Triple

T21494133
Position Surface form Disambiguated ID Type / Status
Subject abc conjecture E530309 entity
Predicate relatedTo P37 FINISHED
Object Roth’s 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: Roth’s theorem | Statement: [abc conjecture, relatedTo, Roth’s theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Roth’s theorem
Context triple: [abc conjecture, relatedTo, Roth’s theorem]
  • A. Roth theorem chosen
    Roth's theorem is a fundamental result in Diophantine approximation that gives an essentially optimal bound on how well algebraic irrational numbers can be approximated by rational numbers.
  • 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. Graham–Rothschild theorem
    The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
  • 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. Hales–Jewett theorem
    The Hales–Jewett theorem is a fundamental result in Ramsey theory that guarantees the existence of large monochromatic combinatorial lines in high-dimensional grids under any finite coloring.
  • 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.