Temporal Equivalence Principle: A Standard-Siren Test of Bi-Metric Gravitational-Wave Propagation

Canonical model scope. The governing TEP radiation rule fixes Ξ(z)=d_L GW/d_L matter=1/(1+z), with detector-frame mass widetilde M/(1+z) and conventionally reported GR source mass widetilde M/(1+z)². The canonical distance map is evaluated directly on the independent 51-event sample: it returns χ² = 69.2 against the ΛCDM baseline χ² = 74.3 at equal degrees of freedom (Δχ² = +5.1, mildly preferring the canonical map at H_0 = 50 km/s/Mpc — ~25% below the corpus-anchored value of 66.7), conditioned on ΛCDM-referenced distance posteriors and host-marginalized redshifts. The remaining numerical likelihood results below evaluate the historical exponential template; they remain reproducible results for that template and have not yet been recomputed with the full canonical mass and selection mapping. The canonical interface is implemented and checked against the cached event identities and redshift provenance. Standard ΛCDM assumes that gravitational waves and electromagnetic radiation propagate through the same effective distance-redshift relation. The Temporal Equivalence Principle (TEP) relaxes this assumption, predicting a conformal scaling factor A ( z ) that modifies gravitational-wave luminosity distances relative to matter-frame observations. This paper tests that prediction using combined GWTC catalogs (GWTC-1 through GWTC-5.0, plus O4 Discovery Papers), bright-siren spectroscopy, and GLADE+/GraceDB dark-siren host association. The lab-fixed model uses A ( z ) = exp( β A φ 0 [(1+ z ) n − 1]) with β A = −1 and φ 0 = +0.013 (dimensionless, φ 0 = φ / M Pl ), so A ( z ) departs below unity with growing redshift-dependent amplitude, the direction required by the endpoint identity 1+ z = A 0 / A em at positive redshift. With corrected per-event distance uncertainties and hierarchical Bayesian host marginalization, the pipeline identifies 51 events with host-associated redshifts independent of the GWOSC fiducial cosmology (50 from GLADE+/DESI plus the bright siren GW170817) and 56 events with GWOSC-catalog fallback redshifts. The primary analysis excludes fallback redshifts to avoid ΛCDM circularity: the independent-only sample gives ΛCDM H 0 = 59.8 km/s/Mpc and lab-fixed TEP H 0 = 59.6 km/s/Mpc (Δχ² ≡ χ² ΛCDM − χ² TEP = +0.13, |ΔBIC| < 2). A secondary full-sample diagnostic (107 events, including fallback redshifts) gives ΛCDM H 0 = 64.6 km/s/Mpc and TEP H 0 = 64.4 km/s/Mpc (Δχ² = +0.16). The joint MCMC fit to ( H 0 , φ 0 , n , β ) with 64 walkers × 10000 steps gives posterior mean H 0 = 58.5 ± 4.8 km/s/Mpc, φ 0 = +0.001 ± 0.031, n = 1.73 ± 0.88, β fit = −0.08 ± 3.15; the lab-calibrated values ( φ 0 = +0.013, n = 1.0, β A = −1.0) are consistent within 1 σ , and 74.4% of the joint posterior mass lies on the corpus-consistent sign βφ 0 < 0 ( A ( z ) < 1). The corresponding joint ΔBIC = −11.9 (independent sample; −14.2 on the full sample) reflects the three-parameter information penalty rather than a fit deficit. The redshift-dependent matched-filter residual test recovers the corpus-sign structure at Z = +2.59 (γ = +95 ± 37, with the sign-flipped control disfavored), although the fitted amplitude exceeds the locked normalization by about two orders of magnitude and the redshift-shuffle control ( p = 0.10) does not yet exclude a noise origin. The current sample is underpowered to bound the predicted amplitude. Version: v0.1 (Maputo) — 30 September 2026 This initial release registers the canonical endpoint map Ξ(z) = 1/(1+z) and evaluates it on the independent 51-event sample (Δχ² = +5.1 vs ΛCDM at equal d.o.f., conditioned on ΛCDM-referenced distance posteriors); Paper 11 framing is aligned to the conditional Cepheid-response reading. Keywords: Temporal Equivalence Principle, gravitational waves, standard sirens, bi-metric propagation, distance-redshift relation, combined GWTC catalogs Website: https://mlsmawfield.com/tep/lvkRepository: https://github.com/matthewsmawfield/TEP-LVK DOI: 10.5281/zenodo.20572696 Open Science Statement: This work is a preprint and is open to community review, ideas, and collaboration. All analysis code, configuration files, and manuscripts are open source. Feedback and contributions to further test these results are welcome.