A Readout-Layer Rescaling Protocol for Reported Time and Volume:Interface Specification, Estimators, Uncertainty Propagation

Preprint. This paper specifies a readout-layer convention and an estimator/pipeline interface for reporting observational quantities, while keeping the underlying dynamics unchanged. We explicitly separate (i) the dynamical metric used for equations of motion, causal structure, and conservation laws, from (ii) the readout convention used to report inferred quantities. In this framework, the reported measure and proper time are rescaled by a prescribed factor kappa = 1 + alpha (with 1 + alpha > 0), interpreted as a calibration/convention parameter rather than a new dynamical degree of freedom. The core prescription is the readout-layer rescaling of the volume measure and proper time, together with a clear statement of what is held fixed: geodesics, light cones, and dynamical equations remain those of the original metric. When convenient, the same measure rescaling may be represented by a rank-one “time-leg” form. The mathematical proof and conditional uniqueness of that representation are established in the companion mathematical paper: OTSUKA, A. (2026). Rank-One Representation of Measure Rescalings via Time-Leg Renormalization (Version v1). Zenodo. https://doi.org/10.5281/zenodo.18169039 In the present paper we invoke this result only operationally, as an interface for the readout definitions, without assuming any dynamics or coupling associated with the time leg. We then formalize a discrete multiplicative update protocol for the reported volume, V_{n+1} = (1 + alpha) V_n, and record the mechanical mapping from this convention to commonly reported cosmological quantities (e.g., a logarithmic mapping to an effective expansion rate). The physical origin or constraints on alpha are intentionally not derived here; they are treated as inputs to be supplied by separate theoretical work. No claim is made about “degeneracy repair” for det(g) = 0 configurations. The purpose of this manuscript is to provide a transparent, reproducible interface specification that prevents misreadings such as “the dynamics has been modified,” and that can be referenced consistently across subsequent papers.