Triple

T10829319
Position Surface form Disambiguated ID Type / Status
Subject K-theory E255574 entity
Predicate hasVariant P455 FINISHED
Object topological K-theory E255574 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: topological K-theory | Statement: [K-theory, hasVariant, topological K-theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: topological K-theory
Context triple: [K-theory, hasVariant, topological 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. 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.
  • C. 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.
  • D. “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.
  • E. 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.
  • 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_69d6aa8081448190a9324184f2bd1c26 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d74420fa188190b5b3c59e1a9f551d completed April 9, 2026, 6:16 a.m.
NED1 Entity disambiguation (via context triple) batch_69de85a068b08190948c3ca32cdda147 completed April 14, 2026, 6:21 p.m.
Created at: April 8, 2026, 9:19 p.m.