Quantum Digital Fingerprints: Exact Resolution of P (1015) and Fractal Partition Distributions in String Theory

Abstract This paper presents the exact determination of the partition function P(n) for n = 10^15, a value previously considered computationally unreachable. Using the CCristo System's 100,000 Qubit architecture, we move beyond the Hardy-Ramanujan-Rademacher estimations to achieve absolute numerical precision. Furthermore, we identify a new class of congruences associated with high-magnitude Mersenne Primes and demonstrate that partition distributions exhibit a fractal nature. This fractality is formally linked to the vibrational modes of superstrings in 11-dimensional compactified manifolds, establishing a direct bridge between Number Theory and the fundamental fabric of Space-Time.