Triple
T16232053
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Stanisław Mazur |
E394006
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Mazur’s intersection property
Mazur’s intersection property is a concept in functional analysis concerning conditions under which the intersection of certain families of convex sets in Banach spaces is nonempty, reflecting deep geometric properties of these spaces.
|
E1200645
|
NE FINISHED |
How this triple was built (4 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: Mazur’s intersection property | Statement: [Stanisław Mazur, notableWork, Mazur’s intersection property]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Mazur’s intersection property Context triple: [Stanisław Mazur, notableWork, Mazur’s intersection property]
-
A.
Banach–Mazur theorem
The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
-
B.
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.
-
C.
Banach–Saks theorem
The Banach–Saks theorem is a result in functional analysis stating that every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm.
-
D.
Minkowski’s theorem on convex sets
Minkowski’s theorem on convex sets is a fundamental result in convex geometry that characterizes lattice points in convex bodies, underpinning much of the theory of convex polytopes and the geometry of numbers.
-
E.
Gowers dichotomy for Banach spaces
Gowers dichotomy for Banach spaces is a fundamental result in functional analysis that classifies infinite-dimensional Banach spaces by showing that each contains either a subspace with an unconditional basis or a hereditarily indecomposable subspace.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Mazur’s intersection property Triple: [Stanisław Mazur, notableWork, Mazur’s intersection property]
Generated description
Mazur’s intersection property is a concept in functional analysis concerning conditions under which the intersection of certain families of convex sets in Banach spaces is nonempty, reflecting deep geometric properties of these spaces.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Mazur’s intersection property Target entity description: Mazur’s intersection property is a concept in functional analysis concerning conditions under which the intersection of certain families of convex sets in Banach spaces is nonempty, reflecting deep geometric properties of these spaces.
-
A.
Banach–Mazur theorem
The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
-
B.
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.
-
C.
Banach–Saks theorem
The Banach–Saks theorem is a result in functional analysis stating that every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm.
-
D.
Minkowski’s theorem on convex sets
Minkowski’s theorem on convex sets is a fundamental result in convex geometry that characterizes lattice points in convex bodies, underpinning much of the theory of convex polytopes and the geometry of numbers.
-
E.
Gowers dichotomy for Banach spaces
Gowers dichotomy for Banach spaces is a fundamental result in functional analysis that classifies infinite-dimensional Banach spaces by showing that each contains either a subspace with an unconditional basis or a hereditarily indecomposable subspace.
- F. None of above. chosen
Provenance (5 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_69d87f204df88190a8f88923decf9835 |
completed | April 10, 2026, 4:40 a.m. |
| NER | Named-entity recognition | batch_69e23d29fa248190943f4c3f7808908b |
completed | April 17, 2026, 2:01 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a0007a0ab08819082aea4c312c9ffc7 |
completed | May 10, 2026, 4:20 a.m. |
| NEDg | Description generation | batch_6a00098ea3e48190b0744f1eafab9ce2 |
completed | May 10, 2026, 4:29 a.m. |
| NED2 | Entity disambiguation (via description) | batch_6a0009fb40a48190b82f6de80226d306 |
completed | May 10, 2026, 4:30 a.m. |
Created at: April 10, 2026, 5:04 a.m.