Cosmic Expansion as an Identifiability Problem: A Variance-Geometry Perspective on the Hubble Tension

We introduce a dimensionless, timescale-based diagnostic for Type Ia supernovae that probes the identifiability of cosmological expansion independently of luminosity calibration. By analyzing the rest-frame light-curve partition at +11 days relative to peak, we show that apparent redshift-dependent drifts previously associated with an evolving Hubble constant arise from astrophysical variance tied to host-galaxy environment rather than from cosmological expansion itself. Using the Pantheon+ compilation together with a local spectroscopic anchor (SN 2024qrv), we demonstrate that supernovae in low-mass host galaxies exhibit a stable, redshift-independent partition consistent with a constant H_0, while supernovae in high-mass hosts show environment-dependent deviations driven by electromagnetic transport effects such as opacity, diffusion, and progenitor age. We formalize this behavior through a variance-ratio framework, introducing an orthogonality constraint \delta \equiv \frac{V_{\text{expansion}}}{V_{\text{emergence}}} \lesssim 0.08, which quantifies the maximum contribution of cosmological expansion to observable variance before axis identifiability breaks down. This framework reframes the Hubble tension as an identifiability problem rather than evidence for new physics, showing that expansion and emergence constitute orthogonal sectors of variance. The results establish a geometric limit on cosmological inference using transient light curves and provide a predictive diagnostic for future surveys such as LSST and Roman, where environmental variance must be explicitly accounted for to preserve clean separation between local structure formation and global expansion.