Triple

T10807775
Position Surface form Disambiguated ID Type / Status
Subject Richard S. Hamilton E255012 entity
Predicate notableWork P4 FINISHED
Object The formation of singularities in the Ricci flow E889125 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: The formation of singularities in the Ricci flow | Statement: [Richard S. Hamilton, notableWork, The formation of singularities in the Ricci flow]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: The formation of singularities in the Ricci flow
Context triple: [Richard S. Hamilton, notableWork, The formation of singularities in the Ricci flow]
  • A. "Finite extinction time for the solutions to the Ricci flow on certain three-manifolds"
    "Finite extinction time for the solutions to the Ricci flow on certain three-manifolds" is a landmark mathematical paper by Grigori Perelman that advances the analysis of Ricci flow in three dimensions and plays a key role in his proof of the Poincaré conjecture.
  • B. Hamilton’s Harnack inequalities for Ricci flow
    Hamilton’s Harnack inequalities for Ricci flow are fundamental differential inequalities that provide monotonicity and curvature control along solutions to the Ricci flow, playing a key role in the analysis of geometric evolution and singularity formation.
  • C. Hamilton’s compactness theorem for Ricci flow chosen
    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. Three-manifolds with positive Ricci curvature
    "Three-manifolds with positive Ricci curvature" is a landmark 1982 paper by Richard S. Hamilton that introduced the Ricci flow and launched the modern geometric analysis approach to understanding the topology of three-dimensional manifolds.
  • E. Ricci flow
    Ricci flow is a geometric evolution equation that smoothly deforms the metric of a Riemannian manifold in a way analogous to heat diffusion, playing a central role in Grigori Perelman's proof of the Poincaré conjecture.
  • 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_69e15499158481908391f411420b19fc completed April 16, 2026, 9:28 p.m.
Created at: April 8, 2026, 9:18 p.m.