Triple

T19050473
Position Surface form Disambiguated ID Type / Status
Subject Dirichlet E466243 entity
Predicate knownFor P22 FINISHED
Object Dirichlet divisor problem — 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 divisor problem | Statement: [Dirichlet, knownFor, Dirichlet divisor problem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Dirichlet divisor problem
Context triple: [Dirichlet, knownFor, Dirichlet divisor problem]
  • A. Dirichlet hyperbola method chosen
    The Dirichlet hyperbola method is a technique in analytic number theory used to estimate sums of arithmetic functions by splitting double sums along a hyperbola to obtain asymptotic formulas.
  • B. Selberg–Delange method results
    Selberg–Delange method results are asymptotic formulas in analytic number theory that precisely describe the average order and distribution of multiplicative arithmetic functions using complex-analytic techniques.
  • C. Multiplicative Number Theory I. Classical Theory (Hugh L. Montgomery, Robert C. Vaughan)
    Multiplicative Number Theory I. Classical Theory (by Hugh L. Montgomery and Robert C. Vaughan) is a foundational graduate-level textbook that systematically develops the classical theory of multiplicative number theory, including Dirichlet characters, L-functions, and the distribution of prime numbers.
  • D. Multiplicative Number Theory
    Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
  • E. Siegel–Walfisz theorem
    The Siegel–Walfisz theorem is a result in analytic number theory that gives strong uniform estimates for the distribution of prime numbers in arithmetic progressions with relatively small moduli.
  • 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.