Paper XXXII - Operational Time Dilation from Supernova Temporal Structure

DOI: 10.5281/zenodo.18009862 Operational Time Dilation from Supernova Temporal Structure Paper XXXII of the Ordered-Dynamics Reconstruction Program Paul Cooneya aIndependent Researcher, Innisfil, Ontario, Canada E-mail: paul.co[email protected]to.ca Abstract. We present the first empirical test of operational time scaling within the OrderedDynamics Reconstruction Program (ODRP), using the temporal structure of Type Ia supernova light curves. By generalizing the rest-frame phase mapping employed in standard lightcurve models, we isolate redshift-dependent temporal scaling as an observable independent of luminosity calibration and distance assumptions. Synthetic injection–recovery tests demonstrate that the inference pipeline reliably detects genuine time-scaling signals while rejecting artifacts of noise, cadence, or covariance structure. The results are interpreted strictly as constraints on allowable operational time-scaling behavior and do not invoke cosmological expansion, dark energy, or distance–redshift relations. Contents 1 Program context 1 2 Temporal observables in supernova light curves 1 2.1 Generalized phase mapping 2 3 Data and preprocessing 2 4 Likelihood and inference 2 5 Synthetic injection–recovery 2 5.1 Null injections 2 5.2 Non-null injections 2 5.3 Negative controls 2 6 Results 3 7 Interpretation 3 8 Conclusion 3 Contents 1 Program context The Ordered-Dynamics Reconstruction Program (ODRP) proceeds by separating temporal and spatial observables prior to interpretation. Papers I–XXX establish the theoretical and operational framework of the program without direct use of observational data. Paper XXXI defines the empirical ingestion, validation, and failure-detection infrastructure for all data-driven ODRP analyses. The present paper constitutes the first application of that infrastructure to real observational data. The specific objective of this work is to test whether the temporal structure of Type Ia supernova light curves constrains operational time scaling independently of distance or luminosity calibration. 2 Temporal observables in supernova light curves Type Ia supernovae exhibit reproducible temporal structure that can be parameterized and compared across redshift. Standard light-curve models such as SALT2 describe this structure in terms of a rest-frame phase variable obtained by correcting observed time by a factor (1+z). Within the ODRP framework, this correction is not assumed a priori. Instead, we treat the mapping between observed time and rest-frame phase as an empirical object to be tested. – 1 – 2.1 Generalized phase mapping We define a generalized operational phase mapping ϕ=tobs g(z),(2.1) where tobs is the observed time relative to maximum light and g(z) is an unknown operational time-scaling function. The conventional (1 + z) mapping corresponds to g(z) = 1 + zbut is not imposed. 3 Data and preprocessing We analyze publicly available Type Ia supernova light-curve data processed using standard photometric pipelines. Light curves are modeled using the SALT2 framework [1], with the generalized phase mapping applied prior to template fitting. All covariance information provided with the data is retained. No recalibration or redshift-dependent modification of luminosity parameters is performed. 4 Likelihood and inference The likelihood follows the unified Gaussian form defined in Paper XXXI [3]. The data vector consists of photometric residuals after SALT2 template fitting under the generalized phase mapping. Operational time-scaling parameters are inferred jointly with standard SALT2 nuisance parameters. No distance or luminosity parameters enter the inference. 5 Synthetic injection–recovery Prior to interpretation of real data, we perform synthetic injection–recovery tests. 5.1 Null injections Synthetic light curves generated with g(z) = 1+zare recovered without spurious time-scaling detection. 5.2 Non-null injections Injected deviations from (1 + z) scaling are recovered without significant bias over a range of amplitudes compatible with observational sensitivity. 5.3 Negative controls Redshift scrambling, cadence perturbation, and covariance truncation invalidate recovery as expected, confirming sensitivity to genuine temporal structure. – 2 – 6 Results Applying the validated inference pipeline to real supernova data, we obtain constraints on the allowable form of the operational time-scaling function g(z). Within current uncertainties, the data are consistent with the conventional (1 + z) scaling. However, the analysis permits a finite class of bounded deviations that cannot be excluded by temporal data alone. No correlation is observed between inferred time scaling and luminosity parameters, confirming separation of temporal and distance observables. 7 Interpretation The results constrain operational time scaling at the level of supernova temporal structure. They do not constitute a test of cosmological expansion, nor do they imply a distance–redshift relation. The admissible class of g(z) functions defined here serves as an empirical input to subsequent ODRP papers, where clocks and distances are confronted jointly with independent observables. 8 Conclusion We have presented the first empirical constraint on operational time scaling within the ODRP, using supernova light-curve temporal structure alone. Synthetic validation demonstrates that the analysis detects genuine time-scaling signals while rejecting artifacts. This paper establishes clocks as an independently testable observable and provides the temporal foundation for subsequent distance-based analyses within the program. References [1] J. Guy et al.,SALT2: Using Distant Supernovae to Improve the Use of Type Ia Supernovae as Distance Indicators,Astron. Astrophys. 466 (2007) 11–21, astro-ph/0701828. [2] I. M. H. Etherington, On the Definition of Distance in General Relativity,Philos. Mag. 15 (1933) 761–773. [3] P. Cooney, Operational Data Ingestion and Validation in Bounded Dynamical Systems, Zenodo (2025), doi:10.5281/zenodo.17925621. [4] P. Cooney, Operational Time Dilation from Supernova Temporal Structure, Zenodo (2025). – 3 –