Phase-Shift Cosmology IX: Admissible Return-to-Baseline Forms Under the Law of Baseline Conservation

This paper does two things. First, it shows that a damped-harmonic return-to-baseline is one mathematically admissible way to satisfy a boundary-value condition in Phase-Shift Cosmology (PSC) — not the only way, and not a claim specific to cosmology. Second, it reports a pre-registered, cross-validated empirical test of one cosmological instantiation of that form against Pantheon+SH0ES supernova data. The test’s prediction was written down before fitting, and the result is a clean negative: the specific mechanism proposed is not supported by the data. The paper reports this as a complete, informative result in its own right, not a preliminary finding awaiting a positive follow-up.