This study proposes that local curvature minima in the partition function p(n)p(n)p(n) are associated with modular congruence phenomena. Analyzing second discrete differences up to n=5000n=5000n=5000, we observe that known congruences (mod 5, 7, 11) align with curvature-collapse points. Furthermore, the method suggests potential hidden congruences at larger primes such as 17, 19, 23, 29, and beyond. This introduces the Partition Threshold Collapse Conjecture as a structural explanation for modular congruence behavior in combinatorial number theory.