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.