Triple

T10462163
Position Surface form Disambiguated ID Type / Status
Subject Selberg class E246701 entity
Predicate hasConjecture P38260 FINISHED
Object Selberg orthonormality conjecture
The Selberg orthonormality conjecture is a conjecture in analytic number theory asserting an orthogonality relation for coefficients of L-functions in the Selberg class, analogous to the orthogonality of characters.
E246701 NE FINISHED

How this triple was built (5 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 orthonormality conjecture | Statement: [Selberg class, hasConjecture, Selberg orthonormality conjecture]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Selberg orthonormality conjecture
Context triple: [Selberg class, hasConjecture, Selberg orthonormality conjecture]
  • A. 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.
  • B. Montgomery's pair correlation conjecture
    Montgomery's pair correlation conjecture is a deep number-theoretic prediction about the statistical spacing of the nontrivial zeros of the Riemann zeta function, linking them to eigenvalues of random matrices and suggesting profound connections between number theory and quantum physics.
  • C. Siegel’s theorem on zeros of L-functions
    Siegel’s theorem on zeros of L-functions is a result in analytic number theory that gives strong bounds on how close nontrivial zeros of Dirichlet L-functions can approach 1, with deep implications for the distribution of primes in arithmetic progressions.
  • D. 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.
  • E. 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.
  • 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 orthonormality conjecture
Triple: [Selberg class, hasConjecture, Selberg orthonormality conjecture]
Generated description
The Selberg orthonormality conjecture is a conjecture in analytic number theory asserting an orthogonality relation for coefficients of L-functions in the Selberg class, analogous to the orthogonality of characters.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Selberg orthonormality conjecture
Target entity description: The Selberg orthonormality conjecture is a conjecture in analytic number theory asserting an orthogonality relation for coefficients of L-functions in the Selberg class, analogous to the orthogonality of characters.
  • A. Selberg class chosen
    The Selberg class is a collection of Dirichlet series with specific analytic properties introduced to generalize and axiomatize L-functions in number theory.
  • B. Montgomery's pair correlation conjecture
    Montgomery's pair correlation conjecture is a deep number-theoretic prediction about the statistical spacing of the nontrivial zeros of the Riemann zeta function, linking them to eigenvalues of random matrices and suggesting profound connections between number theory and quantum physics.
  • C. Siegel’s theorem on zeros of L-functions
    Siegel’s theorem on zeros of L-functions is a result in analytic number theory that gives strong bounds on how close nontrivial zeros of Dirichlet L-functions can approach 1, with deep implications for the distribution of primes in arithmetic progressions.
  • D. 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.
  • E. 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.
  • F. None of above.
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: hasConjecture
Context triple: [Selberg class, hasConjecture, Selberg orthonormality conjecture]
  • A. associatedConjecture chosen
    Indicates that one entity is linked or connected to a particular conjecture, typically as its subject, source, or relevant context.
  • B. relatedConjecture
    Indicates that one conjecture is connected or associated with another conjecture, such as by similarity, dependency, or thematic relation.
  • C. refinedConjecture
    Indicates that a previously stated conjecture has been modified or made more precise, resulting in a refined version of the original conjecture.
  • D. conjecturedSign
    Indicates that one entity is proposed or hypothesized to be the sign, symbol, or indicator of another entity, without confirmed certainty.
  • E. hasTheorem
    Indicates that one entity (typically a mathematical theory, field, or work) includes, establishes, or is associated with a particular theorem.
  • F. None of above.

Provenance (6 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_69d381c16c248190a2fe5b471e584e9c completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d50884fac48190af22e181b1492557 completed April 7, 2026, 1:37 p.m.
NED1 Entity disambiguation (via context triple) batch_69d89fcc84b48190a39de0d9b9111ebd completed April 10, 2026, 6:59 a.m.
NEDg Description generation batch_69d8a1656b348190ba932d03402d6a4d completed April 10, 2026, 7:06 a.m.
NED2 Entity disambiguation (via description) batch_69d8a2b82bb48190899f37a967fef444 completed April 10, 2026, 7:11 a.m.
PD Predicate disambiguation batch_69d4fb7d353c8190a73f439a956c7606 completed April 7, 2026, 12:41 p.m.
Created at: April 6, 2026, 12:19 p.m.