Triple
T19050670
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Dirichlet eta function |
E466247
|
entity |
| Predicate | relatedConcept |
P37
|
FINISHED |
| Object |
Dirichlet lambda function
The Dirichlet lambda function is a special function in analytic number theory closely related to the Riemann zeta function, defined as an alternating series over odd integers and used in the study of L-functions and prime number distributions.
|
E466247
|
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: Dirichlet lambda function | Statement: [Dirichlet eta function, relatedConcept, Dirichlet lambda function]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Dirichlet lambda function Context triple: [Dirichlet eta function, relatedConcept, Dirichlet lambda function]
-
A.
Dirichlet eta function
The Dirichlet eta function is an alternating Dirichlet series closely related to the Riemann zeta function and used in analytic number theory, particularly for studying series convergence and analytic continuation.
-
B.
von Mangoldt function Λ(n)
The von Mangoldt function Λ(n) is an arithmetic function in number theory that encodes the distribution of prime powers by assigning log p to integers n that are powers of a prime p and 0 otherwise.
-
C.
Liouville function
The Liouville function is a completely multiplicative arithmetic function that assigns values based on the parity of the total number of prime factors of an integer, playing a key role in analytic number theory and the study of prime distribution.
-
D.
Dirichlet series
A Dirichlet series is an infinite series of the form ∑ aₙ/nˢ, fundamental in analytic number theory for studying arithmetic functions and L-functions.
-
E.
Hurwitz zeta function
The Hurwitz zeta function is a complex analytic function that generalizes the Riemann zeta function by introducing a shift parameter, playing a key role in analytic number theory and special function 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: Dirichlet lambda function Triple: [Dirichlet eta function, relatedConcept, Dirichlet lambda function]
Generated description
The Dirichlet lambda function is a special function in analytic number theory closely related to the Riemann zeta function, defined as an alternating series over odd integers and used in the study of L-functions and prime number distributions.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Dirichlet lambda function Target entity description: The Dirichlet lambda function is a special function in analytic number theory closely related to the Riemann zeta function, defined as an alternating series over odd integers and used in the study of L-functions and prime number distributions.
-
A.
Dirichlet eta function
chosen
The Dirichlet eta function is an alternating Dirichlet series closely related to the Riemann zeta function and used in analytic number theory, particularly for studying series convergence and analytic continuation.
-
B.
von Mangoldt function Λ(n)
The von Mangoldt function Λ(n) is an arithmetic function in number theory that encodes the distribution of prime powers by assigning log p to integers n that are powers of a prime p and 0 otherwise.
-
C.
Liouville function
The Liouville function is a completely multiplicative arithmetic function that assigns values based on the parity of the total number of prime factors of an integer, playing a key role in analytic number theory and the study of prime distribution.
-
D.
Dirichlet series
A Dirichlet series is an infinite series of the form ∑ aₙ/nˢ, fundamental in analytic number theory for studying arithmetic functions and L-functions.
-
E.
Hurwitz zeta function
The Hurwitz zeta function is a complex analytic function that generalizes the Riemann zeta function by introducing a shift parameter, playing a key role in analytic number theory and special function 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_69d8dd040fb881909af2a964f65ad208 |
completed | April 10, 2026, 11:20 a.m. |
| NER | Named-entity recognition | batch_69e5dc02597c8190b39fd2c7b7e42258 |
completed | April 20, 2026, 7:55 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a05c553eaf481909a8e07efec1f58c5 |
completed | May 14, 2026, 12:51 p.m. |
| NEDg | Description generation | batch_6a05c8e3015c819081b70695b9571e1c |
completed | May 14, 2026, 1:06 p.m. |
| NED2 | Entity disambiguation (via description) | batch_6a05c95848b88190bf2a9a37b3d51b55 |
completed | May 14, 2026, 1:08 p.m. |
Created at: April 10, 2026, 12:03 p.m.