Triple

T12027018
Position Surface form Disambiguated ID Type / Status
Subject Noncommutative Geometry (1994 book) E286303 entity
Predicate subject P450 FINISHED
Object K-theory E255574 NE FINISHED

Named-entity recognition

Before disambiguation, gpt-5-mini classified whether the object phrase is a named entity — the step behind the object's NE type shown above.

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: K-theory | Statement: [Noncommutative Geometry (1994 book), subject, K-theory]

Disambiguation candidates (1 decision)

The exact options the model was shown at each disambiguation step, with the option it chose highlighted — the evidence behind this triple's disambiguated ids.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: K-theory
Context triple: [Noncommutative Geometry (1994 book), subject, K-theory]
  • A. K-theory chosen
    K-theory is a branch of algebraic topology and algebraic geometry that studies vector bundles and generalized cohomology theories using algebraic and categorical methods.
  • B. Quillen K-theory
    Quillen K-theory is a sophisticated algebraic K-theory framework defined via higher K-groups of exact or Waldhausen categories, providing deep invariants of rings, schemes, and topological spaces that generalize and extend earlier constructions such as Milnor K-theory.
  • C. 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.
  • D. 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.
  • E. “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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 batches)

Stage Batch ID Job type Status
creating batch_69d6ab4669e48190b59246358b0383ab elicitation completed
NER batch_69d903f02638819091e0cc0e93fa5ea7 ner completed
NED1 batch_69f49d4f4c80819082ffc0c5aa3505a0 ned_source_triple completed
Created at: April 8, 2026, 9:47 p.m.