Triple

T11219236
Position Surface form Disambiguated ID Type / Status
Subject h-cobordism theorem E265515 entity
Predicate relatedConcept P37 FINISHED
Object Whitehead torsion
Whitehead torsion is an algebraic invariant from simple homotopy theory that measures the failure of a homotopy equivalence between finite CW-complexes to be a simple homotopy equivalence, playing a key role in high-dimensional manifold topology.
E265515 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: Whitehead torsion | Statement: [h-cobordism theorem, relatedConcept, Whitehead torsion]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Whitehead torsion
Context triple: [h-cobordism theorem, relatedConcept, Whitehead torsion]
  • A. Thom cobordism theory
    Thom cobordism theory is a foundational branch of algebraic topology developed by René Thom that classifies manifolds up to cobordism using homotopy-theoretic and characteristic class methods.
  • B. Whitehead product in homotopy theory
    The Whitehead product in homotopy theory is a bilinear operation on homotopy groups that captures how spheres can be nontrivially linked or composed within a topological space.
  • C. 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.
  • D. h-cobordism theorem
    The h-cobordism theorem is a fundamental result in differential topology that classifies when two high-dimensional manifolds are diffeomorphic by analyzing the structure of a cobordism between them.
  • E. 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.
  • 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: Whitehead torsion
Triple: [h-cobordism theorem, relatedConcept, Whitehead torsion]
Generated description
Whitehead torsion is an algebraic invariant from simple homotopy theory that measures the failure of a homotopy equivalence between finite CW-complexes to be a simple homotopy equivalence, playing a key role in high-dimensional manifold topology.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Whitehead torsion
Target entity description: Whitehead torsion is an algebraic invariant from simple homotopy theory that measures the failure of a homotopy equivalence between finite CW-complexes to be a simple homotopy equivalence, playing a key role in high-dimensional manifold topology.
  • A. Thom cobordism theory
    Thom cobordism theory is a foundational branch of algebraic topology developed by René Thom that classifies manifolds up to cobordism using homotopy-theoretic and characteristic class methods.
  • B. Whitehead product in homotopy theory
    The Whitehead product in homotopy theory is a bilinear operation on homotopy groups that captures how spheres can be nontrivially linked or composed within a topological space.
  • C. 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.
  • D. h-cobordism theorem chosen
    The h-cobordism theorem is a fundamental result in differential topology that classifies when two high-dimensional manifolds are diffeomorphic by analyzing the structure of a cobordism between them.
  • E. 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.
  • 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_69d6aac59460819089b9848b27f57848 completed April 8, 2026, 7:21 p.m.
NER Named-entity recognition batch_69d7e8eb84c48190b4f3bede254afde2 completed April 9, 2026, 5:59 p.m.
NED1 Entity disambiguation (via context triple) batch_69e4976f38788190855aed6338d819b7 completed April 19, 2026, 8:50 a.m.
NEDg Description generation batch_69e49d37989881909c7e75ddfff06726 completed April 19, 2026, 9:15 a.m.
NED2 Entity disambiguation (via description) batch_69e49f41a1f8819087cc15527dc7ff63 completed April 19, 2026, 9:24 a.m.
Created at: April 8, 2026, 9:30 p.m.