Triple
T11219253
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | h-cobordism theorem |
E265515
|
entity |
| Predicate | standardReference |
P33736
|
FINISHED |
| Object |
John Milnor's book "Lectures on the h-Cobordism Theorem"
John Milnor's "Lectures on the h-Cobordism Theorem" is a classic monograph in differential topology that gives a clear, rigorous exposition of the h-cobordism theorem and its applications to the classification of high-dimensional manifolds.
|
E911351
|
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: John Milnor's book "Lectures on the h-Cobordism Theorem" | Statement: [h-cobordism theorem, standardReference, John Milnor's book "Lectures on the h-Cobordism Theorem"]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: John Milnor's book "Lectures on the h-Cobordism Theorem" Context triple: [h-cobordism theorem, standardReference, John Milnor's book "Lectures on the h-Cobordism Theorem"]
-
A.
M. Hirsch, Differential Topology
*Differential Topology* by M. Hirsch is a classic graduate-level textbook that systematically develops the foundations of differential topology and is widely regarded as a standard reference in the field.
-
B.
J. Munkres, Elementary Differential Topology
"J. Munkres, Elementary Differential Topology" is a classic introductory textbook that rigorously develops the foundations of differential topology, including topics such as smooth manifolds, transversality, and approximation theorems.
-
C.
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.
-
D.
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.
-
E.
Classifying Spaces and Fibrations
"Classifying Spaces and Fibrations" is a mathematical work that develops the theory of classifying spaces in algebraic topology and their relationship to fiber bundles and fibrations.
- 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: John Milnor's book "Lectures on the h-Cobordism Theorem" Triple: [h-cobordism theorem, standardReference, John Milnor's book "Lectures on the h-Cobordism Theorem"]
Generated description
John Milnor's "Lectures on the h-Cobordism Theorem" is a classic monograph in differential topology that gives a clear, rigorous exposition of the h-cobordism theorem and its applications to the classification of high-dimensional manifolds.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: John Milnor's book "Lectures on the h-Cobordism Theorem" Target entity description: John Milnor's "Lectures on the h-Cobordism Theorem" is a classic monograph in differential topology that gives a clear, rigorous exposition of the h-cobordism theorem and its applications to the classification of high-dimensional manifolds.
-
A.
M. Hirsch, Differential Topology
*Differential Topology* by M. Hirsch is a classic graduate-level textbook that systematically develops the foundations of differential topology and is widely regarded as a standard reference in the field.
-
B.
J. Munkres, Elementary Differential Topology
"J. Munkres, Elementary Differential Topology" is a classic introductory textbook that rigorously develops the foundations of differential topology, including topics such as smooth manifolds, transversality, and approximation theorems.
-
C.
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.
-
D.
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.
-
E.
Classifying Spaces and Fibrations
"Classifying Spaces and Fibrations" is a mathematical work that develops the theory of classifying spaces in algebraic topology and their relationship to fiber bundles and fibrations.
- 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_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.