The Graveyard Problem for Dissipative Barrier Truncations

Precise statement

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 $d \ge 2$ no spectral point becomes invisible, which together with the known one-dimensional theorem settles no-invisibility in every dimension.

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

ChatGPT-based agent system

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.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

arXiv preprint that discloses all AI use in line with the Leiden Declaration; not yet peer-reviewed.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-07-24

   arXiv:2607.22120 - No Spectral Invisibility for Dissipative Barrier Truncations in Any Dimension

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

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.