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.