Triple

T36468368
Position Surface form Disambiguated ID Type / Status
Subject Stieltjes measure E898477 entity
Predicate absolutelyContinuousPartHasDensity P185538 FINISHED
Object Radon–Nikodym derivative of F with respect to Lebesgue measure LITERAL 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: Radon–Nikodym derivative of F with respect to Lebesgue measure | Statement: [Stieltjes measure, absolutelyContinuousPartHasDensity, Radon–Nikodym derivative of F with respect to Lebesgue measure]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: absolutelyContinuousPartHasDensity
Context triple: [Stieltjes measure, absolutelyContinuousPartHasDensity, Radon–Nikodym derivative of F with respect to Lebesgue measure]
  • A. isAbsolutelyContinuousWithRespectTo
    Indicates that one measure changes in such a way that it assigns zero measure to every set that another reference measure also considers negligible.
  • B. differentiableAlmostEverywhere
    Indicates that a function is differentiable at all points of its domain except possibly on a set of measure zero (i.e., for almost every point).
  • C. isUncountablePerfectNowhereDenseSubsetOfR
    Indicates that one set is a subset of the real numbers that is uncountable, perfect (closed with no isolated points), and nowhere dense (its closure has empty interior).
  • D. hasLebesgueMeasure
    Indicates that a set is assigned a specific value by the Lebesgue measure, representing its "size" in the sense of measure theory.
  • E. isNowhereDense
    Indicates that a set is so sparse in the space that the closure of the set has empty interior, meaning it contains no nontrivial open subset.
  • F. None of above. chosen

Provenance (4 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_69f76e58ebd88190b75d9b169b59d793 completed May 3, 2026, 3:48 p.m.
NER Named-entity recognition batch_69f7be9d07ac8190adf796cbef60daf6 completed May 3, 2026, 9:31 p.m.
PD Predicate disambiguation batch_69f7bccf05bc8190b61fdb2b2a315811 completed May 3, 2026, 9:23 p.m.
PDg Predicate description generation batch_69f7be9b9ab481908328e0e8d8ac73d4 completed May 3, 2026, 9:31 p.m.
Created at: May 3, 2026, 4:10 p.m.