Triple

T12026596
Position Surface form Disambiguated ID Type / Status
Subject Ben Green E286293 entity
Predicate notableWork P4 FINISHED
Object Green–Tao theorem on arithmetic progressions in the primes E286292 NE FINISHED

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: Green–Tao theorem on arithmetic progressions in the primes | Statement: [Ben Green, notableWork, Green–Tao theorem on arithmetic progressions in the primes]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Green–Tao theorem on arithmetic progressions in the primes
Context triple: [Ben Green, notableWork, Green–Tao theorem on arithmetic progressions in the primes]
  • A. Green–Tao theorem chosen
    The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
  • B. Szemerédi's theorem
    Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
  • C. 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.
  • D. Vinogradov's three-primes theorem
    Vinogradov's three-primes theorem is a landmark result in analytic number theory proving that every sufficiently large odd integer can be expressed as the sum of three prime numbers.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d6ab4669e48190b59246358b0383ab completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d903f02638819091e0cc0e93fa5ea7 completed April 10, 2026, 2:06 p.m.
NED1 Entity disambiguation (via context triple) batch_69f5f646423c819088575a7032e6a9a3 completed May 2, 2026, 1:04 p.m.
Created at: April 8, 2026, 9:47 p.m.