Triple

T12026559
Position Surface form Disambiguated ID Type / Status
Subject Green–Tao theorem E286292 entity
Predicate relatedTo P37 FINISHED
Object Erdős–Turán conjecture on arithmetic progressions E554303 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: Erdős–Turán conjecture on arithmetic progressions | Statement: [Green–Tao theorem, relatedTo, Erdős–Turán conjecture on arithmetic progressions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Erdős–Turán conjecture on arithmetic progressions
Context triple: [Green–Tao theorem, relatedTo, Erdős–Turán conjecture on arithmetic progressions]
  • A. Erdős–Turán conjecture chosen
    The Erdős–Turán conjecture is an unsolved problem in additive number theory asserting that any subset of the positive integers with divergent sum of reciprocals must contain 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. Erdős discrepancy problem
    The Erdős discrepancy problem is a famous question in combinatorial number theory that asks whether every infinite ±1 sequence has arbitrarily large discrepancy along some homogeneous arithmetic progression.
  • D. Green–Tao theorem
    The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
  • 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_69f60a5f724c819082aa589372dff020 completed May 2, 2026, 2:29 p.m.
Created at: April 8, 2026, 9:47 p.m.