Triple
T12014689
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Thom–Mather stratification |
E285993
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Whitney conditions A and B |
E53942
|
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: Whitney conditions A and B | Statement: [Thom–Mather stratification, relatedTo, Whitney conditions A and B]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Whitney conditions A and B Context triple: [Thom–Mather stratification, relatedTo, Whitney conditions A and B]
-
A.
Whitney stratification
chosen
Whitney stratification is a method in differential topology for decomposing singular spaces into smoothly compatible manifolds (strata) that fit together under specific regularity conditions, enabling rigorous analysis of singularities.
-
B.
Whitney approximation theorem
The Whitney approximation theorem is a fundamental result in differential topology stating that any continuous function between smooth manifolds can be uniformly approximated by smooth functions.
-
C.
Lefschetz hyperplane theorem
The Lefschetz hyperplane theorem is a fundamental result in algebraic geometry and topology that relates the topology (especially homology and homotopy groups) of a smooth projective variety to that of its hyperplane sections.
-
D.
Castelnuovo–Mumford regularity
Castelnuovo–Mumford regularity is an invariant in commutative algebra and algebraic geometry that measures the complexity of the minimal graded free resolution of a module or sheaf, often used to control vanishing of cohomology and bounds on generators.
-
E.
Singular Points of Complex Hypersurfaces
"Singular Points of Complex Hypersurfaces" is a foundational monograph in singularity theory that systematically studies the local and topological properties of singularities arising in complex algebraic and analytic hypersurfaces.
- 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_69d6ab45a368819084fce08bf0dc3705 |
completed | April 8, 2026, 7:23 p.m. |
| NER | Named-entity recognition | batch_69d903d884488190b4450a98088208ef |
completed | April 10, 2026, 2:06 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f48b4535f48190ac5b2cabb4daf4af |
completed | May 1, 2026, 11:15 a.m. |
Created at: April 8, 2026, 9:47 p.m.