Triple

T11961206
Position Surface form Disambiguated ID Type / Status
Subject dominated convergence theorem E284672 entity
Predicate comparedTo P278 FINISHED
Object Fatou's lemma 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's lemma | Statement: [dominated convergence theorem, comparedTo, Fatou's lemma]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Fatou's lemma
Context triple: [dominated convergence theorem, comparedTo, Fatou's lemma]
  • A. 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.
  • B. 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.
  • C. 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.
  • 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. Riemann–Lebesgue lemma
    The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
  • 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_69f48a83c2448190bb40c199afef2ec2 completed May 1, 2026, 11:12 a.m.
Created at: April 8, 2026, 9:45 p.m.