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.