Triple

T23367472
Position Surface form Disambiguated ID Type / Status
Subject Max Karoubi E593363 entity
Predicate notableWork P4 FINISHED
Object K-Theory: An Introduction
"K-Theory: An Introduction" is a foundational textbook by Max Karoubi that systematically develops algebraic and topological K-theory for advanced mathematics students and researchers.
E1583491 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: K-Theory: An Introduction | Statement: [Max Karoubi, notableWork, K-Theory: An Introduction]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: K-Theory: An Introduction
Context triple: [Max Karoubi, notableWork, K-Theory: An Introduction]
  • A. 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.
  • 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. 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.
  • 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. 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.
  • 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: K-Theory: An Introduction
Triple: [Max Karoubi, notableWork, K-Theory: An Introduction]
Generated description
"K-Theory: An Introduction" is a foundational textbook by Max Karoubi that systematically develops algebraic and topological K-theory for advanced mathematics students and researchers.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: K-Theory: An Introduction
Target entity description: "K-Theory: An Introduction" is a foundational textbook by Max Karoubi that systematically develops algebraic and topological K-theory for advanced mathematics students and researchers.
  • A. 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.
  • 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. 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.
  • 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. 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.
  • 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_69e25d2593c88190bcdf4a716a94ccb2 completed April 17, 2026, 4:17 p.m.
NER Named-entity recognition batch_69f1a0ad621881908a909f236e6e9c90 completed April 29, 2026, 6:09 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0c5dd964f081909aa71493fe6e07c7 completed May 19, 2026, 12:55 p.m.
NEDg Description generation batch_6a0c5f27dbac8190a633ff61bc3321bd completed May 19, 2026, 1:01 p.m.
NED2 Entity disambiguation (via description) batch_6a0c5fd0c4e88190901c08e6c969e7ac completed May 19, 2026, 1:04 p.m.
Created at: April 17, 2026, 5:32 p.m.