b on [-1/2, 1/2], Z_b = 2 sin(b/2)/b (b = sqrt2 is Montgomery-Taylor).
phi_b = eta_b^2 * eta_b^2 (int phi_b = 1), K_b = Fourier transform of eta_b^2.
Window statistics: phi_b(0), M_b = int phi_b |alpha| d alpha; w = 0 value 1 - M_b.
All results are numerical (local optimisation / LP), not certified. Python 3 + numpy + scipy (+ cvxpy for the SDP).
Run everything from this directory (paths are relative: ./t2, ./m2). The window is chosen by the environment variable WINB.

t2/w3_window.py b [Ps] [starts]   J = 1 honest-adversary LP (periodic columns of simple points, doubles, triples and
                                  off-line pairs; column generation; machinery t2_lp.py / t2_fast.py from post 72).
                                  out/w3_b*.txt: P <= 12. b = 1.414 reproduces the MT value 0.676437.
t2/w2_families.py, w1_p40.py      G0 (J = 2, Fejer + MT): duals [0.999601, -1.746495, 0.723701] (opposite signs).

m2/clip_ceiling_w.py c L          T-C ceilings, doubles interacting (clipped at c), periodic laws L <= 12.
m2/clip_ceiling_noint_w.py        same with doubles credited 4 and no interaction.
                                  out/tCb_int_{mt,b16,b18}.txt: 0.67653 / 0.67867 / 0.68059;
                                  out/tCb_noint_{mt,b18}.txt: 0.67370 / 0.67291 (c = 2).
m2/tstar_robust_w.py c deltas     single pair T*(c), many starts (lattice, coincident, near-triple piles, dense, random).
m2/tstar_sdp3_w.py n N step deltas  SDP majorant ratio r(delta) for the single-pair proof route.
m2/tstar_mpk_w.py delta ks        k pairs inside a double lattice (multi-pair blocks), min T*(2).
                                  MT reference outputs: out/tMPk_0.25.txt, out/tNT2_c2.txt.
m2/lp_wideband4_w.py B m X ...    two-point real-configuration certificate h = K^2 - beta F - sin^2(pi x) rho (lattice-tight);
                                  value 1 - M_b/beta. cert_scan.sh scans b. out/cert_scan.txt, out/lpwb4w_*.txt.
m2/lp_wbrelax_w.py B m eps0       same without lattice tightness: E >= (1 + V - eps) N + beta D, value 1 - (M_b + eps)/beta.
m2/many_blocks_w.py delta seed    T-MB: many pair blocks per period (P = 60), minimise W(pairs) = (E - N(1+V))/D - 1
                                  (true loss per defect zero, negated). out/tMB_b16_d*.txt (b = 1.6), out/tMB_0.*.txt (MT),
                                  out/tMB_mtcal_d0.25.txt (MT calibration of the generalised script).
m2/tstar_kzero.py SRC             T-KZ: near-doubles straddling the zeros of K. Run as
                                  WINB=1.6 python3 m2/tstar_kzero.py m2/tstar_multipair_w.py   -> out/tKZ_b16.txt (MT: out/tKZ.txt)
t2/out/w3r_b1.6.txt               J = 1 LP at b = 1.6 (P <= 12, 10 starts): 0.678533.
m2/out/cert_scan2.txt             certificate near the optimum: b = 1.55-1.6, B = 4-5: value 0.6751-0.6752.
t2/out/w3r_b1.8_P24.txt, _P16.txt  robustness of the b = 1.8 LP value: 0.680424 (P <= 24), 0.680416 (P <= 16).
m2/clip_dipole_w.py               clipped vs unclipped loss of the relaxed nearest dipole (double + vacancy):
                                  out/clipdip_{mtcal,b16,b18}.txt (clipping costs 1.3e-5 / 3.6e-5 / 1.0e-4 per defect zero).
m2/dipole_slack.py CERT P         splits the two-point certificate's slack on the relaxed dipole into Fourier and
                                  off-coincidence parts (out/dipole_slack.txt).
m2/sf_periodicity.py P         structure factor I(xi), I(xi+1), I(xi+2) of the relaxed dipole (out/sf_periodicity_b18.txt).
