Triple
T14334598
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Ramanujan–Petersson conjecture |
E355436
|
entity |
| Predicate | relatedProblem |
P37
|
FINISHED |
| Object |
Selberg eigenvalue conjecture
The Selberg eigenvalue conjecture is a major open problem in analytic number theory and spectral theory that predicts a specific lower bound for the nontrivial eigenvalues of the Laplace operator on certain arithmetic hyperbolic surfaces.
|
E1094044
|
NE FINISHED |
How this triple was built (4 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Selberg eigenvalue conjecture | Statement: [Ramanujan–Petersson conjecture, relatedProblem, Selberg eigenvalue conjecture]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Selberg eigenvalue conjecture Context triple: [Ramanujan–Petersson conjecture, relatedProblem, Selberg eigenvalue conjecture]
-
A.
Selberg trace formula
The Selberg trace formula is a fundamental result in analytic number theory and spectral theory that relates lengths of closed geodesics on a Riemannian manifold to the spectrum of its Laplace operator, serving as a non-abelian analogue of the Poisson summation formula.
-
B.
Ramanujan–Petersson conjecture
The Ramanujan–Petersson conjecture is a fundamental statement in number theory and the theory of modular forms that predicts strong bounds on the Fourier coefficients of modular cusp forms, with deep connections to automorphic forms and the Langlands program.
-
C.
Hilbert–Pólya conjecture
The Hilbert–Pólya conjecture is an unproven idea in number theory suggesting that the nontrivial zeros of the Riemann zeta function correspond to eigenvalues of a suitable self-adjoint operator, offering a potential spectral approach to proving the Riemann hypothesis.
-
D.
Selberg class
The Selberg class is a collection of Dirichlet series with specific analytic properties introduced to generalize and axiomatize L-functions in number theory.
-
E.
Selberg zeta function
The Selberg zeta function is an analytic function associated with the lengths of closed geodesics on a Riemannian manifold, playing a central role in spectral theory and the study of automorphic forms.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Selberg eigenvalue conjecture Triple: [Ramanujan–Petersson conjecture, relatedProblem, Selberg eigenvalue conjecture]
Generated description
The Selberg eigenvalue conjecture is a major open problem in analytic number theory and spectral theory that predicts a specific lower bound for the nontrivial eigenvalues of the Laplace operator on certain arithmetic hyperbolic surfaces.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Selberg eigenvalue conjecture Target entity description: The Selberg eigenvalue conjecture is a major open problem in analytic number theory and spectral theory that predicts a specific lower bound for the nontrivial eigenvalues of the Laplace operator on certain arithmetic hyperbolic surfaces.
-
A.
Selberg trace formula
The Selberg trace formula is a fundamental result in analytic number theory and spectral theory that relates lengths of closed geodesics on a Riemannian manifold to the spectrum of its Laplace operator, serving as a non-abelian analogue of the Poisson summation formula.
-
B.
Ramanujan–Petersson conjecture
The Ramanujan–Petersson conjecture is a fundamental statement in number theory and the theory of modular forms that predicts strong bounds on the Fourier coefficients of modular cusp forms, with deep connections to automorphic forms and the Langlands program.
-
C.
Hilbert–Pólya conjecture
The Hilbert–Pólya conjecture is an unproven idea in number theory suggesting that the nontrivial zeros of the Riemann zeta function correspond to eigenvalues of a suitable self-adjoint operator, offering a potential spectral approach to proving the Riemann hypothesis.
-
D.
Selberg class
The Selberg class is a collection of Dirichlet series with specific analytic properties introduced to generalize and axiomatize L-functions in number theory.
-
E.
Selberg zeta function
The Selberg zeta function is an analytic function associated with the lengths of closed geodesics on a Riemannian manifold, playing a central role in spectral theory and the study of automorphic forms.
- F. None of above. chosen
Provenance (5 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69d8278fa2108190bc0d0e7939c1eb03 |
completed | April 9, 2026, 10:26 p.m. |
| NER | Named-entity recognition | batch_69de8c20d2148190bb534bef338e871d |
completed | April 14, 2026, 6:49 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69fd469634688190980df59ee482b792 |
completed | May 8, 2026, 2:12 a.m. |
| NEDg | Description generation | batch_69fd47e2b8d481909ed8274a96615b36 |
completed | May 8, 2026, 2:18 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69fd4879b2688190ac208545ae226c93 |
completed | May 8, 2026, 2:20 a.m. |
Created at: April 10, 2026, 1:13 a.m.