Triple
T11085841
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Dedekind zeta function |
E262117
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Hecke L-functions |
E358024
|
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 L-functions | Statement: [Dedekind zeta function, relatedTo, Hecke L-functions]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hecke L-functions Context triple: [Dedekind zeta function, relatedTo, Hecke L-functions]
-
A.
L-functions
chosen
L-functions are complex analytic functions, often arising from number theory and algebraic geometry, that encode deep arithmetic information and generalize the Riemann zeta function.
-
B.
Dirichlet L-functions
Dirichlet L-functions are complex analytic functions built from Dirichlet characters that generalize the Riemann zeta function and play a central role in number theory, particularly in the study of primes in arithmetic progressions.
-
C.
Artin L-functions
Artin L-functions are complex analytic functions attached to Galois representations that generalize Dirichlet L-functions and play a central role in number theory and the study of arithmetic properties of fields.
-
D.
Euler products for automorphic L-functions
Euler products for automorphic L-functions are infinite product expansions attached to automorphic representations that encode deep arithmetic information and generalize the classical Euler product of the Riemann zeta function to a broad class of L-functions in the Langlands program.
-
E.
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.
- 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_69d6aa9983c08190b0ef61603b69feac |
completed | April 8, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69d799c2c7d4819087ac793153340178 |
completed | April 9, 2026, 12:21 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e42d66ded88190877a20a10f012d6b |
completed | April 19, 2026, 1:18 a.m. |
Created at: April 8, 2026, 9:27 p.m.