Triple

T6801315

Position	Surface form	Disambiguated ID	Type / Status
Subject	Poincaré–Hopf theorem	`E156192`	entity
Predicate	statementForm	`P28574`	FINISHED
Object	sum of indices of isolated zeros of a vector field on a compact manifold equals the Euler characteristic of the manifold	`—`	LITERAL FINISHED

Named-entity recognition

Before disambiguation, gpt-5-mini classified whether the object phrase is a named entity — the step behind the object's LITERAL type shown above.

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: sum of indices of isolated zeros of a vector field on a compact manifold equals the Euler characteristic of the manifold | Statement: [Poincaré–Hopf theorem, statementForm, sum of indices of isolated zeros of a vector field on a compact manifold equals the Euler characteristic of the manifold]

Provenance (2 batches)

Stage	Batch ID	Job type	Status
creating	`batch_69c68826e6a48190a3d220b541e639de`	elicitation	completed
NER	`batch_69c6d7ca96008190ba79563c2a9a9b0e`	ner	completed

Created at: March 27, 2026, 2:16 p.m.