Paper XXIV - Type Ia Supernova Distance Residuals and Operational Distance Structure

DOI: 10.5281/zenodo.18009930 Type Ia Supernova Distance Residuals and Operational Distance Structure Paper XXXIV of the Ordered-Dynamics Reconstruction Program Paul Cooneya aIndependent Researcher, Innisfil, Ontario, Canada E-mail: paul.co[email protected]to.ca Abstract. We analyze Type Ia supernova distance residuals within the Ordered-Dynamics Reconstruction Program (ODRP) to constrain operational distance structure independently of clock physics. Operational time scaling is fixed using supernova temporal structure and strong gravitational lensing, and luminosity distances are inferred without assuming a specific cosmological expansion history. Synthetic injection–recovery tests demonstrate that genuine redshift-dependent distance structure is identifiable and cannot be absorbed by standard light-curve nuisance parameters. The results are interpreted strictly as constraints on allowable operational distance operators and do not invoke dark energy, cosmic acceleration, or metric expansion. Contents 1 Program context 1 2 Supernova distances as operational observables 1 3 Operational luminosity distance operator 2 4 Data and preprocessing 2 5 Likelihood and nuisance parameters 2 6 Synthetic injection–recovery 2 6.1 Null injections 2 6.2 Distance deformation injections 2 6.3 Negative controls 2 7 Results 3 8 Interpretation 3 9 Conclusion 3 Contents 1 Program context The Ordered-Dynamics Reconstruction Program proceeds by empirically separating clocks and distances prior to physical interpretation. Paper XXXI defines the data ingestion and validation framework. Paper XXXII constrains operational time scaling using supernova temporal structure, and Paper XXXIII verifies clock– distance consistency using strong gravitational lensing time delays. The present paper constitutes the first distance-only empirical analysis in the ODRP. Operational time scaling is fixed, and supernova luminosity distances are used to constrain the shape of an operational distance–redshift relation without invoking a cosmological expansion model. 2 Supernova distances as operational observables Type Ia supernovae provide relative distance information through standardized luminosity relations. Observationally, the distance modulus is inferred from light-curve shape and color parameters using models such as SALT2. Within the ODRP, these observables are treated as constraints on an operational luminosity distance operator Dop L(z) rather than as measurements of a metric distance derived from an expansion history. – 1 – 3 Operational luminosity distance operator We define an operational luminosity distance operator Dop L(z) through µ(z) = 5 log10Dop L(z) 10 pc ,(3.1) where µ(z) is the observed distance modulus after light-curve standardization. No assumption is made that Dop L(z) arises from a Friedmann–Lemaˆıtre– Robertson– Walker metric or any specific dynamical model. Operational time scaling g(z) is fixed using independent constraints from Papers XXXII and XXXIII and does not enter the distance inference as a free degree of freedom. 4 Data and preprocessing We analyze publicly available Type Ia supernova datasets processed using standard photometric pipelines and light-curve fitting procedures. Light curves are modeled using SALT2 [1], with temporal structure corrected using the independently constrained operational time scaling. All published covariance matrices and systematic uncertainties are retained. No recalibration is performed to enforce agreement with any cosmological model. 5 Likelihood and nuisance parameters The likelihood follows the unified Gaussian structure defined in Paper XXXI [3]. The data vector consists of standardized distance moduli. Standard SALT2 nuisance parameters (stretch, color, absolute magnitude offset) are included and marginalized over. These parameters are not permitted to introduce redshiftdependent structure beyond that supported by the data. 6 Synthetic injection–recovery We validate the distance inference pipeline using synthetic injection–recovery tests. 6.1 Null injections Synthetic supernova samples generated with baseline operational distance operators are recovered without spurious distance deformation. 6.2 Distance deformation injections Injected redshift-dependent deformations of Dop L(z) are recovered without significant bias. The recovery demonstrates that distance structure cannot be absorbed by SALT2 nuisance parameters. 6.3 Negative controls Redshift scrambling, covariance truncation, and misassignment of nuisance parameters invalidate recovery as expected. – 2 – 7 Results Applying the validated pipeline to real supernova data, we obtain constraints on the shape of the operational luminosity distance operator. Within current uncertainties, the inferred distance structure is compatible with the admissible operator space defined in Paper XXXV. A finite class of bounded deformations cannot be excluded by supernova distances alone. No statistically significant correlation is observed between inferred distance structure and light-curve nuisance parameters. 8 Interpretation The results constrain operational distance structure independently of clock physics. They do not determine an expansion rate, cosmic acceleration, or dark energy density. The admissible family of Dop L(z) functions defined here provides a distance-only empirical input to subsequent synthesis and BAO analyses within the ODRP. 9 Conclusion We have constrained operational distance structure using Type Ia supernova distance residuals with clocks fixed by independent temporal probes. Synthetic validation demonstrates identifiability of genuine distance deformations. This paper establishes distances as independently testable observables within the ODRP and provides the spatial foundation for subsequent multi-probe synthesis and BAO analyses. 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). [5] P. Cooney, Strong Gravitational Lensing Time Delays and Operational Time–Distance Structure, Zenodo (2025). [6] P. Cooney, Type Ia Supernova Distance Residuals and Operational Distance Structure, Zenodo (2025). [7] P. Cooney, Synthesis of Operational Time and Distance Constraints, Zenodo (2025). – 3 –