Triple
T18299160
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hecke theory |
E438309
|
entity |
| Predicate | focusesOn |
P31
|
FINISHED |
| Object | Hecke operators |
—
|
NE NERFINISHED |
How this triple was built (2 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 operators | Statement: [Hecke theory, focusesOn, Hecke operators]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hecke operators Context triple: [Hecke theory, focusesOn, Hecke operators]
-
A.
Hecke operators
chosen
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.
-
B.
Hecke eigenvalues
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.
-
C.
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.
-
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.
Atkin–Lehner theory
Atkin–Lehner theory is a framework in the theory of modular forms that studies their symmetries and decompositions using certain involutions and operators, refining the structure of spaces of modular forms and newforms.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
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.