Triple
T16232044
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Stanisław Mazur |
E394006
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Mazur–Ulam theorem
The Mazur–Ulam theorem is a fundamental result in functional analysis stating that every surjective isometry between real normed vector spaces is necessarily affine.
|
E1200642
|
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–Ulam theorem | Statement: [Stanisław Mazur, notableWork, Mazur–Ulam theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Mazur–Ulam theorem Context triple: [Stanisław Mazur, notableWork, Mazur–Ulam theorem]
-
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–Stone theorem
The Banach–Stone theorem is a fundamental result in functional analysis that characterizes compact Hausdorff spaces via isometric isomorphisms between their spaces of continuous real- or complex-valued functions.
-
C.
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.
-
D.
Banach–Steinhaus theorem
The Banach–Steinhaus theorem is a fundamental result in functional analysis that characterizes when a family of continuous linear operators is uniformly bounded, with major implications for the behavior of sequences of operators on Banach spaces.
-
E.
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.
- 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–Ulam theorem Triple: [Stanisław Mazur, notableWork, Mazur–Ulam theorem]
Generated description
The Mazur–Ulam theorem is a fundamental result in functional analysis stating that every surjective isometry between real normed vector spaces is necessarily affine.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Mazur–Ulam theorem Target entity description: The Mazur–Ulam theorem is a fundamental result in functional analysis stating that every surjective isometry between real normed vector spaces is necessarily affine.
-
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–Stone theorem
The Banach–Stone theorem is a fundamental result in functional analysis that characterizes compact Hausdorff spaces via isometric isomorphisms between their spaces of continuous real- or complex-valued functions.
-
C.
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.
-
D.
Banach–Steinhaus theorem
The Banach–Steinhaus theorem is a fundamental result in functional analysis that characterizes when a family of continuous linear operators is uniformly bounded, with major implications for the behavior of sequences of operators on Banach spaces.
-
E.
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.
- 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.