The Kuga-Satake Hodge conjecture for K3 surfaces

Claims that the Kuga-Satake correspondence is algebraic for every smooth projective complex K3 surface, with the fixed normalization and the full even-Clifford target, and also for isogenous Kuga-Satake models. Combined with the quadratic-locus companion it gives the Hodge conjecture for every self-power of every projective K3 surface. It does not address non-projective K3 surfaces or integral coefficients.

Withdrawn by the authors. OpenAI's withdrawal notice of 6 October 2026: "The proof relies on an adaptation of the flawed stabilization-trace construction in Algebraicity of Weil classes on split abelian eightfolds. The sign error in that construction prevents the required signed-double-point cancellation. The resulting gap leaves this paper's claimed algebraicity theorem unproved." The notice adds that the withdrawal concerns the proof and does not assert that the statement is false. The conjecture is open again. Claims that the Kuga-Satake correspondence is algebraic for every smooth projective complex K3 surface, with the fixed normalization and the full even-Clifford target, and also for isogenous Kuga-Satake models. Combined with the quadratic-locus companion it gives the Hodge conjecture for every self-power of every projective K3 surface. It does not address non-projective K3 surfaces or integral coefficients.