Differential Clock Rates from Spatially Varying Metric Signature: Consistency with Pantheon+ Supernova Evidence for Differential Cosmic Expansion

We consider the observational consequences of a spatially varying metric signature, parameterised by a dimensionless phase parameter φ that modifies the time-time component of the metric: g₀₀ = −(1 − 2φ). If φ correlates with local energy density—small in overdense environments and larger in underdense voids—the resulting metric produces differential clock rates between voids and filaments. We show that electromagnetic and gravitational wave propagation speeds are identically modified by this metric, so multi-messenger constraints such as GW170817 (|Δc|/c < 10⁻¹⁵) are automatically satisfied. We note that Seifert, Lane, Wiltshire et al. (2024–2025) have reported very strong Bayesian evidence (ln B > 5) for differential expansion between cosmic voids and filaments in the Pantheon+ Type Ia supernova dataset, consistent with this prediction. The spatially varying signature hypothesis is observationally degenerate with the Timescape backreaction model at the level of current data; we identify three specific tests that could break this degeneracy. We also note the achromatic CMB void temperature anomaly reported by Hansen et al. (2025) as a potentially related observation whose theoretical mechanism within this framework requires further development.