Fourier timing scores depend on the time origin in 33 selected Kepler pairs at fixed beat frequencies

A common change of time origin leaves a fitted timing curve unchanged. We tested how this choice changes a Fourier timing score that uses marginal coefficient errors. We used public Holczer transit times and the 59 pairs in its Table 8. Fixed beat frequencies and stated coverage rules gave 33 pairs, 4851 unique timings, and 29 stars. The median score range across common origins was 11.1% of the nominal absolute score. The range exceeded 10% for 19 pairs and reached 51.0%. No selected pair changed score sign. Removing a line before the wave fit gave 23 of 33 ranges above 10%. We give an invariant comparison, Q = -(b1 dot b2)/sqrt(trace(C1 C2)), with full wave covariance matrices. A common orthogonal rotation leaves Q unchanged. Independent zero-mean wave errors give Q mean zero and variance one under the stated covariance model. Q is not generally normal and does not give planet detection significance. Direct refits, a second source parser, Gaussian transit simulations, and a fresh analysis check the calculation. The package preserves inputs, provenance, code, fit covariances, selection decisions, controls, and figures. The result measures a coordinate effect in this selected sample. It does not revise planet confirmations or test published permutation probabilities.

Kepler · transit timing variations · Fourier score · time origin · covariance · rotation invariance · reproducible research