Triple
T15977108
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Cauchy functional equation |
E387476
|
entity |
| Predicate | impliesUnderMeasurability |
P121125
|
FINISHED |
| Object | f(x) = ax for some constant a |
—
|
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: f(x) = ax for some constant a | Statement: [Cauchy functional equation, impliesUnderMeasurability, f(x) = ax for some constant a]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: impliesUnderMeasurability Context triple: [Cauchy functional equation, impliesUnderMeasurability, f(x) = ax for some constant a]
-
A.
measurability
Indicates that a quantity, property, or outcome can be defined, quantified, or assessed using a consistent measurement framework.
-
B.
hasNonMeasurableSets
Indicates that within a given set or space, there exist subsets that are not measurable under the specified measure or sigma-algebra.
-
C.
hasLebesgueMeasure
Indicates that a set is assigned a specific value by the Lebesgue measure, representing its "size" in the sense of measure theory.
-
D.
isCountablyAdditive
Indicates that a measure or function preserves additivity over countable collections, meaning the value on a countable union of disjoint sets equals the sum of its values on each set.
-
E.
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.
- 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_69d86da94ccc819083d187f5dc6a123e |
completed | April 10, 2026, 3:25 a.m. |
| NER | Named-entity recognition | batch_69e17d4d08f481909f38b75e3f42d9ab |
completed | April 17, 2026, 12:22 a.m. |
| PD | Predicate disambiguation | batch_69e142d9d8e881909b559a3e3ca21d24 |
completed | April 16, 2026, 8:13 p.m. |
| PDg | Predicate description generation | batch_69e17d48cc9c8190b03fd07ae2e9dfd8 |
completed | April 17, 2026, 12:22 a.m. |
Created at: April 10, 2026, 4:54 a.m.