Triple
T12735376
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Euler products for automorphic L-functions |
E304347
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Rankin–Selberg L-functions
Rankin–Selberg L-functions are complex analytic functions in number theory constructed from pairs of automorphic forms, encoding deep arithmetic information through their Euler product expansions and functional equations.
|
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: Rankin–Selberg L-functions | Statement: [Euler products for automorphic L-functions, relatedTo, Rankin–Selberg L-functions]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Rankin–Selberg L-functions Context triple: [Euler products for automorphic L-functions, relatedTo, Rankin–Selberg L-functions]
-
A.
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.
-
B.
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.
-
C.
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.
-
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.
Siegel’s theorem on zeros of L-functions
Siegel’s theorem on zeros of L-functions is a result in analytic number theory that gives strong bounds on how close nontrivial zeros of Dirichlet L-functions can approach 1, with deep implications for the distribution 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: Rankin–Selberg L-functions Triple: [Euler products for automorphic L-functions, relatedTo, Rankin–Selberg L-functions]
Generated description
Rankin–Selberg L-functions are complex analytic functions in number theory constructed from pairs of automorphic forms, encoding deep arithmetic information through their Euler product expansions and functional equations.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Rankin–Selberg L-functions Target entity description: Rankin–Selberg L-functions are complex analytic functions in number theory constructed from pairs of automorphic forms, encoding deep arithmetic information through their Euler product expansions and functional equations.
-
A.
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.
-
B.
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.
-
C.
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.
-
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.
Siegel’s theorem on zeros of L-functions
Siegel’s theorem on zeros of L-functions is a result in analytic number theory that gives strong bounds on how close nontrivial zeros of Dirichlet L-functions can approach 1, with deep implications for the distribution 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_69f684eba2508190966d084cc21dc1ea |
completed | May 2, 2026, 11:12 p.m. |
| NEDg | Description generation | batch_69f685dac5cc8190b4bc2d81186c9266 |
completed | May 2, 2026, 11:16 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69f6869156048190b548ecd04561deb8 |
completed | May 2, 2026, 11:19 p.m. |
Created at: April 9, 2026, 5:26 p.m.