Triple

T11961177
Position Surface form Disambiguated ID Type / Status
Subject monotone convergence theorem E284671 entity
Predicate isStrongerThan P2373 FINISHED
Object Fatou lemma in the monotone case E284673 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: Fatou lemma in the monotone case | Statement: [monotone convergence theorem, isStrongerThan, Fatou lemma in the monotone case]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Fatou lemma in the monotone case
Context triple: [monotone convergence theorem, isStrongerThan, Fatou lemma in the monotone case]
  • A. Fatou lemma (in some formulations)
    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.
  • B. Fatou's lemma chosen
    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.
  • C. monotone convergence theorem
    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.
  • D. 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.
  • E. Doob’s maximal inequalities
    Doob’s maximal inequalities are fundamental results in probability theory that provide bounds on the maximum value of a martingale or submartingale in terms of its expected terminal value, playing a key role in convergence and limit theorems.
  • 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.