Mirror Symmetry Reduces Knot Homologies to 1D A-Model via Categorical Equivalence — E8 Intelligence Research

FINDING: Mirror symmetry in Aganagic's framework reduces knot homologies (Khovanov/Knot Floer) to a 1D A-model with a lambda parameter, linking topological invariants to symplectic geometry via a D-model (derived category) — a categorical equivalence between A-branes and B-branes. | MATH: The core is the identification of knot Floer homology \( {HFK}(K) \) with the Lagrangian intersection Floer homology of a knot conormal \( L_K ⊂ T^*S^3 \), under SYZ mirror symmetry. The lambda parameter \( λ \) (likely the equivariant variable in the deformed A-model) encodes the \(sl(2)\) weight grading. The Abouzaid family Floer cohomology provides the functor \( F: D^bA → D^bB \) where \( A \) is the wrapped Fukaya category and \( B \) the coherent sheaf category on the mirror. The conjectured volume-cohomology inequality from the arXiv paper: \( ∃ a>0 \) s.t. \( limc→∞ P( {log {HFK}(K) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com