Triple

T14438382
Position Surface form Disambiguated ID Type / Status
Subject L-function E358024 entity
Predicate hasSpecialCase P7025 FINISHED
Object Rankin–Selberg L-function
The Rankin–Selberg L-function is an analytic number theory object constructed from pairs of automorphic forms (or representations), encoding deep arithmetic information through their convolution.
E1100853 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: Rankin–Selberg L-function | Statement: [L-function, hasSpecialCase, Rankin–Selberg L-function]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Rankin–Selberg L-function
Context triple: [L-function, hasSpecialCase, Rankin–Selberg L-function]
  • A. L-functions
    L-functions are complex analytic functions, often arising from number theory and algebraic geometry, that encode deep arithmetic information and generalize the Riemann zeta function.
  • B. Dirichlet L-functions
    Dirichlet L-functions are complex analytic functions built from Dirichlet characters that generalize the Riemann zeta function and play a central role in number theory, particularly in the study of primes in arithmetic progressions.
  • C. Euler products for automorphic L-functions
    Euler products for automorphic L-functions are infinite product expansions attached to automorphic representations that encode deep arithmetic information and generalize the classical Euler product of the Riemann zeta function to a broad class of L-functions in the Langlands program.
  • 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. Artin L-functions
    Artin L-functions are complex analytic functions attached to Galois representations that generalize Dirichlet L-functions and play a central role in number theory and the study of arithmetic properties of fields.
  • 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: Rankin–Selberg L-function
Triple: [L-function, hasSpecialCase, Rankin–Selberg L-function]
Generated description
The Rankin–Selberg L-function is an analytic number theory object constructed from pairs of automorphic forms (or representations), encoding deep arithmetic information through their convolution.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Rankin–Selberg L-function
Target entity description: The Rankin–Selberg L-function is an analytic number theory object constructed from pairs of automorphic forms (or representations), encoding deep arithmetic information through their convolution.
  • A. L-functions
    L-functions are complex analytic functions, often arising from number theory and algebraic geometry, that encode deep arithmetic information and generalize the Riemann zeta function.
  • B. Dirichlet L-functions
    Dirichlet L-functions are complex analytic functions built from Dirichlet characters that generalize the Riemann zeta function and play a central role in number theory, particularly in the study of primes in arithmetic progressions.
  • C. Euler products for automorphic L-functions
    Euler products for automorphic L-functions are infinite product expansions attached to automorphic representations that encode deep arithmetic information and generalize the classical Euler product of the Riemann zeta function to a broad class of L-functions in the Langlands program.
  • 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. Artin L-functions
    Artin L-functions are complex analytic functions attached to Galois representations that generalize Dirichlet L-functions and play a central role in number theory and the study of arithmetic properties of fields.
  • 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_69d8279402a88190821ffa39ae15bccf completed April 9, 2026, 10:26 p.m.
NER Named-entity recognition batch_69de914a45ec81909ab8ccf302047d7f completed April 14, 2026, 7:11 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd648b8f348190be11645b371b4102 completed May 8, 2026, 4:20 a.m.
NEDg Description generation batch_69fd66952aa08190b10ef03dd85413ae completed May 8, 2026, 4:29 a.m.
NED2 Entity disambiguation (via description) batch_69fd66f535288190a05acc74844bdbc9 completed May 8, 2026, 4:30 a.m.
Created at: April 10, 2026, 1:18 a.m.