Triple

T16574842
Position Surface form Disambiguated ID Type / Status
Subject Mikhail Gromov E402682 entity
Predicate notableFor P22 FINISHED
Object Gromov–Hausdorff convergence
Gromov–Hausdorff convergence is a notion in metric geometry that formalizes when a sequence of metric spaces becomes increasingly similar in shape and structure, up to isometry.
E608816 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–Hausdorff convergence | Statement: [Mikhail Gromov, notableFor, Gromov–Hausdorff convergence]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gromov–Hausdorff convergence
Context triple: [Mikhail Gromov, notableFor, Gromov–Hausdorff convergence]
  • 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. Perelman’s entropy functionals
    Perelman’s entropy functionals are analytic quantities introduced by Grigori Perelman to study the behavior and singularities of the Ricci flow, playing a central role in his proof of the Poincaré and geometrization conjectures.
  • C. 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.
  • D. 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.
  • E. Hausdorff metric
    The Hausdorff metric is a distance function that measures how far two subsets of a metric space are from each other, widely used in topology, geometry, and shape analysis.
  • 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–Hausdorff convergence
Triple: [Mikhail Gromov, notableFor, Gromov–Hausdorff convergence]
Generated description
Gromov–Hausdorff convergence is a notion in metric geometry that formalizes when a sequence of metric spaces becomes increasingly similar in shape and structure, up to isometry.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gromov–Hausdorff convergence
Target entity description: Gromov–Hausdorff convergence is a notion in metric geometry that formalizes when a sequence of metric spaces becomes increasingly similar in shape and structure, up to isometry.
  • 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. Perelman’s entropy functionals
    Perelman’s entropy functionals are analytic quantities introduced by Grigori Perelman to study the behavior and singularities of the Ricci flow, playing a central role in his proof of the Poincaré and geometrization conjectures.
  • C. 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.
  • D. 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.
  • E. Hausdorff metric chosen
    The Hausdorff metric is a distance function that measures how far two subsets of a metric space are from each other, widely used in topology, geometry, and shape analysis.
  • F. None of above.

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.