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.