The Hodge conjecture for products of K3 surfaces
Claims the rational Hodge conjecture in every degree for every finite product of projective complex K3 surfaces, with no restriction on Picard numbers, periods or endomorphism fields, including powers of one surface. On the way it re-proves algebraicity of the exact Kuga-Satake correspondence. It says nothing about the integral Hodge conjecture or about hyperkahler varieties beyond what follows.
Exact FrontierDelta
Scope and record
Occurred: Sep 10, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: contested. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: The Hodge conjecture for products of K3 surfaces · Hodge conjecture for products of K3 surfaces
Confidence: Not scored
Registry verification: contested · announcement · retracted
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
Lineage and corrections
The Hodge conjecture for products of K3 surfaces parent of this event
Claims the rational Hodge conjecture in every degree for every finite product of projective complex K3 surfaces, with no restriction on Picard numbers, periods or endomorphism fields, including powers of one surface. On the way it re-proves algebraicity of the exact Kuga-Satake correspondence. It says nothing about the integral Hodge conjecture or about hyperkahler varieties beyond what follows. parent of this event
VibeMathed record: The Hodge conjecture for products of K3 surfaces evidence for this event
The rational Hodge conjecture for products of K3 surfaces (OpenAI, 2026-10-04) evidence for this event
Algebraicity of Kuga-Satake correspondences for K3 surfaces (OpenAI, 2026-10-03) evidence for this event
Algebraic Kuga-Satake correspondences and Hodge conjectures on a K3 quadratic locus (OpenAI, 2026-09-30) evidence for this event
Earlier edition (September 30, 2026) evidence for this event
A conditional reduction for algebraic Kuga-Satake correspondences (OpenAI, 2026-09-10) evidence for this event
Hodge, The topological invariants of algebraic varieties, ICM 1950 Proceedings evidence for this event
Retraction notice on GitHub evidence for this event
OpenAI withdrawal notice (6 October 2026) evidence for this event
This event attributed to Unreleased internal OpenAI model
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