Triple

T16574844
Position Surface form Disambiguated ID Type / Status
Subject Mikhail Gromov E402682 entity
Predicate notableFor P22 FINISHED
Object Gromov compactness theorem
The Gromov compactness theorem is a fundamental result in symplectic geometry and geometric analysis that provides compactness for families of pseudoholomorphic curves (or Riemannian manifolds with bounded geometry) up to bubbling and degeneration.
E1221214 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: Gromov compactness theorem | Statement: [Mikhail Gromov, notableFor, Gromov compactness theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gromov compactness theorem
Context triple: [Mikhail Gromov, notableFor, Gromov compactness theorem]
  • A. Cheeger–Gromov compactness theorem
    The Cheeger–Gromov compactness theorem is a fundamental result in Riemannian geometry that gives conditions under which a sequence of Riemannian manifolds has a subsequence converging (in the Gromov–Hausdorff or smooth sense) to a limit space.
  • B. Mostow rigidity theorem
    The Mostow rigidity theorem is a fundamental result in geometry and topology stating that, in dimensions greater than two, the large-scale geometry of a complete finite-volume hyperbolic manifold is uniquely determined by its fundamental group, implying strong rigidity for such structures.
  • C. McDuff–Salamon theory of J-holomorphic curves
    The McDuff–Salamon theory of J-holomorphic curves is a foundational framework in symplectic geometry that systematically develops the analysis, topology, and applications of pseudoholomorphic curves in symplectic manifolds.
  • D. Hamilton’s compactness theorem for Ricci flow
    Hamilton’s compactness theorem for Ricci flow is a fundamental result in geometric analysis that provides conditions under which a sequence of Ricci flows on Riemannian manifolds subconverges to a limiting Ricci flow, enabling powerful compactness and convergence arguments in the study of geometric evolution.
  • E. Ahlfors finiteness theorem
    The Ahlfors finiteness theorem is a fundamental result in the theory of Kleinian groups stating that, under suitable discreteness and analyticity conditions, the quotient of the domain of discontinuity has finite topological type.
  • 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: Gromov compactness theorem
Triple: [Mikhail Gromov, notableFor, Gromov compactness theorem]
Generated description
The Gromov compactness theorem is a fundamental result in symplectic geometry and geometric analysis that provides compactness for families of pseudoholomorphic curves (or Riemannian manifolds with bounded geometry) up to bubbling and degeneration.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gromov compactness theorem
Target entity description: The Gromov compactness theorem is a fundamental result in symplectic geometry and geometric analysis that provides compactness for families of pseudoholomorphic curves (or Riemannian manifolds with bounded geometry) up to bubbling and degeneration.
  • A. Cheeger–Gromov compactness theorem
    The Cheeger–Gromov compactness theorem is a fundamental result in Riemannian geometry that gives conditions under which a sequence of Riemannian manifolds has a subsequence converging (in the Gromov–Hausdorff or smooth sense) to a limit space.
  • B. Mostow rigidity theorem
    The Mostow rigidity theorem is a fundamental result in geometry and topology stating that, in dimensions greater than two, the large-scale geometry of a complete finite-volume hyperbolic manifold is uniquely determined by its fundamental group, implying strong rigidity for such structures.
  • C. McDuff–Salamon theory of J-holomorphic curves
    The McDuff–Salamon theory of J-holomorphic curves is a foundational framework in symplectic geometry that systematically develops the analysis, topology, and applications of pseudoholomorphic curves in symplectic manifolds.
  • D. Hamilton’s compactness theorem for Ricci flow
    Hamilton’s compactness theorem for Ricci flow is a fundamental result in geometric analysis that provides conditions under which a sequence of Ricci flows on Riemannian manifolds subconverges to a limiting Ricci flow, enabling powerful compactness and convergence arguments in the study of geometric evolution.
  • E. Ahlfors finiteness theorem
    The Ahlfors finiteness theorem is a fundamental result in the theory of Kleinian groups stating that, under suitable discreteness and analyticity conditions, the quotient of the domain of discontinuity has finite topological type.
  • 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.