Triple

T21494454
Position Surface form Disambiguated ID Type / Status
Subject analytic number theory E530316 entity
Predicate centralTheorem P16614 FINISHED
Object Dirichlet's theorem on arithmetic progressions — 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's theorem on arithmetic progressions | Statement: [analytic number theory, centralTheorem, Dirichlet's theorem on arithmetic progressions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Dirichlet's theorem on arithmetic progressions
Context triple: [analytic number theory, centralTheorem, Dirichlet's theorem on arithmetic progressions]
  • A. Dirichlet's theorem on arithmetic progressions chosen
    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.
  • B. Linnik’s theorem on the least prime in an arithmetic progression
    Linnik’s theorem on the least prime in an arithmetic progression is a result in analytic number theory that gives an explicit upper bound, depending only on the modulus, for the size of the smallest prime in any given coprime residue class.
  • C. Piatetski-Shapiro prime number theorem
    The Piatetski-Shapiro prime number theorem is a result in analytic number theory that establishes the existence of infinitely many primes among the values of certain non-integer power sequences, such as ⌊n^c⌋ for suitable real exponents c.
  • D. Euclid's theorem on the infinitude of primes
    Euclid's theorem on the infinitude of primes is a foundational result in number theory proving that there are infinitely many prime numbers.
  • 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_69e0c45bd15481909fba5910765cdda2 completed April 16, 2026, 11:13 a.m.
NER Named-entity recognition batch_69e9ea567244819091863350fedae3ae completed April 23, 2026, 9:45 a.m.
Created at: April 16, 2026, 6:23 p.m.