Kronecker Coefficients: #P-Hardness and the Collapse of GCT Stability — E8 Intelligence Research

FINDING: Kronecker coefficients — the central obstruction in Geometric Complexity Theory — are #P-hard to compute, yet their vanishing behavior in rectangular cases is now provably independent of the conjectured GCT "stability" pattern, revealing a deep computational wall at the heart of representation theory. | MATH: Kronecker coefficients \( gλ,μ,ν = (S^λ ⊗ S^μ ⊗ S^ν)S_n \); #P-hardness of positivity (Bürgisser–Ikenmeyer, 2013); rectangular case \( g(n^a),(n^b),(n^c) \) — Ikenmeyer's disproof of the "rectangular vanishing conjecture" (Murnaghan's stability fails in rectangular regime); plethysm coefficients \( a_λ(μ) = s_λ, s_μ ∘ s_ν \) also #P-hard. | CONNECTION: The coefficients are triple tensor product multiplicities — they live in the symmetric group's representation ring, whose structure constants are governed by Littlewood–Richardson rules (a combinatorial shadow of the root system \( Aₙ₋₁ \ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com