Triple

T11961178

Position	Surface form	Disambiguated ID	Type / Status
Subject	monotone convergence theorem	`E284671`	entity
Predicate	isSpecialCaseOf	`P2372`	FINISHED
Object	Lebesgue dominated convergence theorem (with monotone domination)	`E284672`	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: Lebesgue dominated convergence theorem (with monotone domination) | Statement: [monotone convergence theorem, isSpecialCaseOf, Lebesgue dominated convergence theorem (with monotone domination)]

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Lebesgue dominated convergence theorem (with monotone domination)
Context triple: [monotone convergence theorem, isSpecialCaseOf, Lebesgue dominated convergence theorem (with monotone domination)]

A. dominated convergence theorem chosen
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.
B. 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.
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 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.
E. 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.
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.