Triple

T18299095
Position Surface form Disambiguated ID Type / Status
Subject Hecke operators E438307 entity
Predicate usedToDefine P773 FINISHED
Object Hecke eigenvalues — NE NERFINISHED

How this triple was built (3 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: Hecke eigenvalues | Statement: [Hecke operators, usedToDefine, Hecke eigenvalues]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hecke eigenvalues
Context triple: [Hecke operators, usedToDefine, Hecke eigenvalues]
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Hecke characters
    Hecke characters are generalized algebraic number field characters (or Grössencharaktere) that play a central role in class field theory and the study of L-functions.
  • E. 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.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Hecke eigenvalues
Target entity description: Hecke eigenvalues are the scalar values by which Hecke operators act on eigenforms or automorphic forms, encoding deep arithmetic information such as Fourier coefficients and connections to L-functions.
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Hecke characters
    Hecke characters are generalized algebraic number field characters (or Grössencharaktere) that play a central role in class field theory and the study of L-functions.
  • E. 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.
  • F. None of above. chosen

Provenance (2 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_69d8b915e3e881909125d760c15d0c29 completed April 10, 2026, 8:47 a.m.
NER Named-entity recognition batch_69e5017d96588190ac1e326803142976 completed April 19, 2026, 4:23 p.m.
Created at: April 10, 2026, 10:35 a.m.