Triple

T12422601
Position Surface form Disambiguated ID Type / Status
Subject Otton Nikodym E296811 entity
Predicate hasNotableTheorem P29208 FINISHED
Object Nikodym convergence theorem E981549 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: Nikodym convergence theorem | Statement: [Otton Nikodym, hasNotableTheorem, Nikodym convergence theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Nikodym convergence theorem
Context triple: [Otton Nikodym, hasNotableTheorem, Nikodym convergence theorem]
  • A. Nikodym convergence theorem chosen
    The Nikodym convergence theorem is a fundamental result in measure theory that generalizes the Lebesgue dominated convergence theorem by characterizing when convergence of integrals holds under weaker conditions on the dominating measures.
  • 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. Nikodym set
    A Nikodym set is a pathological subset of the plane in geometric measure theory that intersects almost every line in a very small (often measure-zero) way while still having full measure in a region, illustrating extreme irregular behavior of measurable sets.
  • D. Lebesgue differentiation theorem
    The Lebesgue differentiation theorem is a fundamental result in real analysis stating that, for an integrable function, the averages over shrinking neighborhoods converge almost everywhere to the function’s pointwise value.
  • 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_69d6ada0640c81908c061d7fb3d47786 completed April 8, 2026, 7:33 p.m.
NER Named-entity recognition batch_69d9541ace208190a5149b6f18fa196d completed April 10, 2026, 7:48 p.m.
NED1 Entity disambiguation (via context triple) batch_69f63f0265fc81909a6288d11b78c2f9 completed May 2, 2026, 6:14 p.m.
Created at: April 8, 2026, 9:55 p.m.