Triple

T11961391
Position Surface form Disambiguated ID Type / Status
Subject Tonelli's theorem E284676 entity
Predicate isSpecialCaseOf P2372 FINISHED
Object Fubini–Tonelli theorem E284675 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: Fubini–Tonelli theorem | Statement: [Tonelli's theorem, isSpecialCaseOf, Fubini–Tonelli theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Fubini–Tonelli theorem
Context triple: [Tonelli's theorem, isSpecialCaseOf, Fubini–Tonelli theorem]
  • A. Fubini's theorem chosen
    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. 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.
  • C. Tonelli's theorem
    Tonelli's theorem is a fundamental result in measure theory that justifies interchanging the order of integration for non-negative measurable functions in iterated Lebesgue integrals.
  • D. Beppo Levi's lemma
    Beppo Levi's lemma, also known as the monotone convergence theorem, is a fundamental result in measure theory that guarantees the convergence of integrals for non-decreasing sequences of non-negative measurable functions.
  • E. Carathéodory’s extension theorem
    Carathéodory’s extension theorem is a fundamental result in measure theory that guarantees a unique extension of a pre-measure defined on an algebra of sets to a complete measure on the generated σ-algebra.
  • 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_69d9037848f481908276716675464464 completed April 10, 2026, 2:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69f48a83c2448190bb40c199afef2ec2 completed May 1, 2026, 11:12 a.m.
Created at: April 8, 2026, 9:45 p.m.