Numerical Calibration and Structural Consistency Tests of the Informational Scalar in Relational Gravity: From Nuclear Binding Energies to Scalar Field Cosmology

This paper presents a numerical calibration and structural consistency test of the informational scalar sector in Relational Gravity (RG). Starting from measured nuclear binding energies (AME2020), we compute an effective coherence fraction that predicts a late-time deviation of the dark-energy equation-of-state parameter δw ≈ +0. 07. We then reconstruct the corresponding scalar effective field theory (EFT) parameters under a minimal quadratic potential ansatz and evolve the cosmological background equations to compute the resulting equation-of-state evolution w (a). The work performs an explicit micro-to-macro numerical closure test: AME2020 → nuclear coherence fraction → δwₙuclear → scalar EFT parameters → cosmological evolution → δwₛcalar. The calibration establishes numerical consistency between the nuclear-derived deviation and the scalar-field cosmology under the stated assumptions. Robustness is tested via initial-condition basin scans and projection-integral sensitivity analysis. All figures, numerical values, and uncertainty estimates are reproducible using the associated computational reproduction kit available on Zenodo. This work does not perform cosmological likelihood fitting. Instead, it provides a fully reproducible internal calibration baseline for the RG scalar background sector prior to observational confrontation.