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OpenAI · proposed Hodge theorem for CM abelian varieties
Provider preprint in the October 2026 public collection. The selected manuscript is a proposal here; a release announcement is not independent expert acceptance.
1 cited passage ↓1 problem ↓Record fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb ↓
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The provider claims rational Hodge for every complex CM abelian variety in all dimensions and codimensions, including finite products and powers.
Passage ID: hodge-conjecture:hodge-openai-cm:v1
Source item: Theorem 1.1 and definition of CM type, PDF page 1
Source record: openai-hodge-cm@git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Explicit citations in versioned problem publications. A citation records a use; it does not confer proof or independent verification.
Problem publication v15
Source assessment
Proposed
Proposed source assertion awaiting assessment
Only the cited assertion with its exact assumptions. This report does not resolve the canonical Problem or establish independent OpenMath mathematical review.
Observed Oct 10, 2026
Research activity
Company AI proposals: CM algebraicity and specialized rationality
The October release proposes two distinct mathematical scopes: CM Hodge classes and rationality of pairings after good reduction.
The original manuscripts are pinned and linked. Their dependencies, independent review and any formal correspondence remain unassessed; neither is promoted to established progress.
History
OpenAI’s proposed all-dimensional CM case
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No OpenMath execution recorded
External manuscript. No OpenMath proof execution, formalization or independent mathematical acceptance is inferred.
Resource revision: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
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6e3e66a407773ad5091d4cb48d9b4dc55a69c58fb0948a88daf19f3bb21bf27bRecorded authorship
OpenAI
The provider attributes this manuscript to its internal AI model. Mathematical acceptance, paper-to-formal correspondence and independent reproduction are not established by OpenMath.
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OpenAI · proposed Hodge theorem for CM abelian varieties
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