2604.00598 Partition-Theoretic Congruence Discovery Pipeline: Ramanujan Congruences, Tau Function, Overpartitions, and New k-Colored Congruences
We present a fully reproducible 10-step computational pipeline for partition-theoretic congruence exploration. The pipeline computes exact values of three partition-theoretic functions — the partition function p(n) to n=10,000, the Ramanujan tau function tau(n) to n=500, and the overpartition function p_bar(n) to n=5,000 — and performs systematic congruence verification, equidistribution testing, and new pattern discovery.