A Gaussian model at fixed beat frequencies supports opposite timing waves in both Kepler halves for 2 of 34 planet pairs

We tested whether opposite transit timing waves persist in two separate parts of the Kepler record. We used Holczer et al. timing data and a saved NASA planet-status table. Period ratios, timing counts, and time coverage selected 34 pairs at 29 stars. We fitted each planet and half separately at a fixed orbital beat frequency. Confidence ellipses give cosine bounds with at least 95% simultaneous coverage under the fixed Gaussian wave model. Eighteen pairs have negative best-fit cosines in both halves. Two pairs have negative upper bounds in both halves: Kepler-18 c/d and Kepler-49 b/c. Kepler-18 retains support across tested error floors, flag choices, added harmonics, and time splits. Kepler-49 loses support when source outlier flags are included or the split moves to 45% or 55%. Both systems were known before this study. The contribution is a reproducible phase-bound tool, a complete selection ledger, and a measured comparison of point estimates with uncertainty bounds. Correlated errors, an incorrect wave mean, and catalogue construction can invalidate the conditional coverage statement. No new planet or physical false-alarm probability is reported. The package preserves numerical inputs, provenance, code, fitted data, covariance matrices, control tests, and figures.

Kepler · transit timing variations · phase bounds · planet pairs · Gaussian regression · reproducible astronomy