A Preregistered Admissibility‑Based Forecast for Type Ia Supernova Residuals

This preregistered technical note presents explicit, testable forecasts for Type Ia supernova (SN Ia) distance–modulus residuals, scatter trends, and host‑mass effects within the constraint‑first admissibility framework. Working in the Dual‑Invariant (minimal‑uncertainty) gauge, we define a basis‑independent metric for standardized light‑curve parameters and residuals. All calibration, astrophysical, and observational requirements are encoded in the Construct Law Equation, producing a unified admissibility ledger for zero‑points, color law, K‑corrections, selection biases, host‑mass steps, and lensing scatter. Parameter evolution and nuisance terms are governed by the Master Structure Equation, which enforces normal‑cone/KKT boundary reactions that prevent overfitting and ensure that residual curvature and redshift‑evolution remain admissible. Maximal Admissibility Surfaces (MAS) act as quantitative caps on allowable trends—such as bounds on $\langle\Delta\mu(z)\rangle$, scatter scaling, and host–mass evolution—and create clear, falsifiable predictions for new SN Ia releases. The result is a concise, forward‑looking prediction note that links supernova cosmology directly to the admissibility framework, providing a transparent and testable set of forecasts for Pantheon+, DES‑SN, Foundation, and future high‑precision surveys.