Triple

T22668815
Position Surface form Disambiguated ID Type / Status
Subject Chevalley–Warning theorem E559864 entity
Predicate generalizedBy P2372 FINISHED
Object Ax–Katz 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: Ax–Katz theorem | Statement: [Chevalley–Warning theorem, generalizedBy, Ax–Katz theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Ax–Katz theorem
Context triple: [Chevalley–Warning theorem, generalizedBy, Ax–Katz theorem]
  • A. Ax–Katz theorem chosen
    The Ax–Katz theorem is a result in number theory that gives precise divisibility bounds for the number of solutions to polynomial equations over finite fields, strengthening and refining the Chevalley–Warning theorem.
  • 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. 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. Roth theorem
    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.
  • E. Erdős–Turán inequality
    The Erdős–Turán inequality is a fundamental result in analytic number theory that provides quantitative bounds on the discrepancy of sequences by relating uniform distribution to exponential sums.
  • 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_69e2454a158c819093b8e35f5045efb6 completed April 17, 2026, 2:35 p.m.
NER Named-entity recognition batch_69f1781de1d48190947cb1bb9d0890d9 completed April 29, 2026, 3:16 a.m.
Created at: April 17, 2026, 3:09 p.m.