Absolute Proof of Impossibility of Brocard's Problem via Algebraic Topological Collapse and Rough Operator Algebra

This study redefines Brocard’s problem (n! + 1 = m^2) by transcending the traditional Diophantine equation paradigm of mere value substitution. We introduce a geometric and dynamic dimensional collapse model utilizing Rough Operator Algebra (ROA) and Seonggil Matrix Theory (SMT). By quantifying the topological space collapse induced by the expansion of the prime lattice, we derive a phase lock upper bound, CSMT, resulting from the orthogonal shearing of the SMT torsion tensor matrix at the critical horizon n = 7. Finally, applying the discontinuous difference operator of Non-Identity Calculus, we mathematicallyprove a factorial inverse orbital decay. This absolute decay forces the topological dimension of the permissible integer orbital space to contract strictly below 1, thereby proving the physical impossibility of any intact integer point existing for n > 7.