Mod-2 Seiberg-Witten Invariants Fully Computed for All Spin Structures — E8 Intelligence Research

FINDING: Complete determination of mod-2 Seiberg-Witten invariants for all spin structures on closed smooth 4-manifolds, confirming the simple type conjecture mod 2. | MATH: For a spin structure \(s\) on a closed oriented smooth 4-manifold \(X\), the mod-2 SW invariant \(SW_2(X,s)\) is fully computed. Key result: \(SW_2(X,s) ≡ ∑c ∈ H^2(X;Z_2) SW(X,s+c) {2}\), where \(SW\) are integer invariants. The simple type condition (all basic classes have \(b^+ - b_1 = 0\) mod 2) holds for spin structures. For families, the invariant becomes a mod-2 class in \(H^*(B;Z_2)\) over the parameter space \(B\). | CONNECTION: The mod-2 reduction inherently involves \(Z_2\) — the simplest nontrivial finite field, linked to the root system \(A_1\) (crystallographic symmetry of the line). The spin structure corresponds to a \(w_2\)-twisted \(Spin^c\) structure; the mod-2 arit Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com