Triple
T2652997
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Whitney stratification |
E53942
|
entity |
| Predicate | relatedConcept |
P37
|
FINISHED |
| Object |
Thom–Mather stratification
Thom–Mather stratification is a refined notion of stratification in differential topology that imposes strong regularity and control conditions on how smooth strata fit together, generalizing and strengthening Whitney stratifications.
|
E285993
|
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: Thom–Mather stratification | Statement: [Whitney stratification, relatedConcept, Thom–Mather stratification]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Thom–Mather stratification Context triple: [Whitney stratification, relatedConcept, Thom–Mather stratification]
-
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.
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.
-
C.
Milnor fibration
Milnor fibration is a fundamental construction in singularity theory and differential topology that describes how the complement of a complex hypersurface singularity fibers over the circle, revealing the local topological structure of the singularity.
-
D.
Atiyah–Bott fixed-point theorem
The Atiyah–Bott fixed-point theorem is a fundamental result in equivariant cohomology that expresses global invariants, such as indices of elliptic operators, in terms of local data at the fixed points of a group action.
-
E.
Topology from the Differentiable Viewpoint
"Topology from the Differentiable Viewpoint" is a classic introductory monograph on differential topology that presents key concepts such as smooth manifolds, vector bundles, and characteristic classes in a concise and accessible style.
- 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: Thom–Mather stratification Triple: [Whitney stratification, relatedConcept, Thom–Mather stratification]
Generated description
Thom–Mather stratification is a refined notion of stratification in differential topology that imposes strong regularity and control conditions on how smooth strata fit together, generalizing and strengthening Whitney stratifications.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Thom–Mather stratification Target entity description: Thom–Mather stratification is a refined notion of stratification in differential topology that imposes strong regularity and control conditions on how smooth strata fit together, generalizing and strengthening Whitney stratifications.
-
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.
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.
-
C.
Milnor fibration
Milnor fibration is a fundamental construction in singularity theory and differential topology that describes how the complement of a complex hypersurface singularity fibers over the circle, revealing the local topological structure of the singularity.
-
D.
Atiyah–Bott fixed-point theorem
The Atiyah–Bott fixed-point theorem is a fundamental result in equivariant cohomology that expresses global invariants, such as indices of elliptic operators, in terms of local data at the fixed points of a group action.
-
E.
Topology from the Differentiable Viewpoint
"Topology from the Differentiable Viewpoint" is a classic introductory monograph on differential topology that presents key concepts such as smooth manifolds, vector bundles, and characteristic classes in a concise and accessible style.
- F. None of above. chosen
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.