Triple
T10807801
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | geometrization conjecture |
E255013
|
entity |
| Predicate | proofMethod |
P7024
|
FINISHED |
| Object | Ricci flow with surgery |
E48279
|
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: Ricci flow with surgery | Statement: [geometrization conjecture, proofMethod, Ricci flow with surgery]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Ricci flow with surgery Context triple: [geometrization conjecture, proofMethod, Ricci flow with surgery]
-
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 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.
-
C.
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.
-
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
chosen
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_69e21649a6308190878432635d523686 |
completed | April 17, 2026, 11:15 a.m. |
Created at: April 8, 2026, 9:18 p.m.