WHERE THE INTERSECTIONS WEAVE — I Direction-Dependent Residuals in Type Ia Supernova Distance Moduli and Degeneracy with Analysis-Variable Space

In the distance-modulus residuals of Type Ia supernovae, a signal dependent on the angle θ from the CMB dipole axis was detected in the z = 0.35–0.55 range of the Pantheon+ data. Weighted cos θ regression of bin averages using diagonal errors yielded a nominal 2.74σ deviation. Because the isotropic ΛCDM model predicts zero θ dependence, this deviation is noteworthy. This paper reports the observational fact while simultaneously raising methodological issues inherent in the generation process of public catalogs. Code audit of the Pantheon+ data-processing pipeline (SNANA/BBC and SuperCal-Fragilistic calibration) confirmed, at the code level, pathways by which survey- and field-specific correction structures can indirectly absorb spatially correlated signals. To quantify this degeneracy, artificial cos θ-type signals centered near z ≈ 0.45 were injected into the actual catalog configurations of JLA (740 supernovae) and Pantheon+ (1,590 data rows), and projection tests that mimic the analysis model used in the pipeline were performed. In the local region z = 0.35–0.55, an approximately 22% degeneracy between the injected signal and the analysis-variable space was observed. This degeneracy rate was nearly identical across two compilations of different generations and configurations (JLA: 22%, Pantheon+: 22.5%). Consequently, the weakness of directional signals in processed catalogs cannot be equated with weakness in nature. “Signal not detected” and “signal does not exist” must be distinguished; for unmodeled direction- dependent signals, degeneracy with the analysis-variable space cannot be ignored a priori. This paper advances no new physical theory. It reports the observational facts, the structural properties of the pipeline, and the results of the signal-injection and variable-projection tests, and draws attention to the reanalysis of existing data and the detectability of direction-dependent signals in future surveys.