Kronecker Coefficients: The Unyielding Core of the VP vs. VNP Problem — E8 Intelligence Research

FINDING: Orbit closure separation in Geometric Complexity Theory reduces VP vs. VNP to the representation-theoretic comparison of the determinant and permanent — a problem whose core obstruction is the vanishing of Kronecker and plethysm coefficients, with no closed-form known for even the simplest counting sequences (OEIS A000003). | MATH: The permanent is \(per_n = ∑σ ∈ S_n ∏_i xi,σ(i)\); the determinant is \(_n = ∑σ ∈ S_n sgn(σ) ∏_i xi,σ(i)\). The orbit closure question: \({GLn^2 · per_n} ⊆ {GLn^2 · _n}\)? This is equivalent to whether the multiplicity \(cλ,μ,ν = χ^λ ⊗ χ^μ, χ^ν \) (Kronecker coefficients) or \(a_λ = χ^λ, Sym^d(χ^μ) \) (plethysm) vanish for certain triples/partitions. The partition algebra approach (arXiv:1210.5579) gives uniform bounds: Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com