PSC Paper 3 Revision 10: Fitting a Logarithmic Redshift–Distance Law to Pantheon+SH0ES; Full-Covariance Results and Limits

An earlier version of this paper reported χ2 ν = 0.439 for a Phase-Shift Cosmology (PSC) distance-modulus model on Pantheon+SH0ES and presented it as an empirical verification that beat ΛCDM. Those claims are withdrawn. The 0.439 used diagonal errors only; with the full STAT+SYS covariance, the PSC model with one extra scale term gives χ2 = 1753.4 (χ2/dof =1.032), statistically identical to flat ΛCDM (1752.5, 1.031). PSC ties; it does not win. The tie survives the standard z > 0.01 cut for this form (∆χ2 = +0.3) but not for the exponent-free variant (+8.4). The one-parameter PSC form without the extra term is worse than ΛCDM by ∆χ2 ≈ 72 and worse than the empty-universe (Milne) model by ≈ 47. The quoted κΨ0 =1.1215×10−4 Mpc−1 was not determined by the fit: it is exactly degenerate with the magnitude offset. The physical value is κΨ0 = H0/c ≈ 2.44 × 10−4 Mpc−1. The extra scale term has no derivation and appears to compensate for a dimming factor the earlier model lacked. Supernova magnitudes at this precision do not discriminate PSC from ΛCDM or from generic two-parameter smooth curves.