Triple

T10641438
Position Surface form Disambiguated ID Type / Status
Subject Harish-Chandra character formula E250730 entity
Predicate relatedTo P37 FINISHED
Object Langlands classification
The Langlands classification is a fundamental framework in representation theory that systematically describes all irreducible admissible representations of a real or p-adic reductive group in terms of data from its parabolic subgroups and their characters.
E877880 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: Langlands classification | Statement: [Harish-Chandra character formula, relatedTo, Langlands classification]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Langlands classification
Context triple: [Harish-Chandra character formula, relatedTo, Langlands classification]
  • A. Langlands program
    The Langlands program is a far-reaching web of conjectures and theories in number theory and representation theory that seeks deep connections between Galois groups and automorphic forms, unifying many areas of modern mathematics.
  • B. Representation Theory and Automorphic Functions
    "Representation Theory and Automorphic Functions" is a seminal mathematical work by Israel Gelfand that develops the connections between representation theory of groups and the theory of automorphic forms, with deep applications in number theory and harmonic analysis.
  • C. Deligne–Lusztig theory
    Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
  • D. Langlands dual group
    The Langlands dual group is an algebraic group constructed from a given reductive group by interchanging its root and coroot data, playing a central role in the Langlands program’s connections between number theory and representation theory.
  • E. Hecke theory
    Hecke theory is a branch of number theory centered on Hecke operators and modular forms, providing powerful tools to study arithmetic properties of modular forms and related objects.
  • 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: Langlands classification
Triple: [Harish-Chandra character formula, relatedTo, Langlands classification]
Generated description
The Langlands classification is a fundamental framework in representation theory that systematically describes all irreducible admissible representations of a real or p-adic reductive group in terms of data from its parabolic subgroups and their characters.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Langlands classification
Target entity description: The Langlands classification is a fundamental framework in representation theory that systematically describes all irreducible admissible representations of a real or p-adic reductive group in terms of data from its parabolic subgroups and their characters.
  • A. Langlands program
    The Langlands program is a far-reaching web of conjectures and theories in number theory and representation theory that seeks deep connections between Galois groups and automorphic forms, unifying many areas of modern mathematics.
  • B. Representation Theory and Automorphic Functions
    "Representation Theory and Automorphic Functions" is a seminal mathematical work by Israel Gelfand that develops the connections between representation theory of groups and the theory of automorphic forms, with deep applications in number theory and harmonic analysis.
  • C. Deligne–Lusztig theory
    Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
  • D. Langlands dual group
    The Langlands dual group is an algebraic group constructed from a given reductive group by interchanging its root and coroot data, playing a central role in the Langlands program’s connections between number theory and representation theory.
  • E. Hecke theory
    Hecke theory is a branch of number theory centered on Hecke operators and modular forms, providing powerful tools to study arithmetic properties of modular forms and related objects.
  • 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_69d6aa5a4c4881908f39be6efe5981e5 completed April 8, 2026, 7:19 p.m.
NER Named-entity recognition batch_69d6dfcd19648190882380d2c90be486 completed April 8, 2026, 11:07 p.m.
NED1 Entity disambiguation (via context triple) batch_69d97a4555e48190be39c0a7698b4282 completed April 10, 2026, 10:31 p.m.
NEDg Description generation batch_69d97cc07100819088683a0d79b2baa0 completed April 10, 2026, 10:42 p.m.
NED2 Entity disambiguation (via description) batch_69d97e0cda0c8190af5013b971b2ad3c completed April 10, 2026, 10:47 p.m.
Created at: April 8, 2026, 9:05 p.m.