Triple

T11961145
Position Surface form Disambiguated ID Type / Status
Subject monotone convergence theorem E284671 entity
Predicate alsoKnownAs P39 FINISHED
Object Beppo Levi theorem 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: Beppo Levi theorem | Statement: [monotone convergence theorem, alsoKnownAs, Beppo Levi theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Beppo Levi theorem
Context triple: [monotone convergence theorem, alsoKnownAs, Beppo Levi theorem]
  • A. Fubini's theorem
    Fubini's theorem is a fundamental result in measure theory that allows the evaluation of double integrals as iterated integrals under suitable integrability conditions.
  • 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. 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. Arzelà–Ascoli theorem
    The Arzelà–Ascoli theorem is a fundamental result in analysis that characterizes the relative compactness of families of functions via uniform boundedness and equicontinuity.
  • E. Bose–Nair theorem
    The Bose–Nair theorem is a result in combinatorial design theory that provides conditions for the existence and construction of certain balanced incomplete block designs, contributing to the foundations of modern combinatorics and coding theory.
  • 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_69f4592fa9a48190a0450e3d0c57c4d3 completed May 1, 2026, 7:41 a.m.
Created at: April 8, 2026, 9:45 p.m.