Triple

T10807891
Position Surface form Disambiguated ID Type / Status
Subject Hamilton’s compactness theorem E255015 entity
Predicate relatedTo P37 FINISHED
Object Gromov’s precompactness theorem E888038 NE FINISHED

How this triple was built (2 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’s precompactness theorem | Statement: [Hamilton’s compactness theorem, relatedTo, Gromov’s precompactness theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Gromov’s precompactness theorem
Context triple: [Hamilton’s compactness theorem, relatedTo, Gromov’s precompactness theorem]
  • A. Cheeger–Gromov compactness theorem chosen
    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. Rellich–Kondrachov compactness theorem
    The Rellich–Kondrachov compactness theorem is a fundamental result in functional analysis and the theory of Sobolev spaces that guarantees the compactness of certain embedding operators, playing a key role in the study of partial differential equations.
  • D. 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.
  • E. Hamilton’s compactness theorem
    Hamilton’s compactness theorem is a fundamental result in geometric analysis that provides conditions under which a sequence of Riemannian manifolds with controlled curvature and injectivity radius admits a smoothly convergent subsequence.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d6aa61c15c8190a1839550c56e75e1 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d733b506488190921e6a1f4168dd9e completed April 9, 2026, 5:05 a.m.
NED1 Entity disambiguation (via context triple) batch_69deb0d849888190be46616ecc97c2b1 completed April 14, 2026, 9:25 p.m.
Created at: April 8, 2026, 9:18 p.m.