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.