Geometric Complexity Theory: The Invariant-Theoretic Assault on P vs NP — E8 Intelligence Research

FINDING: The search results are dominated by expository material on Geometric Complexity Theory (GCT) — the invariant-theoretic attack on P vs NP — plus one unrelated LHCb particle decay paper. No new solved competition problem or breakthrough invariant-theoretic result is presented; the core mathematical content is the GCT framework itself. | MATH: GCT core: permanent vs determinant (Valiant's conjecture). Key objects: \( Det_n̄ \) (orbit closure of determinant in \( Sym^n(Cn^2) \)) and \( Perm_m \) (permanent). The separation requires showing \( Perm_m ∉ Det_n̄ \) for \( n = poly(m) \). Invariant theory enters via: (1) coordinate rings \( C[Det_n̄]_{SLn^2} \) and \( C[Perm_m̄]_{SLm^2} \) — the rings of invariants under the special linear group action; (2) the stabilizer of the determinant is \( SL_n × SL_n Z_2 \) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com