Observational Phase-Coherent Residual Modulation in Type Ia Supernova Hubble Diagrams

We analyze a reported nonlinear-phase modulation in Type Ia supernovaHubble-diagram residuals, emphasizing visualization, cross-compilation phasecoherence, look-elsewhere effects, waveform choice, endpoint artifacts, andpassband systematics. In a reconstructed 7687-entry diagnostic sample from sixcompilations, the normalized coordinate u=(z+qz²)/(1+q) with one Fourierharmonic gives $q=0.080$, $T=0.05263$, 19 cycles over 0≤ z≤1,A=0.0160±0.0028 mag, and Δχ²=31.91. Five compilation phases liewithin 0.056 cycles of the joint phase; DES is weaker and offset by 0.140cycles. A cubic coordinate improves Δχ² by only 1.05, while secondand third harmonics add only 1.19 and 1.53. Repeating the fullcoordinate-period-waveform search in 10,000 null realizations gives globalprobabilities 3.0×10⁻⁴, 4.0×10⁻⁴, and 2.9×10⁻³for raw, AIC-adjusted, and BIC-adjusted statistics. Paired MODEL009 light-curverefits cover 1529/1580 Pantheon+ entries; despite a 26.2 mmag weighted-rmsdistance perturbation, the fitted phase and amplitude remain stable. Themodulation is robust to this spectral-model perturbation.