Triple

T2652909
Position Surface form Disambiguated ID Type / Status
Subject Hassler Whitney E53940 entity
Predicate hasConceptNamedAfter P3325 FINISHED
Object Whitney sum
The Whitney sum is a construction in differential topology that combines two vector bundles over the same base space into a new vector bundle whose fibers are direct sums of the original fibers.
E285917 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 sum | Statement: [Hassler Whitney, hasConceptNamedAfter, Whitney sum]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Whitney sum
Context triple: [Hassler Whitney, hasConceptNamedAfter, Whitney sum]
  • A. 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.
  • B. Chern classes
    Chern classes are fundamental topological invariants in differential and algebraic geometry that classify complex vector bundles and capture their curvature and twisting properties.
  • C. Minkowski sum
    The Minkowski sum is a fundamental operation in geometry and convex analysis that combines two sets by adding every vector in one set to every vector in the other, widely used in areas such as optimization, robotics, and computational geometry.
  • D. 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.
  • E. Characteristic Classes
    Characteristic Classes is a foundational mathematical text in differential topology and geometry that systematically develops the theory of characteristic classes for vector bundles and fiber bundles.
  • 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 sum
Triple: [Hassler Whitney, hasConceptNamedAfter, Whitney sum]
Generated description
The Whitney sum is a construction in differential topology that combines two vector bundles over the same base space into a new vector bundle whose fibers are direct sums of the original fibers.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Whitney sum
Target entity description: The Whitney sum is a construction in differential topology that combines two vector bundles over the same base space into a new vector bundle whose fibers are direct sums of the original fibers.
  • A. 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.
  • B. Chern classes
    Chern classes are fundamental topological invariants in differential and algebraic geometry that classify complex vector bundles and capture their curvature and twisting properties.
  • C. Minkowski sum
    The Minkowski sum is a fundamental operation in geometry and convex analysis that combines two sets by adding every vector in one set to every vector in the other, widely used in areas such as optimization, robotics, and computational geometry.
  • D. 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.
  • E. Characteristic Classes
    Characteristic Classes is a foundational mathematical text in differential topology and geometry that systematically develops the theory of characteristic classes for vector bundles and fiber bundles.
  • 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_69af99416924819099d4acb1a2d60e0c completed March 10, 2026, 4:08 a.m.
NED2 Entity disambiguation (via description) batch_69af99adadb08190a44f2286b25bf0aa completed March 10, 2026, 4:10 a.m.
Created at: March 6, 2026, 9:53 p.m.