Triple

T11961265
Position Surface form Disambiguated ID Type / Status
Subject Fatou's lemma E284673 entity
Predicate relatedTo P37 FINISHED
Object monotone convergence theorem E284671 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: monotone convergence theorem | Statement: [Fatou's lemma, relatedTo, monotone convergence theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: monotone convergence theorem
Context triple: [Fatou's lemma, relatedTo, monotone convergence theorem]
  • A. monotone convergence theorem chosen
    The monotone convergence theorem is a fundamental result in measure theory stating that the integral of a pointwise increasing sequence of nonnegative measurable functions equals the limit of their integrals.
  • B. dominated convergence theorem
    The dominated convergence theorem is a fundamental result in measure theory that provides conditions under which one can interchange limits and integrals for sequences of functions bounded by an integrable dominating function.
  • C. Vitali convergence theorem
    The Vitali convergence theorem is a result in measure theory that gives conditions under which pointwise convergence of a sequence of integrable functions implies convergence of their integrals, strengthening the dominated convergence theorem via uniform integrability.
  • D. Fatou's lemma
    Fatou's lemma is a fundamental result in measure theory that provides an inequality relating the integral of the pointwise limit inferior of a sequence of nonnegative measurable functions to the limit inferior of their integrals.
  • E. Bolzano–Weierstrass theorem
    The Bolzano–Weierstrass theorem is a fundamental result in real analysis stating that every bounded infinite sequence in ℝⁿ has a convergent subsequence.
  • 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_69d6ab2eaeb881909f7914758f859413 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d9036941948190b150369094551731 completed April 10, 2026, 2:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69f471d625c88190baed4ea08853988a completed May 1, 2026, 9:26 a.m.
Created at: April 8, 2026, 9:45 p.m.