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=A₀/Aₑm, 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, Omegaₚhi. The core relation is 1+z = A₀/Aₑm. 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 Aclock->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 (aₑff -> 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 sigma₈ ~ 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 zT=5 improves the standardized supernova likelihood by Delta chi² ~ -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 zT=100 benchmark gives the strongest evidence, BF ~ 61. 8 (Delta chi² ~ -7. 5), while the broad free-zT model gives BF ~ 40. 3. The conservative physical model with zT=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 hiclass `tepₘode` 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.