Triple
T11219355
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Milnor K-theory |
E265518
|
entity |
| Predicate | defines |
P264
|
FINISHED |
| Object | Milnor K-groups |
E265518
|
NE FINISHED |
How this triple was built (2 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: Milnor K-groups | Statement: [Milnor K-theory, defines, Milnor K-groups]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Milnor K-groups Context triple: [Milnor K-theory, defines, Milnor K-groups]
-
A.
Milnor K-theory
chosen
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.
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.
-
C.
proof of the Milnor conjecture
The proof of the Milnor conjecture is Vladimir Voevodsky’s landmark result in algebraic K-theory and Galois cohomology that established a deep connection between Milnor K-theory and étale cohomology, earning him the Fields Medal.
-
D.
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.
-
E.
Witt group of quadratic forms
The Witt group of quadratic forms is an algebraic structure that classifies nondegenerate quadratic forms over a field up to stable equivalence, with addition given by orthogonal sum and inverses given by taking opposite forms.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69e4ad1c57908190a5c65ea4738722e3 |
completed | April 19, 2026, 10:23 a.m. |
Created at: April 8, 2026, 9:30 p.m.