GCT's Orbit Closures and Coefficient Obstructions in P vs NP — E8 Intelligence Research

FINDING: Geometric Complexity Theory (GCT) reformulates P vs NP as the separation of orbit closures of specific polynomial representations, using plethysm and Kronecker coefficients as obstruction witnesses. | MATH: Core objects: \( Orb(Δ_n)̄ \) (determinant) vs \( Orb(perm_n)̄ \) (permanent). Key coefficients: \( s_λ(perm_n) \) (plethysm), \( gλ,μ,ν \) (Kronecker). The vanishing of these coefficients in certain representations provides algebraic obstructions. No explicit constants or ratios appear; the structure is purely combinatorial/algebraic. | CONNECTION: The plethysm and Kronecker coefficients are indexed by integer partitions \( λ \), which correspond to Young diagrams — these encode the representation theory of \( GL_n \) and \( S_n \). The orbit closures live in affine spaces whose coordinate rings are graded by these partitions. The deepest geometric link: the stabilizer of the determinant is the h Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com