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Precise statement
Zhao's Generalized Vanishing Conjecture asks whether, for a differential operator with constant coefficients, $\Lambda^m(P^m) = 0$ for all large $m$ forces $\Lambda^m(P^m Q) = 0$ for all large $m$.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement
fidelity, correctness, priority, or novelty.
What AI did
GPT-5.6 Sol
The initial paper (Alexander Dvorsky) used "as an interactive research assistant": the paper credits it with testing the homogenized five-variable construction, generating computational verification code and locating relevant literature, with all computations and references independently verified afterwards.
A second paper (Roy van Rijn) used OpenAI's Codex to close the conjecture completely. It proofs that the conjecture holds for n <= 2 and fails at dimension 3 (counter-example provided in the paper). Codex monitored/ran several experiments and the human steered the experiments.
The preprints have (as of yet) no independent review. The counterexample can be checked directly, the proof has additional Python calculations and Lean verification.
The Generalized Vanishing Conjecture: The Two-Variable Theorem and the First Failing Dimension
For n <= 2, we proof that the Generalized Vanishing Conjecture holds, and we have a failure at dimension 3 (including a counter-example).
This improves the original failure at dimension 5.
Known method families
construction (source-reported)
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
VibeMath has not independently verified the mathematical claim.
AI-attempt independence and training-data exposure are unknown unless explicitly documented.
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.