Triple
T2652980
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Whitney stratification |
E53942
|
entity |
| Predicate | condition |
P127
|
FINISHED |
| Object |
Whitney condition A
Whitney condition A is a regularity criterion in singularity theory that restricts how tangent spaces of strata behave near singular points in a Whitney stratification.
|
E53942
|
NE FINISHED |
How this triple was built (4 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 condition A | Statement: [Whitney stratification, condition, Whitney condition A]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Whitney condition A Context triple: [Whitney stratification, condition, Whitney condition A]
-
A.
Whitney stratification
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.
Weierstrass preparation theorem
The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
-
D.
Whitney embedding theorem
The Whitney embedding theorem is a fundamental result in differential topology stating that any smooth n-dimensional manifold can be embedded as a submanifold of Euclidean space of sufficiently high dimension (specifically \(\mathbb{R}^{2n}\)).
-
E.
Weingarten map
The Weingarten map is a differential geometric operator on a surface that encodes how the surface’s normal vector field changes, thereby describing the surface’s extrinsic curvature.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Whitney condition A Triple: [Whitney stratification, condition, Whitney condition A]
Generated description
Whitney condition A is a regularity criterion in singularity theory that restricts how tangent spaces of strata behave near singular points in a Whitney stratification.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Whitney condition A Target entity description: Whitney condition A is a regularity criterion in singularity theory that restricts how tangent spaces of strata behave near singular points in a Whitney stratification.
-
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.
Weierstrass preparation theorem
The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
-
D.
Whitney embedding theorem
The Whitney embedding theorem is a fundamental result in differential topology stating that any smooth n-dimensional manifold can be embedded as a submanifold of Euclidean space of sufficiently high dimension (specifically \(\mathbb{R}^{2n}\)).
-
E.
Weingarten map
The Weingarten map is a differential geometric operator on a surface that encodes how the surface’s normal vector field changes, thereby describing the surface’s extrinsic curvature.
- F. None of above.
Provenance (5 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_69ab495e192081909c77b622e8e7e15a |
completed | March 6, 2026, 9:38 p.m. |
| NER | Named-entity recognition | batch_69abd93197f48190b04faf358b503204 |
completed | March 7, 2026, 7:52 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69af98ce81fc8190b7c6c66acfcb87c7 |
completed | March 10, 2026, 4:06 a.m. |
| NEDg | Description generation | batch_69af9942390081909fd17fa20386fed6 |
completed | March 10, 2026, 4:08 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69af99af3c8c8190b1342dd4bd5866e2 |
completed | March 10, 2026, 4:10 a.m. |
Created at: March 6, 2026, 9:53 p.m.