Triple

T11961163
Position Surface form Disambiguated ID Type / Status
Subject monotone convergence theorem E284671 entity
Predicate implies P1661 FINISHED
Object 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.
 E956270 NE FINISHED

How this triple was built (4 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 some formulations) | Statement: [monotone convergence theorem, implies, Fatou lemma (in some formulations)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Fatou lemma (in some formulations)
Context triple: [monotone convergence theorem, implies, Fatou lemma (in some formulations)]
  • A. Limite
    Limite is a 1931 Brazilian silent experimental film by Mário Peixoto, renowned for its avant-garde visual style and status as a landmark of early Latin American cinema.
  • B. Levy
    Levy is a variant spelling of the name Levi, commonly used as a Jewish surname and sometimes as a given name.
  • C. Fat Lever
    Fat Lever is a former NBA All-Star point guard known for his all-around play and prolific triple-doubles during the 1980s.
  • D. Faltine
    Faltine are powerful extra-dimensional energy beings in the Marvel Universe, known for their immense mystical abilities and for producing entities like Dormammu.
  • E. PE-LIM
    PE-LIM is the ISO 3166-2 code that designates the Lima Region of Peru.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Fatou lemma (in some formulations)
Triple: [monotone convergence theorem, implies, Fatou lemma (in some formulations)]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Fatou lemma (in some formulations)
Target entity description: 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.
  • A. Limite
    Limite is a 1931 Brazilian silent experimental film by Mário Peixoto, renowned for its avant-garde visual style and status as a landmark of early Latin American cinema.
  • B. Levy
    Levy is a variant spelling of the name Levi, commonly used as a Jewish surname and sometimes as a given name.
  • C. Fat Lever
    Fat Lever is a former NBA All-Star point guard known for his all-around play and prolific triple-doubles during the 1980s.
  • D. Faltine
    Faltine are powerful extra-dimensional energy beings in the Marvel Universe, known for their immense mystical abilities and for producing entities like Dormammu.
  • E. PE-LIM
    PE-LIM is the ISO 3166-2 code that designates the Lima Region of Peru.
  • F. None of above. chosen

Provenance (5 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.
NEDg Description generation batch_69f4645ef63881909b46937f73d637a3 completed May 1, 2026, 8:29 a.m.
NED2 Entity disambiguation (via description) batch_69f465be4db08190882898a17d077019 completed May 1, 2026, 8:35 a.m.
Created at: April 8, 2026, 9:45 p.m.