Triple

T22539295
Position Surface form Disambiguated ID Type / Status
Subject Endre Szemerédi E557241 entity
Predicate notableWork P4 FINISHED
Object "On sets of integers containing no k elements in arithmetic progression" — 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: "On sets of integers containing no k elements in arithmetic progression" | Statement: [Endre Szemerédi, notableWork, "On sets of integers containing no k elements in arithmetic progression"]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: "On sets of integers containing no k elements in arithmetic progression"
Context triple: [Endre Szemerédi, notableWork, "On sets of integers containing no k elements in arithmetic progression"]
  • A. Szemerédi's theorem chosen
    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.
  • B. 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.
  • C. 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.
  • D. Gowers inverse theorem in additive combinatorics
    The Gowers inverse theorem in additive combinatorics is a fundamental result that characterizes functions with large Gowers uniformity norms by showing they must correlate with structured objects such as polynomial phase functions, underpinning much of modern higher-order Fourier analysis.
  • E. Erdős–Turán conjecture
    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.
  • 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_69e11e58662081909ae346ab384514ca completed April 16, 2026, 5:37 p.m.
NER Named-entity recognition batch_69f15f302cd4819098c97ca4fa96363e completed April 29, 2026, 1:30 a.m.
Created at: April 16, 2026, 8:51 p.m.