Triple
T16474963
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | measure theory |
E400163
|
entity |
| Predicate | usesConcept |
P531
|
FINISHED |
| Object | Fatou 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 lemma | Statement: [measure theory, usesConcept, Fatou lemma]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Fatou lemma Context triple: [measure theory, usesConcept, Fatou 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_69d883813098819084f5409539723b59 |
completed | April 10, 2026, 4:58 a.m. |
| NER | Named-entity recognition | batch_69e32dd43cf88190881a5cbc80da1490 |
completed | April 18, 2026, 7:08 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a004f5f238881909b5f2fb41da3f932 |
completed | May 10, 2026, 9:26 a.m. |
Created at: April 10, 2026, 5:13 a.m.