Triple
T10829240
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | J. H. C. Whitehead |
E255572
|
entity |
| Predicate | notableConcept |
P201
|
FINISHED |
| Object |
Whitehead product
The Whitehead product is a fundamental operation in algebraic topology that combines homotopy classes of maps to produce higher-order homotopy information, playing a key role in the structure of homotopy groups of spheres and related spaces.
|
E886921
|
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 product | Statement: [J. H. C. Whitehead, notableConcept, Whitehead product]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Whitehead product Context triple: [J. H. C. Whitehead, notableConcept, Whitehead product]
-
A.
Künneth formula
The Künneth formula is a fundamental result in algebraic topology and homological algebra that expresses the (co)homology of a product space or object in terms of the (co)homology of its factors.
-
B.
Eilenberg–Zilber theorem
The Eilenberg–Zilber theorem is a fundamental result in algebraic topology that establishes a chain homotopy equivalence between the singular chain complex of a product space and the tensor product of the singular chain complexes of the factors.
-
C.
Hopf invariant
The Hopf invariant is a topological integer-valued invariant that classifies certain continuous maps between spheres, playing a central role in homotopy theory and the study of higher-dimensional linking.
-
D.
Alexander–Spanier cohomology
Alexander–Spanier cohomology is a cohomology theory in algebraic topology defined using cochains on all finite subsets of a space, notable for its generality and close relationship to Čech and singular cohomology.
-
E.
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.
- 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 product Triple: [J. H. C. Whitehead, notableConcept, Whitehead product]
Generated description
The Whitehead product is a fundamental operation in algebraic topology that combines homotopy classes of maps to produce higher-order homotopy information, playing a key role in the structure of homotopy groups of spheres and related spaces.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Whitehead product Target entity description: The Whitehead product is a fundamental operation in algebraic topology that combines homotopy classes of maps to produce higher-order homotopy information, playing a key role in the structure of homotopy groups of spheres and related spaces.
-
A.
Künneth formula
The Künneth formula is a fundamental result in algebraic topology and homological algebra that expresses the (co)homology of a product space or object in terms of the (co)homology of its factors.
-
B.
Eilenberg–Zilber theorem
The Eilenberg–Zilber theorem is a fundamental result in algebraic topology that establishes a chain homotopy equivalence between the singular chain complex of a product space and the tensor product of the singular chain complexes of the factors.
-
C.
Hopf invariant
The Hopf invariant is a topological integer-valued invariant that classifies certain continuous maps between spheres, playing a central role in homotopy theory and the study of higher-dimensional linking.
-
D.
Alexander–Spanier cohomology
Alexander–Spanier cohomology is a cohomology theory in algebraic topology defined using cochains on all finite subsets of a space, notable for its generality and close relationship to Čech and singular cohomology.
-
E.
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.
- 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_69d6aa8081448190a9324184f2bd1c26 |
completed | April 8, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69d734d3eab88190b30a3025b6b2b0bc |
completed | April 9, 2026, 5:10 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69de85a068b08190948c3ca32cdda147 |
completed | April 14, 2026, 6:21 p.m. |
| NEDg | Description generation | batch_69de8956d9f081909d076c5e413c1f74 |
completed | April 14, 2026, 6:37 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69de8e80fe80819088ac76bb5abc58f0 |
completed | April 14, 2026, 6:59 p.m. |
Created at: April 8, 2026, 9:19 p.m.