Precise Predictor of Twin Prime Counts in Prime–Square Windows: A Deterministic Modular Method with Full Replicability

Building immediately off the Rail-Phase Hypothesis for Twin Primes, an exact formula has been established for the number of twin prime pairs in every interval between consecutive prime squares. The approach is inspired by the combinatorial disturbance viewpoint developed in residue–phase analyses of twin primes, where prime squares act as structural reset points. This paper provides a clean, general formula that deterministically counts twin primes in every prime-square windows.