A curved Crab spin-down baseline reduces errors in 37 later records under a fixed early fit

A smooth baseline is needed to measure a lasting change in the Crab pulsar's rate of slowing. We compare a straight baseline with a curved baseline that assumes a constant braking index. Both models use the same early data and four fitted parameters. We fit data from 2015 to 2022 and test 37 later timing records through 8 July 2025. The curved model reduces the root mean squared error from 13.43 to 8.49 units of 10^-15 Hz/s. This is a 36.8 percent reduction. All eight sensitivity checks also favor the curved model. The fitted lasting shift changes from -440.21 to -430.38 units with equal record weights. The result shows that baseline curvature matters for this continuation and shift estimate. The test is retrospective. One stress test perturbed the early data and fitted both models again. Its 95 percent gain range included zero. Timing noise and early-fit uncertainty limit the physical interpretation. The package contains numerical data, source hashes, code, predictions, figures, and reproduction steps.

Crab pulsar · spin-down · braking index · glitch recovery · public data · prediction test · timing noise · reproducible analysis