Triple

T2314515
Position Surface form Disambiguated ID Type / Status
Subject Michael Atiyah E51031 entity
Predicate notableWork P4 FINISHED
Object “Introduction to Commutative Algebra” (with Ian G. Macdonald)
“Introduction to Commutative Algebra” (with Ian G. Macdonald) is a classic introductory textbook that provides a concise, rigorous foundation in commutative algebra, widely used by advanced undergraduates and beginning graduate students in mathematics.
E255578 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: “Introduction to Commutative Algebra” (with Ian G. Macdonald) | Statement: [Michael Atiyah, notableWork, “Introduction to Commutative Algebra” (with Ian G. Macdonald)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: “Introduction to Commutative Algebra” (with Ian G. Macdonald)
Context triple: [Michael Atiyah, notableWork, “Introduction to Commutative Algebra” (with Ian G. Macdonald)]
  • A. Moderne Algebra
    Moderne Algebra is a foundational 20th-century textbook that systematically developed abstract algebra and helped shape the modern axiomatic approach to the subject.
  • B. Castelnuovo–Mumford regularity
    Castelnuovo–Mumford regularity is an invariant in commutative algebra and algebraic geometry that measures the complexity of the minimal graded free resolution of a module or sheaf, often used to control vanishing of cohomology and bounds on generators.
  • C. Hilbert’s syzygy theorem
    Hilbert’s syzygy theorem is a fundamental result in commutative algebra that describes the finite length and structure of free resolutions of modules over polynomial rings.
  • D. Categories for the Working Mathematician
    Categories for the Working Mathematician is a foundational textbook in category theory that systematically develops the subject and its applications for professional mathematicians.
  • E. Auslander–Buchsbaum formula
    The Auslander–Buchsbaum formula is a fundamental result in commutative algebra that relates the projective dimension of a finitely generated module over a Noetherian local ring to the depth of the module and the depth of the ring.
  • 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: “Introduction to Commutative Algebra” (with Ian G. Macdonald)
Triple: [Michael Atiyah, notableWork, “Introduction to Commutative Algebra” (with Ian G. Macdonald)]
Generated description
“Introduction to Commutative Algebra” (with Ian G. Macdonald) is a classic introductory textbook that provides a concise, rigorous foundation in commutative algebra, widely used by advanced undergraduates and beginning graduate students in mathematics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: “Introduction to Commutative Algebra” (with Ian G. Macdonald)
Target entity description: “Introduction to Commutative Algebra” (with Ian G. Macdonald) is a classic introductory textbook that provides a concise, rigorous foundation in commutative algebra, widely used by advanced undergraduates and beginning graduate students in mathematics.
  • A. Moderne Algebra
    Moderne Algebra is a foundational 20th-century textbook that systematically developed abstract algebra and helped shape the modern axiomatic approach to the subject.
  • B. Castelnuovo–Mumford regularity
    Castelnuovo–Mumford regularity is an invariant in commutative algebra and algebraic geometry that measures the complexity of the minimal graded free resolution of a module or sheaf, often used to control vanishing of cohomology and bounds on generators.
  • C. Hilbert’s syzygy theorem
    Hilbert’s syzygy theorem is a fundamental result in commutative algebra that describes the finite length and structure of free resolutions of modules over polynomial rings.
  • D. Categories for the Working Mathematician
    Categories for the Working Mathematician is a foundational textbook in category theory that systematically develops the subject and its applications for professional mathematicians.
  • E. Auslander–Buchsbaum formula
    The Auslander–Buchsbaum formula is a fundamental result in commutative algebra that relates the projective dimension of a finitely generated module over a Noetherian local ring to the depth of the module and the depth of the ring.
  • 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_69a88b074b908190ae983dbca7757d88 completed March 4, 2026, 7:41 p.m.
NER Named-entity recognition batch_69abc61d41f88190983f8947667b4c7a completed March 7, 2026, 6:30 a.m.
NED1 Entity disambiguation (via context triple) batch_69ae895f5420819087b403e9772dce9a completed March 9, 2026, 8:48 a.m.
NEDg Description generation batch_69ae8af65eb88190b17d74e7411967cc completed March 9, 2026, 8:55 a.m.
NED2 Entity disambiguation (via description) batch_69ae8ba02cec8190917c0e17d3fedb0e completed March 9, 2026, 8:58 a.m.
Created at: March 4, 2026, 7:49 p.m.