Triple

T10388472
Position Surface form Disambiguated ID Type / Status
Subject Vladimir Voevodsky E244828 entity
Predicate notableWork P4 FINISHED
Object 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.
E858913 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: proof of the Milnor conjecture | Statement: [Vladimir Voevodsky, notableWork, proof of the Milnor conjecture]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: proof of the Milnor conjecture
Context triple: [Vladimir Voevodsky, notableWork, proof of the Milnor conjecture]
  • A. 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.
  • B. Standard Conjectures on Algebraic Cycles
    The Standard Conjectures on Algebraic Cycles are a set of deep, still unproven hypotheses in algebraic geometry that aim to provide a foundational theory of algebraic cycles and their cohomological properties, underpinning much of the modern theory of motives.
  • 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. Beilinson conjectures
    Beilinson conjectures are a set of deep conjectures in arithmetic geometry that relate special values of L-functions to algebraic K-theory and motivic cohomology, generalizing phenomena seen in cases like the Birch and Swinnerton-Dyer conjecture.
  • E. Hirzebruch signature theorem
    The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
  • 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: proof of the Milnor conjecture
Triple: [Vladimir Voevodsky, notableWork, proof of the Milnor conjecture]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: proof of the Milnor conjecture
Target entity description: 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.
  • A. 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.
  • B. Standard Conjectures on Algebraic Cycles
    The Standard Conjectures on Algebraic Cycles are a set of deep, still unproven hypotheses in algebraic geometry that aim to provide a foundational theory of algebraic cycles and their cohomological properties, underpinning much of the modern theory of motives.
  • 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. Beilinson conjectures
    Beilinson conjectures are a set of deep conjectures in arithmetic geometry that relate special values of L-functions to algebraic K-theory and motivic cohomology, generalizing phenomena seen in cases like the Birch and Swinnerton-Dyer conjecture.
  • E. Hirzebruch signature theorem
    The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
  • 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_69d381b5116081908d85227bab6d3c0c completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d4e9a59d688190b1da1ea0ed48fafa completed April 7, 2026, 11:25 a.m.
NED1 Entity disambiguation (via context triple) batch_69d795aa3afc8190aed1ca11556ae34f completed April 9, 2026, 12:03 p.m.
NEDg Description generation batch_69d7989cc318819083f325f4b223cf71 completed April 9, 2026, 12:16 p.m.
NED2 Entity disambiguation (via description) batch_69d799917ab881909a947ad8059652c6 completed April 9, 2026, 12:20 p.m.
Created at: April 6, 2026, 12:05 p.m.