Triple

T10269808
Position Surface form Disambiguated ID Type / Status
Subject Chern classes E240803 entity
Predicate relatedTo P37 FINISHED
Object Stiefel–Whitney classes
Stiefel–Whitney classes are characteristic classes in algebraic topology that assign cohomology invariants to real vector bundles, capturing their topological and orientability properties.
E853116 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: Stiefel–Whitney classes | Statement: [Chern classes, relatedTo, Stiefel–Whitney classes]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Stiefel–Whitney classes
Context triple: [Chern classes, relatedTo, Stiefel–Whitney classes]
  • A. Pontryagin classes
    Pontryagin classes are characteristic classes associated with real vector bundles that capture topological information about the bundle’s curvature and play a central role in differential topology and geometry.
  • 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. 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.
  • D. Hirzebruch signature theorem
    The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
  • E. Hirzebruch genera
    Hirzebruch genera are topological invariants in algebraic topology and differential geometry that generalize characteristic classes to classify and study manifolds.
  • 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: Stiefel–Whitney classes
Triple: [Chern classes, relatedTo, Stiefel–Whitney classes]
Generated description
Stiefel–Whitney classes are characteristic classes in algebraic topology that assign cohomology invariants to real vector bundles, capturing their topological and orientability properties.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Stiefel–Whitney classes
Target entity description: Stiefel–Whitney classes are characteristic classes in algebraic topology that assign cohomology invariants to real vector bundles, capturing their topological and orientability properties.
  • A. Pontryagin classes
    Pontryagin classes are characteristic classes associated with real vector bundles that capture topological information about the bundle’s curvature and play a central role in differential topology and geometry.
  • 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. 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.
  • D. Hirzebruch signature theorem
    The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
  • E. Hirzebruch genera
    Hirzebruch genera are topological invariants in algebraic topology and differential geometry that generalize characteristic classes to classify and study manifolds.
  • 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_69d381a94c1881908fc38fc263d9b9c2 completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d4d270fb088190ba43b6f24e881b94 completed April 7, 2026, 9:46 a.m.
NED1 Entity disambiguation (via context triple) batch_69d6f80c25888190a3e8a2c513df7043 completed April 9, 2026, 12:51 a.m.
NEDg Description generation batch_69d6fcaca55c81908a48ac2a0ce24b85 completed April 9, 2026, 1:11 a.m.
NED2 Entity disambiguation (via description) batch_69d6fd772bc08190bf270f5fc767fb29 completed April 9, 2026, 1:14 a.m.
Created at: April 6, 2026, 11:35 a.m.