Triple

T10807932
Position Surface form Disambiguated ID Type / Status
Subject Perelman’s entropy functionals E255016 entity
Predicate hasComponent P35 FINISHED
Object Perelman’s \\mathcal{F}-functional E255016 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: Perelman’s \\mathcal{F}-functional | Statement: [Perelman’s entropy functionals, hasComponent, Perelman’s \\mathcal{F}-functional]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Perelman’s \\mathcal{F}-functional
Context triple: [Perelman’s entropy functionals, hasComponent, Perelman’s \\mathcal{F}-functional]
  • A. Perelman’s entropy functionals chosen
    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.
  • B. Kähler–Ricci flow
    Kähler–Ricci flow is a geometric evolution equation that deforms Kähler metrics on complex manifolds according to their Ricci curvature, playing a central role in complex differential geometry and the study of canonical metrics.
  • 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. Monge–Ampère equation
    The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
  • 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_69de8513fe0881909d6833c85aac03a8 completed April 14, 2026, 6:19 p.m.
Created at: April 8, 2026, 9:18 p.m.