Triple
T12735394
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Euler products for automorphic L-functions |
E304347
|
entity |
| Predicate | builtFrom |
P11047
|
FINISHED |
| Object | Hecke operators |
E438307
|
NE FINISHED |
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: [Euler products for automorphic L-functions, builtFrom, Hecke operators]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hecke operators Context triple: [Euler products for automorphic L-functions, builtFrom, 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 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.
-
C.
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.
-
D.
Eisenstein series
Eisenstein series are special types of complex analytic functions on the upper half-plane (or more general symmetric spaces) that play a central role in the theory of modular and automorphic forms, connecting number theory, representation theory, and harmonic analysis.
-
E.
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.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69d7bdf1426c8190a4402e1c4cdec33a |
completed | April 9, 2026, 2:55 p.m. |
| NER | Named-entity recognition | batch_69d9646b3ca08190b239f0736a01169d |
completed | April 10, 2026, 8:58 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f67c8e2dbc81909c1c85ca699a2679 |
completed | May 2, 2026, 10:37 p.m. |
Created at: April 9, 2026, 5:26 p.m.