Triple

T19050953
Position Surface form Disambiguated ID Type / Status
Subject Dirichlet hyperbola method E466253 entity
Predicate relatedTo P37 FINISHED
Object Dirichlet convolution — NE NERFINISHED

How this triple was built (2 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 convolution | Statement: [Dirichlet hyperbola method, relatedTo, Dirichlet convolution]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Dirichlet convolution
Context triple: [Dirichlet hyperbola method, relatedTo, Dirichlet convolution]
  • A. Dirichlet convolution chosen
    Dirichlet convolution is a binary operation on arithmetic functions that combines them via summation over divisors and plays a central role in multiplicative number theory and Dirichlet series.
  • B. Dirichlet inverse
    The Dirichlet inverse of an arithmetic function is another arithmetic function that, when combined with the original via Dirichlet convolution, yields the identity function concentrated at 1.
  • C. Möbius inversion formula
    The Möbius inversion formula is a fundamental result in number theory that allows one to recover an arithmetic function from its summatory function over divisors using the Möbius function.
  • D. Möbius function
    The Möbius function is a multiplicative arithmetic function in number theory that assigns values based on the prime factorization of integers and plays a central role in inversion formulas and the study of prime distribution.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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.
Created at: April 10, 2026, 12:03 p.m.