Triple

T17671609
Position Surface form Disambiguated ID Type / Status
Subject Goro Shimura E440532 entity
Predicate knownFor P22 FINISHED
Object Shimura correspondence
The Shimura correspondence is a fundamental result in number theory that establishes a deep link between modular forms of half-integral weight and modular forms of integral weight, with important applications to L-functions and arithmetic geometry.
E1281164 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: Shimura correspondence | Statement: [Goro Shimura, knownFor, Shimura correspondence]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Shimura correspondence
Context triple: [Goro Shimura, knownFor, Shimura correspondence]
  • A. Shimura varieties
    Shimura varieties are higher-dimensional algebraic varieties that generalize modular curves and play a central role in the Langlands program by connecting number theory, automorphic forms, and arithmetic geometry.
  • B. 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.
  • C. Deligne bound for Fourier coefficients of modular forms
    The Deligne bound for Fourier coefficients of modular forms is a deep result in number theory, proved by Pierre Deligne, that gives optimal size estimates for the Fourier coefficients of cusp forms and confirms the Ramanujan–Petersson conjecture for modular forms.
  • D. 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.
  • E. Hecke operators
    Hecke operators are algebraic operators acting on modular forms that play a central role in number theory, particularly in understanding congruences, L-functions, and the arithmetic of modular forms.
  • 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: Shimura correspondence
Triple: [Goro Shimura, knownFor, Shimura correspondence]
Generated description
The Shimura correspondence is a fundamental result in number theory that establishes a deep link between modular forms of half-integral weight and modular forms of integral weight, with important applications to L-functions and arithmetic geometry.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Shimura correspondence
Target entity description: The Shimura correspondence is a fundamental result in number theory that establishes a deep link between modular forms of half-integral weight and modular forms of integral weight, with important applications to L-functions and arithmetic geometry.
  • A. Shimura varieties
    Shimura varieties are higher-dimensional algebraic varieties that generalize modular curves and play a central role in the Langlands program by connecting number theory, automorphic forms, and arithmetic geometry.
  • B. 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.
  • C. Deligne bound for Fourier coefficients of modular forms
    The Deligne bound for Fourier coefficients of modular forms is a deep result in number theory, proved by Pierre Deligne, that gives optimal size estimates for the Fourier coefficients of cusp forms and confirms the Ramanujan–Petersson conjecture for modular forms.
  • D. 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.
  • E. Hecke operators
    Hecke operators are algebraic operators acting on modular forms that play a central role in number theory, particularly in understanding congruences, L-functions, and the arithmetic of modular forms.
  • 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.