Triple
T16574869
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Mikhail Gromov |
E402682
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Metric Structures for Riemannian and Non-Riemannian Spaces
"Metric Structures for Riemannian and Non-Riemannian Spaces" is a foundational monograph by Mikhail Gromov that systematically develops the theory of metric spaces and its applications to Riemannian geometry, geometric group theory, and global analysis.
|
E1221219
|
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: Metric Structures for Riemannian and Non-Riemannian Spaces | Statement: [Mikhail Gromov, notableWork, Metric Structures for Riemannian and Non-Riemannian Spaces]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Metric Structures for Riemannian and Non-Riemannian Spaces Context triple: [Mikhail Gromov, notableWork, Metric Structures for Riemannian and Non-Riemannian Spaces]
-
A.
Bochner technique in Riemannian geometry
The Bochner technique in Riemannian geometry is a method that uses Bochner-type identities and curvature conditions to derive vanishing theorems and rigidity results for differential forms and harmonic maps on manifolds.
-
B.
The Geometry of Geodesics
The Geometry of Geodesics is a foundational mathematical monograph that systematically develops the theory of geodesics and metric geometry, particularly in non-Riemannian settings.
-
C.
Lezioni di geometria differenziale
Lezioni di geometria differenziale is a foundational textbook on differential geometry by Italian mathematician Luigi Bianchi, influential in the development of modern geometric theory.
-
D.
Riemannian manifolds
Riemannian manifolds are smooth manifolds equipped with an inner product on each tangent space that allows one to measure lengths, angles, and curvature in a curved geometric setting.
-
E.
Vorlesungen über Differentialgeometrie
Vorlesungen über Differentialgeometrie is a classic multi-volume textbook on differential geometry by Wilhelm Blaschke that significantly shaped the development and teaching of the subject in the 20th century.
- 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: Metric Structures for Riemannian and Non-Riemannian Spaces Triple: [Mikhail Gromov, notableWork, Metric Structures for Riemannian and Non-Riemannian Spaces]
Generated description
"Metric Structures for Riemannian and Non-Riemannian Spaces" is a foundational monograph by Mikhail Gromov that systematically develops the theory of metric spaces and its applications to Riemannian geometry, geometric group theory, and global analysis.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Metric Structures for Riemannian and Non-Riemannian Spaces Target entity description: "Metric Structures for Riemannian and Non-Riemannian Spaces" is a foundational monograph by Mikhail Gromov that systematically develops the theory of metric spaces and its applications to Riemannian geometry, geometric group theory, and global analysis.
-
A.
Bochner technique in Riemannian geometry
The Bochner technique in Riemannian geometry is a method that uses Bochner-type identities and curvature conditions to derive vanishing theorems and rigidity results for differential forms and harmonic maps on manifolds.
-
B.
The Geometry of Geodesics
The Geometry of Geodesics is a foundational mathematical monograph that systematically develops the theory of geodesics and metric geometry, particularly in non-Riemannian settings.
-
C.
Lezioni di geometria differenziale
Lezioni di geometria differenziale is a foundational textbook on differential geometry by Italian mathematician Luigi Bianchi, influential in the development of modern geometric theory.
-
D.
Riemannian manifolds
Riemannian manifolds are smooth manifolds equipped with an inner product on each tangent space that allows one to measure lengths, angles, and curvature in a curved geometric setting.
-
E.
Vorlesungen über Differentialgeometrie
Vorlesungen über Differentialgeometrie is a classic multi-volume textbook on differential geometry by Wilhelm Blaschke that significantly shaped the development and teaching of the subject in the 20th century.
- 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_69d88387363c8190a97a0c942130de97 |
completed | April 10, 2026, 4:58 a.m. |
| NER | Named-entity recognition | batch_69e3595bbbbc8190b023f4872908c031 |
completed | April 18, 2026, 10:13 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a006eea409c8190808170a0b3f4bd17 |
completed | May 10, 2026, 11:41 a.m. |
| NEDg | Description generation | batch_6a006f7ca0dc8190a75d84d9ffbf83e0 |
completed | May 10, 2026, 11:43 a.m. |
| NED2 | Entity disambiguation (via description) | batch_6a00705453c081909e8401024e92b5aa |
completed | May 10, 2026, 11:47 a.m. |
Created at: April 10, 2026, 5:16 a.m.