Triple
T2418337
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | John Milnor |
E52357
|
entity |
| Predicate | hasWritten |
P2831
|
FINISHED |
| Object |
Introduction to Algebraic K-Theory
Introduction to Algebraic K-Theory is a foundational graduate-level textbook by John Milnor that systematically develops the basic concepts and techniques of algebraic K-theory in a concise and influential style.
|
E270737
|
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: Introduction to Algebraic K-Theory | Statement: [John Milnor, hasWritten, Introduction to Algebraic K-Theory]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Introduction to Algebraic K-Theory Context triple: [John Milnor, hasWritten, Introduction to Algebraic K-Theory]
-
A.
Milnor K-theory
Milnor K-theory is an algebraic K-theory constructed from fields using tensor powers of their multiplicative groups modulo Steinberg relations, playing a central role in modern algebraic geometry and number theory.
-
B.
K-theory
K-theory is a branch of algebraic topology and algebraic geometry that studies vector bundles and generalized cohomology theories using algebraic and categorical methods.
-
C.
“K-Theory” (book with Friedrich Hirzebruch and others)
“K-Theory” is a foundational mathematical monograph co-authored by Michael Atiyah, Friedrich Hirzebruch, and others that systematically develops topological K-theory and its applications in geometry and topology.
-
D.
Grothendieck group
The Grothendieck group is an algebraic construction that formally turns a commutative monoid (often arising from isomorphism classes of objects like vector bundles or modules) into an abelian group, playing a central role in K-theory and modern algebraic geometry.
-
E.
Categories for the Working Mathematician
Categories for the Working Mathematician is a foundational textbook in category theory that systematically develops the subject and its applications for professional mathematicians.
- 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: Introduction to Algebraic K-Theory Triple: [John Milnor, hasWritten, Introduction to Algebraic K-Theory]
Generated description
Introduction to Algebraic K-Theory is a foundational graduate-level textbook by John Milnor that systematically develops the basic concepts and techniques of algebraic K-theory in a concise and influential style.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Introduction to Algebraic K-Theory Target entity description: Introduction to Algebraic K-Theory is a foundational graduate-level textbook by John Milnor that systematically develops the basic concepts and techniques of algebraic K-theory in a concise and influential style.
-
A.
Milnor K-theory
Milnor K-theory is an algebraic K-theory constructed from fields using tensor powers of their multiplicative groups modulo Steinberg relations, playing a central role in modern algebraic geometry and number theory.
-
B.
K-theory
K-theory is a branch of algebraic topology and algebraic geometry that studies vector bundles and generalized cohomology theories using algebraic and categorical methods.
-
C.
“K-Theory” (book with Friedrich Hirzebruch and others)
“K-Theory” is a foundational mathematical monograph co-authored by Michael Atiyah, Friedrich Hirzebruch, and others that systematically develops topological K-theory and its applications in geometry and topology.
-
D.
Grothendieck group
The Grothendieck group is an algebraic construction that formally turns a commutative monoid (often arising from isomorphism classes of objects like vector bundles or modules) into an abelian group, playing a central role in K-theory and modern algebraic geometry.
-
E.
Categories for the Working Mathematician
Categories for the Working Mathematician is a foundational textbook in category theory that systematically develops the subject and its applications for professional mathematicians.
- 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_69ab495622948190bc6bc6e4cddaf645 |
completed | March 6, 2026, 9:38 p.m. |
| NER | Named-entity recognition | batch_69abc950516c8190989591673de6b1f7 |
completed | March 7, 2026, 6:44 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69af177ff6508190b549227f4cfd9876 |
completed | March 9, 2026, 6:54 p.m. |
| NEDg | Description generation | batch_69af1aad7cf48190923ca22477614758 |
completed | March 9, 2026, 7:08 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69af1afeb07c8190a03b419d01a6ba8c |
completed | March 9, 2026, 7:09 p.m. |
Created at: March 6, 2026, 9:42 p.m.