Triple

T10808005
Position Surface form Disambiguated ID Type / Status
Subject Kähler–Ricci flow E255017 entity
Predicate relatedTo P37 FINISHED
Object Yau’s solution of the Calabi conjecture E326554 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: Yau’s solution of the Calabi conjecture | Statement: [Kähler–Ricci flow, relatedTo, Yau’s solution of the Calabi conjecture]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Yau’s solution of the Calabi conjecture
Context triple: [Kähler–Ricci flow, relatedTo, Yau’s solution of the Calabi conjecture]
  • A. Donaldson–Uhlenbeck–Yau theorem
    The Donaldson–Uhlenbeck–Yau theorem is a fundamental result in differential and algebraic geometry that characterizes when a holomorphic vector bundle over a compact Kähler manifold admits a Hermitian–Einstein metric, linking geometric stability with the existence of such metrics.
  • B. 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.
  • C. Monge–Ampère equation chosen
    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.
  • D. Yamabe problem
    The Yamabe problem is a fundamental question in differential geometry concerning whether every compact Riemannian manifold admits a metric of constant scalar curvature within a given conformal class.
  • E. 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.
  • 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.