ψ⁸: Reproducible Framework for Lunar Phase Prediction via Retentive Difference Dynamics

This article introduces a fundamentally new method for predicting lunar phases, based on the ψ⁸ framework of retentive difference. Instead of propagating orbital coordinates with classical ephemerides, the method identifies phase events as stable minima of a functional Δψ(t), retained by a node Ξ. This approach establishes a new class of algorithms where phase localization arises from the dynamics of difference itself. Validation against authoritative NASA/USNO almanacs confirms sub-5-second agreement, demonstrating both reproducibility and conceptual novelty. The validation demonstrates that ψ⁸ achieves agreement within ±5 seconds across upcoming lunar phases, confirming its robustness and scientific reproducibility. This work establishes ψ⁸ not as a competing ephemeris, but as an independent architecture of temporal retention, offering a new reproducible pathway for cross-verification of astronomical predictions.