Triple
T12735373
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Euler products for automorphic L-functions |
E304347
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Langlands L-functions
Langlands L-functions are complex analytic functions arising from the Langlands program that generalize classical L-functions by encoding deep connections between automorphic representations and Galois or motivic data.
|
E304347
|
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: Langlands L-functions | Statement: [Euler products for automorphic L-functions, relatedTo, Langlands L-functions]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Langlands L-functions Context triple: [Euler products for automorphic L-functions, relatedTo, Langlands L-functions]
-
A.
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.
-
B.
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.
-
C.
Langlands program
The Langlands program is a far-reaching web of conjectures and theories in number theory and representation theory that seeks deep connections between Galois groups and automorphic forms, unifying many areas of modern mathematics.
-
D.
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.
-
E.
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.
- 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: Langlands L-functions Triple: [Euler products for automorphic L-functions, relatedTo, Langlands L-functions]
Generated description
Langlands L-functions are complex analytic functions arising from the Langlands program that generalize classical L-functions by encoding deep connections between automorphic representations and Galois or motivic data.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Langlands L-functions Target entity description: Langlands L-functions are complex analytic functions arising from the Langlands program that generalize classical L-functions by encoding deep connections between automorphic representations and Galois or motivic data.
-
A.
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.
-
B.
Euler products for automorphic L-functions
chosen
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.
-
C.
Langlands program
The Langlands program is a far-reaching web of conjectures and theories in number theory and representation theory that seeks deep connections between Galois groups and automorphic forms, unifying many areas of modern mathematics.
-
D.
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.
-
E.
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.
- 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_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. |
| NEDg | Description generation | batch_69f67d888d7c8190b9aaeb877984a403 |
completed | May 2, 2026, 10:41 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69f67e0f48e4819085905564f5540f37 |
completed | May 2, 2026, 10:43 p.m. |
Created at: April 9, 2026, 5:26 p.m.