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.