Wide-band LP certificate for Lamzouri's loss on real periodic configurations (MT window).

Files
- lp_wideband4.py    LP that maximises beta for h = K^2 - beta*F - sin^2(pi x)*rho(x).
                     rhohat is piecewise linear, knots k/m, zero at integers, support [-B, B].
                     Run: python3 lp_wideband4.py 2 20 60 1e-6 0 5e-5 1e-6 2.2 1e-5
- cert_B2_m20_sol.npz the solution (beta, rhohat values at the free knots).
- cert_wb.py         certifier, exact rationals plus mpmath interval arithmetic.
                     Run: python3 cert_wb.py cert_B2_m20_sol.npz 20
                     Checks (1) hhat >= 0 on R and (2) h <= K^2 on R\{0}, via the exactly periodic condition Q >= 0 on one period.
- cert_output_B2_m20.txt  output of the certifier ("CERTIFIED", h(0) = 0.0151876).
- wb_check.py        independent checks: direct numerical Fourier transform of h versus the formula for hhat; Q on a fine grid.
- offline_test.py    the off-line pair test (sum of K^2 - h against beta(N+D), alongside the true loss).

Theorem (certified). For every real P-periodic configuration with N = P points counted with multiplicity,
L = n_s - 2N + sum K(x-y)^2 >= N V - (1-beta) D, with 1 - beta = 0.0151876.
- lp_wideband5.py    same LP plus the pair-internal constraints rho(iy) <= beta/(pi^2 y^2) - beta/sinh^2(pi y), y in (0, YMAX]
                     (the off-line-pair diagnostic in section 2 of the post; run without margins:
                      python3 lp_wideband5.py 2 20 60 1e-7 0 1e-6 0 2.2 0 YMAX).
- opsplit_toy.py    operator-split check for an off-line pair in the nearest-dipole environment (section 2).
