Triple
T13035719
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Monge problem in optimal transport |
E326555
|
entity |
| Predicate | domain |
P87
|
FINISHED |
| Object | Euclidean spaces |
E22816
|
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: Euclidean spaces | Statement: [Monge problem in optimal transport, domain, Euclidean spaces]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Euclidean spaces Context triple: [Monge problem in optimal transport, domain, Euclidean spaces]
-
A.
Euclidean space
chosen
Euclidean space is the standard flat, n-dimensional geometric setting of classical geometry and vector calculus, characterized by straight lines, right angles, and the usual distance and dot product.
-
B.
Euclidean metric
The Euclidean metric is the standard distance function on Euclidean space, defined by the square root of the sum of squared coordinate differences between two points.
-
C.
Euclidean geometry
Euclidean geometry is the classical mathematical system that studies flat space and shapes using axioms about points, lines, and angles, forming the foundation of much of traditional mathematics and physics.
-
D.
Euclidean group
The Euclidean group is the group of all distance-preserving transformations of Euclidean space, consisting of rotations, reflections, and translations.
-
E.
Banach–Mazur distance
The Banach–Mazur distance is a numerical measure in functional analysis that quantifies how "far apart" two finite-dimensional normed vector spaces are up to linear isomorphism.
- 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_69d8076cc45c81908123123f43e69266 |
completed | April 9, 2026, 8:09 p.m. |
| NER | Named-entity recognition | batch_69d97f2a71a0819098bb6cf8a4b2208a |
completed | April 10, 2026, 10:52 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f6cbcf11f88190ab1746f973132af1 |
completed | May 3, 2026, 4:15 a.m. |
Created at: April 9, 2026, 8:55 p.m.