Triple

T26971304
Position Surface form Disambiguated ID Type / Status
Subject Hopf conjecture (on Euler characteristic and curvature) E679323 entity
Predicate curvatureCondition P161401 FINISHED
Object everywhere negative sectional curvature LITERAL 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: everywhere negative sectional curvature | Statement: [Hopf conjecture (on Euler characteristic and curvature), curvatureCondition, everywhere negative sectional curvature]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: curvatureCondition
Context triple: [Hopf conjecture (on Euler characteristic and curvature), curvatureCondition, everywhere negative sectional curvature]
  • A. curvatureCondition chosen
    Indicates that a specified geometric object or path satisfies a particular constraint or requirement on its curvature.
  • B. curveCondition
    Indicates that a specific condition or constraint applies to a curve, such as its shape, smoothness, or allowable parameter range.
  • C. usesCurvature
    Indicates that one entity applies or relies on the curvature property or measure of another entity in its operation, definition, or analysis.
  • D. hasCurvatureBehavior
    Indicates how the curvature of an object or path behaves or changes under specified conditions or over a given domain.
  • E. hasCurvatureDivergence
    Indicates that one entity exhibits a difference or variation in curvature relative to another entity or reference.
  • F. None of above.

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_69eeeb507a7081909d516e1fa08b7d29 completed April 27, 2026, 4:51 a.m.
NER Named-entity recognition batch_69f62124ff1081908d66c2ff35ba5e89 completed May 2, 2026, 4:07 p.m.
PD Predicate disambiguation batch_69f61b3ee7b08190a0a1bc5d26b757aa completed May 2, 2026, 3:41 p.m.
Created at: April 27, 2026, 6:39 a.m.