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.