Triple
T21783606
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Artin reciprocity law |
E537778
|
entity |
| Predicate | involves |
P1256
|
FINISHED |
| Object | Hecke characters |
—
|
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 characters | Statement: [Artin reciprocity law, involves, Hecke characters]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hecke characters Context triple: [Artin reciprocity law, involves, Hecke characters]
-
A.
Hecke characters
chosen
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.
-
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 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.
-
D.
Dirichlet characters
Dirichlet characters are completely multiplicative periodic arithmetic functions modulo an integer, fundamental in analytic number theory for constructing Dirichlet L-functions and studying the distribution of primes in arithmetic progressions.
-
E.
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.
- 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_69e0c47198f881908cb0d237266c10e9 |
completed | April 16, 2026, 11:13 a.m. |
| NER | Named-entity recognition | batch_69f046303d54819096b3fab4ab5678e6 |
completed | April 28, 2026, 5:31 a.m. |
Created at: April 16, 2026, 6:52 p.m.