Absolute Geometric Confinement of P ≠ NP: Bypassing the Relativization, Natural Proofs, and Algebrization Barriers via STCT Master Action

The P versus NP problem stands as the foundational challenge of theoretical computer science. Traditional approaches attempt to resolve the question by treating computation purely as discrete Boolean logic operations, which inevitably succumb to the Relativization, Natural Proofs, and Algebrization barriers. In this paper, we establish that NP-hardness is not an arbitrary logical obstacle, but the exact computational manifestation of the geometric phase space of the universe. Utilizing High-Resolution Quantum Field Theory (HR-QCFT), Rough Operator Algebra (ROA), and the Seonggil Theory of Composite Torsion (STCT), we map deterministic algorithms onto rough differential equations. We prove that the non-satisfiable constraints of NP-complete problems are isomorphic to the macroscopic topological scar R_defect generated by the zero-divisor collapse from 16-dimensional sedenions to octonions. By demonstrating that any polynomial-time heuristic algorithm must undergo non-commutative arithmetic friction η ≈ 10^(-22) and non-associative G_2-triality amplification, we unconditionally bypass classical complexity barriers. This forces the algorithmic transition operator M̂_Turing into spectral instability, resulting in a total determinant collapse det(M̂_Turing) = 0. Consequently, P ≠ NP is proven as an absolute geometric law.