Triple
T26971303
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hopf conjecture (on Euler characteristic and curvature) |
E679323
|
entity |
| Predicate | curvatureCondition |
P161401
|
FINISHED |
| Object | everywhere positive 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 positive sectional curvature | Statement: [Hopf conjecture (on Euler characteristic and curvature), curvatureCondition, everywhere positive 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 positive sectional curvature]
-
A.
curveCondition
Indicates that a specific condition or constraint applies to a curve, such as its shape, smoothness, or allowable parameter range.
-
B.
usesCurvature
Indicates that one entity applies or relies on the curvature property or measure of another entity in its operation, definition, or analysis.
-
C.
hasCurvatureBehavior
Indicates how the curvature of an object or path behaves or changes under specified conditions or over a given domain.
-
D.
hasCurvatureDivergence
Indicates that one entity exhibits a difference or variation in curvature relative to another entity or reference.
-
E.
hasCurvatureInvariant
Indicates that one entity possesses a specific curvature-related invariant property or value associated with its geometric or mathematical structure.
- F. None of above. chosen
Provenance (4 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_69f611af72ac819094598dd2530d7411 |
completed | May 2, 2026, 3:01 p.m. |
| PDg | Predicate description generation | batch_69f6125e54e0819088ee33a20efcc9e6 |
completed | May 2, 2026, 3:03 p.m. |
Created at: April 27, 2026, 6:39 a.m.