Triple
T5658022
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Emil Artin |
E124666
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Artin zeta function
The Artin zeta function is a complex analytic function in number theory that generalizes the Riemann zeta function by encoding arithmetic information of Galois representations and number field extensions.
|
E358024
|
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: Artin zeta function | Statement: [Emil Artin, notableWork, Artin zeta function]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Artin zeta function Context triple: [Emil Artin, notableWork, Artin zeta function]
-
A.
Hasse–Weil zeta function
The Hasse–Weil zeta function is an analytic object in number theory that encodes arithmetic information about algebraic varieties over number fields, generalizing the Riemann zeta function and playing a central role in modern arithmetic geometry and conjectures like the Weil conjectures and the Birch–Swinnerton-Dyer conjecture.
-
B.
Dedekind zeta functions
Dedekind zeta functions are number-theoretic functions attached to algebraic number fields that encode their arithmetic properties, such as the distribution of prime ideals and class numbers.
-
C.
L-functions
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.
-
D.
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.
-
E.
Selberg class
The Selberg class is a collection of Dirichlet series with specific analytic properties introduced to generalize and axiomatize L-functions in number theory.
- 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: Artin zeta function Triple: [Emil Artin, notableWork, Artin zeta function]
Generated description
The Artin zeta function is a complex analytic function in number theory that generalizes the Riemann zeta function by encoding arithmetic information of Galois representations and number field extensions.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Artin zeta function Target entity description: The Artin zeta function is a complex analytic function in number theory that generalizes the Riemann zeta function by encoding arithmetic information of Galois representations and number field extensions.
-
A.
Hasse–Weil zeta function
The Hasse–Weil zeta function is an analytic object in number theory that encodes arithmetic information about algebraic varieties over number fields, generalizing the Riemann zeta function and playing a central role in modern arithmetic geometry and conjectures like the Weil conjectures and the Birch–Swinnerton-Dyer conjecture.
-
B.
Dedekind zeta functions
Dedekind zeta functions are number-theoretic functions attached to algebraic number fields that encode their arithmetic properties, such as the distribution of prime ideals and class numbers.
-
C.
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.
-
D.
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.
-
E.
Selberg class
The Selberg class is a collection of Dirichlet series with specific analytic properties introduced to generalize and axiomatize L-functions in number theory.
- F. None of above.
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_69c0082774a481909d7e63fb2aad56ac |
completed | March 22, 2026, 3:17 p.m. |
| NER | Named-entity recognition | batch_69c022fd9b148190bd4aa9c43500949f |
completed | March 22, 2026, 5:12 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c04da37ffc819095f33e7e66e7c1d0 |
completed | March 22, 2026, 8:14 p.m. |
| NEDg | Description generation | batch_69c04edf30448190a60eda49b8b031a0 |
completed | March 22, 2026, 8:19 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69c04fb62690819083327781cb857ccc |
completed | March 22, 2026, 8:23 p.m. |
Created at: March 22, 2026, 3:42 p.m.