The Graveyard Problem for Dissipative Barrier Truncations
The dissipative barrier method suppresses spectral pollution when a differential operator is truncated, but can it hide genuine spectral points? Known as the graveyard problem, the question stayed open in dimension two and above for more than a decade. It cannot: for Schrodinger operators in dimensions no spectral point becomes invisible, which together with the known one-dimensional theorem settles no-invisibility in every dimension.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Argument
- Field
- Computational spectral theory
- Posed by
- Marco Marletta, Sergey Naboko
- Year posed
- 2014
- Years open
- 12y
- Solved
- 2026-07-24
- Model
- ChatGPT-based agent system
- Vendor
- OpenAI
- Collaborators
- Matthew J. Colbrook, Marco Marletta
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 20 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
An unusually candid account, and the reason this entry sits at the lowest tier despite the models mattering. The first author built a system of ChatGPT-based agents to propose, test and attack proofs of the no-invisibility theorem. After false starts, including arguments with real gaps and arguments leaning on results that do not exist, the agents converged on a strategy Marletta and Naboko had already dismissed for want of a reversed Hansmann estimate. The final two lemmas the agents produced were not trusted. Suspecting the idea was a distorted echo of human mathematics in the training data, the authors searched for the uncited human source and instead found two stronger 2024 papers of Gil that supply exactly the reversed estimate. So the agents supplied direction, not the proof.
Verification
arXiv preprint that discloses all AI use in line with the Leiden Declaration; not yet peer-reviewed.
Source
arXiv:2607.22120 - No Spectral Invisibility for Dissipative Barrier Truncations in Any Dimension