Triple

T17671629
Position Surface form Disambiguated ID Type / Status
Subject Goro Shimura E440532 entity
Predicate notableWork P4 FINISHED
Object Introduction to the Arithmetic Theory of Automorphic Functions
Introduction to the Arithmetic Theory of Automorphic Functions is a foundational monograph by Goro Shimura that systematically develops the arithmetic aspects of automorphic forms and their connections to number theory.
E1281167 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: Introduction to the Arithmetic Theory of Automorphic Functions | Statement: [Goro Shimura, notableWork, Introduction to the Arithmetic Theory of Automorphic Functions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Introduction to the Arithmetic Theory of Automorphic Functions
Context triple: [Goro Shimura, notableWork, Introduction to the Arithmetic Theory of Automorphic Functions]
  • A. Automorphic Forms and Representations
    Automorphic Forms and Representations is a foundational mathematical monograph that develops the theory of automorphic forms and their connections to representation theory and number theory.
  • 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. 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. Hecke eigenforms
    Hecke eigenforms are special modular forms that are simultaneous eigenfunctions of all Hecke operators, playing a central role in modern number theory and the theory of automorphic forms.
  • E. Introduction to the Theory of Algebraic Functions of One Variable
    Introduction to the Theory of Algebraic Functions of One Variable is a classic monograph by Claude Chevalley that provides a rigorous, modern foundation for the theory of algebraic function fields in one variable.
  • 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: Introduction to the Arithmetic Theory of Automorphic Functions
Triple: [Goro Shimura, notableWork, Introduction to the Arithmetic Theory of Automorphic Functions]
Generated description
Introduction to the Arithmetic Theory of Automorphic Functions is a foundational monograph by Goro Shimura that systematically develops the arithmetic aspects of automorphic forms and their connections to number theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Introduction to the Arithmetic Theory of Automorphic Functions
Target entity description: Introduction to the Arithmetic Theory of Automorphic Functions is a foundational monograph by Goro Shimura that systematically develops the arithmetic aspects of automorphic forms and their connections to number theory.
  • A. Automorphic Forms and Representations
    Automorphic Forms and Representations is a foundational mathematical monograph that develops the theory of automorphic forms and their connections to representation theory and number theory.
  • 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. 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. Hecke eigenforms
    Hecke eigenforms are special modular forms that are simultaneous eigenfunctions of all Hecke operators, playing a central role in modern number theory and the theory of automorphic forms.
  • E. Introduction to the Theory of Algebraic Functions of One Variable
    Introduction to the Theory of Algebraic Functions of One Variable is a classic monograph by Claude Chevalley that provides a rigorous, modern foundation for the theory of algebraic function fields in one variable.
  • 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_69d8b9e87e18819087104a44dc4dc5b1 completed April 10, 2026, 8:50 a.m.
NER Named-entity recognition batch_69e46f69b11c8190b09add33f81776b3 completed April 19, 2026, 6 a.m.
NED1 Entity disambiguation (via context triple) batch_6a02166234f0819099c452808234e3e4 completed May 11, 2026, 5:48 p.m.
NEDg Description generation batch_6a0217ca2ec881908573b0423c3610f7 completed May 11, 2026, 5:54 p.m.
NED2 Entity disambiguation (via description) batch_6a0218636e048190a48bc7f066c7bee1 completed May 11, 2026, 5:56 p.m.
Created at: April 10, 2026, 9:59 a.m.