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.