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.