The 31 tidal periods (in days) are taken directly from the lpap array in the GEM-LTE parameter file experiments/Feb2026/11/lt.exe.p. For each period T the fit uses two basis functions cos(2πt/T) and sin(2πt/T), where t is time in days from 1962 Jan 1, giving 62 sinusoidal regressors plus an intercept. Ridge regularisation (L2 penalty) prevents near-collinear long-period components from amplifying noise. The normal equations (X′X + λI)β = X′y are solved with Gaussian elimination. Adjusting λ from 10−3 to 103 trades training bias against out-of-sample stability.
LOD anomaly data from experiments/dLOD3.dat: 20,830 daily values spanning 1962.01–2019.03, in units of milliseconds (ms). Tidal periods from GEM-LTE parameter file experiments/Feb2026/11/lt.exe.p (lpap array). Reference epoch: 1962.0 (days counted from 1 Jan 1962). Two entries in the lpap array have negative period values (−3232.6 d and −2120.9 d); a negative period T is mathematically equivalent to the positive period |T| with the sign of the sine coefficient reversed, so both signs are handled correctly by the regression. Their |T| values correspond to long-period tidal cycles (~8.9 yr and ~5.8 yr).