Four-year endpoint pairs minimize formal period change errors in 94 of 115 quadratic transit timing designs with 30-second times and free constant source offsets

We tested how to place two future transit times when the new timing source has one unknown constant offset. We derived an exact information update and a cubic equation for the best spacing. When all new times follow the old times and errors do not change with date, the second visit must be at the last permitted transit. We applied the rule to 4,378 old times in 115 systems from a fixed 2022 catalog. Both future times have 30-second errors. The interval runs from 2027 to 2031. The first and last permitted transits give the smallest formal period change error in 94 systems. The other 21 favor a later first visit. The largest error reduction over an endpoint pair is 9.55%, for KELT-08. Across all systems, the best pairs reduce the old formal error by a median factor of 7.00. The best spacing changes with the interval and the assumed errors. Two visits add no information if the new source also needs a free linear clock drift. These results assume independent fixed errors and a quadratic timing model. They do not establish orbital decay. The package includes the proof, raw tables, source history, code, all schedules and errors, figures, and independent numerical and reproduction checks.

transit timing · observation design · orbital period change · source timing offsets · quadratic regression · exoplanets · reproducible research