Triple

T22964944
Position Surface form Disambiguated ID Type / Status
Subject Bombieri–Vinogradov theorem E571012 entity
Predicate comparedWith P278 FINISHED
Object Siegel–Walfisz theorem 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: Siegel–Walfisz theorem | Statement: [Bombieri–Vinogradov theorem, comparedWith, Siegel–Walfisz theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Siegel–Walfisz theorem
Context triple: [Bombieri–Vinogradov theorem, comparedWith, Siegel–Walfisz theorem]
  • A. Siegel–Walfisz theorem chosen
    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.
  • B. Bombieri–Vinogradov theorem
    The Bombieri–Vinogradov theorem is a major result in analytic number theory that gives strong average estimates for the distribution of prime numbers in arithmetic progressions, approaching what is predicted by the Generalized Riemann Hypothesis.
  • C. Erdős–Wintner theorem
    The Erdős–Wintner theorem is a fundamental result in probabilistic number theory that characterizes when an additive arithmetic function has a limiting distribution.
  • D. Dirichlet's theorem on arithmetic progressions
    Dirichlet's theorem on arithmetic progressions is a fundamental result in number theory stating that any arithmetic progression with first term and difference coprime contains infinitely many prime numbers.
  • E. Erdős–Kac theorem
    The Erdős–Kac theorem is a fundamental result in probabilistic number theory stating that the number of distinct prime factors of a typical integer behaves like a normally distributed random variable.
  • 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_69e245b212a88190b5259caf51606084 completed April 17, 2026, 2:37 p.m.
NER Named-entity recognition batch_69f181f763688190aab8f444a1a71577 completed April 29, 2026, 3:58 a.m.
Created at: April 17, 2026, 3:47 p.m.