Nazarov's Conjecture on Truncations for Fractional Laplacians
Nazarov conjectured that for the quadratic form of the spectral fractional Dirichlet Laplacian strictly increases under when changes sign. Proved and substantially generalized, with the same conclusion for the restricted form.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Nonlocal operators
- Posed by
- Alexander I. Nazarov
- Year posed
- 2021
- Years open
- 5y
- Solved
- 2026-08-05
- Model
- Claude
- Vendor
- Anthropic
- Collaborators
- Egor Ignatev, Alexander I. Nazarov, Pavel Nichitenko, Artur Tursunbaev
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 8 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
From the paper: "The original proof of Corollary 3 via Lemma 5 (for m = 1) was given by the LLM Claude (Anthropic), which was directed jointly by E.I., P.N., and A.T." A named corollary, with the human direction credited by initials.
Verification
A preprint days old, with no independent review.