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.