Triple
T16574850
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Mikhail Gromov |
E402682
|
entity |
| Predicate | notableFor |
P22
|
FINISHED |
| Object |
h-principle in geometry
The h-principle in geometry is a foundational concept introduced by Mikhail Gromov that relates solutions of differential relations to their homotopy-theoretic counterparts, often allowing geometric problems to be reduced to purely topological ones.
|
E1221218
|
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: h-principle in geometry | Statement: [Mikhail Gromov, notableFor, h-principle in geometry]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: h-principle in geometry Context triple: [Mikhail Gromov, notableFor, h-principle in geometry]
-
A.
Smale–Hirsch immersion theorem
The Smale–Hirsch immersion theorem is a fundamental result in differential topology that classifies immersions of manifolds up to regular homotopy in terms of bundle monomorphisms between their tangent bundles.
-
B.
Thom transversality theorem
The Thom transversality theorem is a fundamental result in differential topology that guarantees generic smooth maps are transverse to given submanifolds, underpinning the study of stable phenomena and cobordism.
-
C.
The geometry of four-manifolds
The Geometry of Four-Manifolds is a foundational monograph in differential geometry that develops the theory of smooth four-dimensional manifolds using gauge theory and Yang–Mills instantons.
-
D.
Introduction to Symplectic Topology
Introduction to Symplectic Topology is a foundational graduate-level textbook that systematically develops the theory and applications of symplectic manifolds and symplectic geometry.
-
E.
Nash embedding theorem
The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
- 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: h-principle in geometry Triple: [Mikhail Gromov, notableFor, h-principle in geometry]
Generated description
The h-principle in geometry is a foundational concept introduced by Mikhail Gromov that relates solutions of differential relations to their homotopy-theoretic counterparts, often allowing geometric problems to be reduced to purely topological ones.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: h-principle in geometry Target entity description: The h-principle in geometry is a foundational concept introduced by Mikhail Gromov that relates solutions of differential relations to their homotopy-theoretic counterparts, often allowing geometric problems to be reduced to purely topological ones.
-
A.
Smale–Hirsch immersion theorem
The Smale–Hirsch immersion theorem is a fundamental result in differential topology that classifies immersions of manifolds up to regular homotopy in terms of bundle monomorphisms between their tangent bundles.
-
B.
Thom transversality theorem
The Thom transversality theorem is a fundamental result in differential topology that guarantees generic smooth maps are transverse to given submanifolds, underpinning the study of stable phenomena and cobordism.
-
C.
The geometry of four-manifolds
The Geometry of Four-Manifolds is a foundational monograph in differential geometry that develops the theory of smooth four-dimensional manifolds using gauge theory and Yang–Mills instantons.
-
D.
Introduction to Symplectic Topology
Introduction to Symplectic Topology is a foundational graduate-level textbook that systematically develops the theory and applications of symplectic manifolds and symplectic geometry.
-
E.
Nash embedding theorem
The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
- 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.