Derivation of the late-time equation-of-state correction δw from nuclear binding energies in Relational Gravity

This paper derives the late-time dark energy equation-of-state parameter w₀ = −0.930 ± 0.015 from nuclear binding energies within the Relational Gravity framework. The derivation proceeds through three steps: (1) defining a nuclear coherence fraction ε_nuc from AME2020 Fe/Ni-peak binding energies, (2) defining a coherence projection factor f_CPI as an integral over cosmic structure formation history, and (3) connecting the resulting effective coherence fraction to the equation-of-state deviation via the continuity equation. The paper includes uncertainty budget, sensitivity analysis, and pre-registered falsification criteria committed before MCMC testing against Planck 2018 + DESI DR2 BAO + supernova data.