Temporal Equivalence Principle: A Covariant Alternative to Cosmic Expansion

This paper presents a direct empirical challenge to the necessity of primitive cosmic expansion. In the Temporal Equivalence Principle framework, observed redshift is reconstructed as conformal proper-time transport, 1+z=A_0/A_em, rather than as stretching of a spatial scale factor. Standard cosmology interprets observational redshift and luminosity distance scaling as evidence of a stretching spatial metric, parameterized by the FLRW scale factor a(t). The observational role played by the FLRW scale factor is mapped, within the TEP conformal-frame construction, onto the temporal clock-rate field A(phi). In the tested late-time background sector, the perceived acceleration normally attributed to Dark Energy, Lambda, is reconstructed as the kinetic energy density of the Temporal Shear field, Omega_phi. The core relation is 1+z = A_0/A_em. In the static conformal interpretation developed here, intergalactic separations are not treated as primitively expanding; the apparent expansion is reconstructed through temporal transport. In this framework, the limit conventionally written as a->0 is re-expressed as A_clock->0: a TEP temporal-horizon boundary of observational clock transport, not a zero-volume spatial singularity. The framework is formally closed from the temporal-horizon background (a_eff -> 0) down to linear mode evolution (k ~ 0.5 h/Mpc) through the exact Bellini-Sawicki EFT mapping implemented in TEP-HC (Paper 18), which natively yields sigma_8 ~ 0.825 in agreement with Planck. Using 1,701 Pantheon+ Type Ia supernovae with the full covariance matrix, a pure conformal reconstruction exactly reproduces the Lambda CDM homogeneous distance-modulus relation, demonstrating that the background Hubble diagram does not uniquely select an expanding spatial metric. More strongly, the conservative physical no-Lambda temporal-shear branch with fixed z_T=5 improves the standardized supernova likelihood by Delta chi^2 ~ -3.4 relative to baseline Lambda CDM and achieves a Bayes factor of BF ~ 4.6, classified as "substantial" evidence on the Jeffreys scale. The fixed z_T=100 benchmark gives the strongest evidence, BF ~ 61.8 (Delta chi^2 ~ -7.5), while the broad free-z_T model gives BF ~ 40.3. The conservative physical model with z_T=5 already demonstrates that a matter-only temporal-shear geometry is competitive with Lambda CDM in the late-time SNe distance-redshift sector. These results establish positive supernova-sector evidence that apparent acceleration can be reconstructed as temporal transport rather than primitive dark energy. Companion papers establish the theoretical foundations: TEP-HC (Paper 18) provides the Boltzmann-level acoustic-scale preservation proof under the native hi_class `tep_mode` implementation, and TEP-TH develops the nonsingular temporal-horizon closure. The current paper focuses on the empirical supernova-sector test and the deterministic falsification pipeline. Keywords: temporal equivalence principle – cosmology – dark energy – supernovae – Bayesian inference – modified gravity – temporal shear Website: https://mlsmawfield.com/tep/c0Repository: https://github.com/matthewsmawfield/TEP-C0 DOI: 10.5281/zenodo.20370143 Open Science Statement: This work is a preprint and is open to community review, ideas, and collaboration. All materials required for full reproducibility—including data downloads, analysis scripts, code, and manuscripts—are open-source. Feedback and contributions to further test these results are welcome.