Triple

T6801251
Position Surface form Disambiguated ID Type / Status
Subject Poincaré–Bendixson theorem E156190 entity
Predicate typicalFormulation P12789 FINISHED
Object for a C1 flow on a two-dimensional manifold, a nonempty compact omega-limit set containing only finitely many equilibria is either an equilibrium, a periodic orbit, or a finite union of equilibria and connecting orbits LITERAL FINISHED

How this triple was built (1 step)

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: for a C1 flow on a two-dimensional manifold, a nonempty compact omega-limit set containing only finitely many equilibria is either an equilibrium, a periodic orbit, or a finite union of equilibria and connecting orbits | Statement: [Poincaré–Bendixson theorem, typicalFormulation, for a C1 flow on a two-dimensional manifold, a nonempty compact omega-limit set containing only finitely many equilibria is either an equilibrium, a periodic orbit, or a finite union of equilibria and connecting orbits]

Provenance (2 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_69c68826e6a48190a3d220b541e639de completed March 27, 2026, 1:37 p.m.
NER Named-entity recognition batch_69c6d2e595188190a0bb4b595df3adb2 completed March 27, 2026, 6:56 p.m.
Created at: March 27, 2026, 2:16 p.m.