Triple

T19782753
Position Surface form Disambiguated ID Type / Status
Subject Hahn decomposition theorem E475178 entity
Predicate relatedTo P37 FINISHED
Object Lebesgue decomposition theorem — NE NERFINISHED

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 decomposition theorem | Statement: [Hahn decomposition theorem, relatedTo, Lebesgue decomposition theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Lebesgue decomposition theorem
Context triple: [Hahn decomposition theorem, relatedTo, Lebesgue decomposition theorem]
  • A. Lebesgue decomposition theorem chosen
    The Lebesgue decomposition theorem is a fundamental result in measure theory that states any σ-finite measure can be uniquely decomposed into a part that is absolutely continuous with respect to another measure and a part that is singular to it.
  • B. Hahn decomposition theorem
    The Hahn decomposition theorem is a fundamental result in measure theory that states any signed measure space can be partitioned into a positive set and a negative set on which the measure is respectively nonnegative and nonpositive.
  • C. Lebesgue measure
    Lebesgue measure is the standard way of assigning a consistent notion of "length," "area," or "volume" to subsets of Euclidean space, forming the foundation of modern measure theory and integration.
  • 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. Lévy–Itô decomposition
    The Lévy–Itô decomposition is a fundamental result in probability theory that expresses any Lévy process as the sum of a Brownian motion with drift and a jump process constructed from a Poisson random measure.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69d8e51b014081908b263e167370529a completed April 10, 2026, 11:55 a.m.
NER Named-entity recognition batch_69e653852e848190b8971981a164e8f9 completed April 20, 2026, 4:25 p.m.
Created at: April 10, 2026, 1:49 p.m.