Triple

T10807822
Position Surface form Disambiguated ID Type / Status
Subject geometrization conjecture E255013 entity
Predicate recognizedBy P653 FINISHED
Object Clay Millennium Prize Problem on the Poincaré conjecture E156188 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: Clay Millennium Prize Problem on the Poincaré conjecture | Statement: [geometrization conjecture, recognizedBy, Clay Millennium Prize Problem on the Poincaré conjecture]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Clay Millennium Prize Problem on the Poincaré conjecture
Context triple: [geometrization conjecture, recognizedBy, Clay Millennium Prize Problem on the Poincaré conjecture]
  • A. Poincaré conjecture chosen
    The Poincaré conjecture is a landmark problem in topology that characterizes the three-dimensional sphere among three-dimensional manifolds and was famously solved by Grigori Perelman in the early 2000s.
  • B. Smale’s 18 problems
    Smale’s 18 problems are a celebrated list of major open questions in mathematics proposed by Stephen Smale in 1998 as a successor in spirit to Hilbert’s famous problems.
  • C. "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.
  • D. Smale’s paradox
    Smale’s paradox is a result in differential topology showing that a sphere can be turned inside out in three-dimensional space through smooth deformations without tearing or creasing, challenging intuitive notions of geometry.
  • E. 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.
  • 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.