Triple

T7678476
Position Surface form Disambiguated ID Type / Status
Subject Grigori Perelman E173925 entity
Predicate notableWork P4 FINISHED
Object "The entropy formula for the Ricci flow and its geometric applications" 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: "The entropy formula for the Ricci flow and its geometric applications" | Statement: [Grigori Perelman, notableWork, "The entropy formula for the Ricci flow and its geometric applications"]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: "The entropy formula for the Ricci flow and its geometric applications"
Context triple: [Grigori Perelman, notableWork, "The entropy formula for the Ricci flow and its geometric applications"]
  • 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. 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.
  • C. 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.
  • D. Nirenberg problem in differential geometry
    The Nirenberg problem in differential geometry is a classical question about prescribing Gaussian curvature on the 2-sphere via conformal deformations of the metric.
  • E. 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.
  • 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_69c6995703e0819081de77361b602e78 completed March 27, 2026, 2:51 p.m.
NER Named-entity recognition batch_69c701fd18d88190888144a7d0f228d9 completed March 27, 2026, 10:17 p.m.
NED1 Entity disambiguation (via context triple) batch_69c8a248750481908f0de08aee78c9ba completed March 29, 2026, 3:53 a.m.
Created at: March 27, 2026, 4:01 p.m.