Exact opposite phases gave almost the same mean timing forecast error as separate phases in 26 selected Kepler pairs

We tested whether an exact opposite timing phase improves forecasts for known adjacent Kepler planets. We reused a frozen benchmark and fitted early transit times only. Later times tested each forecast. The main sample had 26 selected pairs around 25 stars. The reference model fitted a separate phase for each member at a fixed beat period. The joint model used opposite phases and nonnegative amplitudes. The primary outcome was the later weighted RMS error ratio for the member with weaker early evidence. We averaged log ratios within stars and then gave stars equal weight. This ratio was 0.973, with a descriptive 95% star bootstrap interval of 0.946 to 0.997. Exactly 13 of 26 weaker members improved. The stronger members had a ratio of 1.024. The combined pair ratio was 0.998, with an interval of 0.988 to 1.010. The largest weaker-member gain came with a 51% error increase in its stronger companion. Moving the date split by 100 days gave weaker-member ratios near one. A same-phase control gave a ratio of 1.352. Numerical checks reproduced the parent scores and agreed with a second fit method. Conditional Gaussian trials showed a cost when the true phases differed from opposition. The result applies to one fixed-frequency model, this selected sample, and a later horizon of at most 423.55 days. Full-record templates, flags, and planet status make the test retrospective. The package preserves source data, provenance, code, figures, all primary predictions, and 5200 simulation scores.

Kepler · transit timing variations · phase constraint · forecast test · reproducible benchmark