Triple

T10543859
Position Surface form Disambiguated ID Type / Status
Subject Carl Ludwig Siegel E248763 entity
Predicate notableWork P4 FINISHED
Object Siegel modular form
A Siegel modular form is a type of complex analytic function defined on the Siegel upper half-space that generalizes classical modular forms to higher dimensions and plays a central role in number theory and algebraic geometry.
E871397 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: Siegel modular form | Statement: [Carl Ludwig Siegel, notableWork, Siegel modular form]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Siegel modular form
Context triple: [Carl Ludwig Siegel, notableWork, Siegel modular form]
  • A. modular j-invariant
    The modular j-invariant is a fundamental modular function that classifies complex elliptic curves up to isomorphism and plays a central role in number theory, complex analysis, and the theory of modular 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. Selberg trace formula
    The Selberg trace formula is a fundamental result in analytic number theory and spectral theory that relates lengths of closed geodesics on a Riemannian manifold to the spectrum of its Laplace operator, serving as a non-abelian analogue of the Poisson summation formula.
  • D. 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.
  • E. 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.
  • 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: Siegel modular form
Triple: [Carl Ludwig Siegel, notableWork, Siegel modular form]
Generated description
A Siegel modular form is a type of complex analytic function defined on the Siegel upper half-space that generalizes classical modular forms to higher dimensions and plays a central role in number theory and algebraic geometry.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Siegel modular form
Target entity description: A Siegel modular form is a type of complex analytic function defined on the Siegel upper half-space that generalizes classical modular forms to higher dimensions and plays a central role in number theory and algebraic geometry.
  • A. modular j-invariant
    The modular j-invariant is a fundamental modular function that classifies complex elliptic curves up to isomorphism and plays a central role in number theory, complex analysis, and the theory of modular 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. Selberg trace formula
    The Selberg trace formula is a fundamental result in analytic number theory and spectral theory that relates lengths of closed geodesics on a Riemannian manifold to the spectrum of its Laplace operator, serving as a non-abelian analogue of the Poisson summation formula.
  • D. 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.
  • E. 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.
  • 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_69d381c733c08190ab1dd6239f5f34ae completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d51911b10481909e6e548879e8de36 completed April 7, 2026, 2:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69d9343c5c308190952596e5254b6a65 completed April 10, 2026, 5:32 p.m.
NEDg Description generation batch_69d938c697f481908a93296ee7f82eae completed April 10, 2026, 5:52 p.m.
NED2 Entity disambiguation (via description) batch_69d940176c988190b7583ce9f2c21898 completed April 10, 2026, 6:23 p.m.
Created at: April 6, 2026, 12:32 p.m.