Homological Mirror Symmetry Unifies Knot Homologies via Chern-Simons — E8 Intelligence Research

FINDING: Homological mirror symmetry (HMS) provides a new categorical framework for computing Khovanov-type knot homologies, unifying Chern-Simons quantum invariants with algebraic geometry via the Aganagic–Vafa mirror construction. | MATH: Core objects: (1) Chern-Simons partition function \( ZCS(M, G) = ∫ DA \, e^{i k SCS[A]} \), with \( SCS = k/4π ∫_M Tr(A dA + 2/3 A A A) \); (2) Khovanov homology \( Hi,j(K) \) as a triply-graded vector space whose graded Euler characteristic recovers the Jones polynomial \( V_K(q) = ∑i,j (-1)^i q^j Hi,j(K) \); (3) Mirror symmetry equivalence: \( D^b(Coh(X̂)) D^b(Fuk(X)) \) — here the "downstairs mirror" is a Landau–Ginzburg model whose category of B-branes (matrix factorizations) computes the knot homology; (4) Conformal blocks of the final algebra (likely \( W1+∞ \) or \( {sl}_N \) at Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com