Triple

T8733479
Position Surface form Disambiguated ID Type / Status
Subject Hasse–Weil zeta function E207313 entity
Predicate studiedIn P770 FINISHED
Object 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.
E753154 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 program | Statement: [Hasse–Weil zeta function, studiedIn, Langlands program]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Langlands program
Context triple: [Hasse–Weil zeta function, studiedIn, Langlands program]
  • A. Galois representations
    Galois representations are homomorphisms from Galois groups of field extensions into matrix groups that encode deep arithmetic information and link number theory with algebraic geometry and modular forms.
  • 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. Weil conjectures
    The Weil conjectures are a set of deep statements about the zeta functions of algebraic varieties over finite fields that guided the development of modern algebraic geometry and were ultimately proved using étale cohomology.
  • D. Iwasawa theory
    Iwasawa theory is a branch of number theory that studies the growth of arithmetic invariants in infinite towers of number fields, particularly using p-adic methods.
  • E. Birch and Swinnerton-Dyer Conjecture
    The Birch and Swinnerton-Dyer Conjecture is a central unsolved problem in number theory that predicts a deep connection between the arithmetic of rational points on an elliptic curve and the behavior of its associated L-function at a specific value.
  • 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 program
Triple: [Hasse–Weil zeta function, studiedIn, Langlands program]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Langlands program
Target entity description: 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.
  • A. Galois representations
    Galois representations are homomorphisms from Galois groups of field extensions into matrix groups that encode deep arithmetic information and link number theory with algebraic geometry and modular forms.
  • 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. Weil conjectures
    The Weil conjectures are a set of deep statements about the zeta functions of algebraic varieties over finite fields that guided the development of modern algebraic geometry and were ultimately proved using étale cohomology.
  • D. Iwasawa theory
    Iwasawa theory is a branch of number theory that studies the growth of arithmetic invariants in infinite towers of number fields, particularly using p-adic methods.
  • E. Birch and Swinnerton-Dyer Conjecture
    The Birch and Swinnerton-Dyer Conjecture is a central unsolved problem in number theory that predicts a deep connection between the arithmetic of rational points on an elliptic curve and the behavior of its associated L-function at a specific value.
  • 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_69ca8358e4008190898471a59b96c301 completed March 30, 2026, 2:06 p.m.
NER Named-entity recognition batch_69cc5d2a26988190acfda17f232e610a completed March 31, 2026, 11:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69cf292d71ec819082095cb7b8b2d39c completed April 3, 2026, 2:42 a.m.
NEDg Description generation batch_69cf2bd4f50c8190bad328e82d299ae0 completed April 3, 2026, 2:54 a.m.
NED2 Entity disambiguation (via description) batch_69cf2cbf60808190a006ee4fb26cde41 completed April 3, 2026, 2:58 a.m.
Created at: March 30, 2026, 6:37 p.m.