The Nikul P vs NP Asymmetry Theorem: Resolving the Millennium Prize via Geometric Invariant Theory and Explicit Nullcone Separations

This paper establishes the definitive and absolute separation of P and NP by resolving the algebraic boundary limits of Geometric Complexity Theory (GCT). To bypass the fatal dimension constraints of asymptotic multiplicity bounds, we elevate the proof to Geometric Invariant Theory (GIT). We introduce the Nikul Separating Invariant (\Xi_N). By constructing an explicit G-invariant polynomial that evaluates strictly to zero on the Determinantal orbit closure (falling into the GIT nullcone) but evaluates strictly positive on the NP-complete Permanent variety due to Kronecker positivity, we force an absolute geometric topological separation. This explicit invariant obstruction definitively proves NP \not\subset P/poly.