Triple
T2314516
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Michael Atiyah |
E51031
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
“Elliptic Operators and Compact Groups” (with Raoul Bott)
“Elliptic Operators and Compact Groups” (with Raoul Bott) is a seminal mathematical paper that develops the theory of equivariant index for elliptic operators under compact Lie group actions, laying key foundations for modern index theory and representation theory.
|
E255579
|
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: “Elliptic Operators and Compact Groups” (with Raoul Bott) | Statement: [Michael Atiyah, notableWork, “Elliptic Operators and Compact Groups” (with Raoul Bott)]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: “Elliptic Operators and Compact Groups” (with Raoul Bott) Context triple: [Michael Atiyah, notableWork, “Elliptic Operators and Compact Groups” (with Raoul Bott)]
-
A.
Atiyah–Singer index theorem
The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
-
B.
Chern–Weil theory
Chern–Weil theory is a framework in differential geometry that constructs characteristic classes of vector bundles from curvature forms, linking topology and geometry through invariant polynomials.
-
C.
L’intégration dans les groupes topologiques et ses applications
L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
-
D.
The Poincaré-Birkhoff-Witt theorem in ring theory
"The Poincaré-Birkhoff-Witt theorem in ring theory" is a mathematical work, attributed here to N. G. de Bruijn, that studies and applies the Poincaré–Birkhoff–Witt theorem in the context of associative and Lie-theoretic ring structures.
-
E.
Produits tensoriels topologiques et espaces nucléaires
"Produits tensoriels topologiques et espaces nucléaires" is a foundational 1953 doctoral thesis in functional analysis that introduced and developed the theory of nuclear spaces and topological tensor products.
- 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: “Elliptic Operators and Compact Groups” (with Raoul Bott) Triple: [Michael Atiyah, notableWork, “Elliptic Operators and Compact Groups” (with Raoul Bott)]
Generated description
“Elliptic Operators and Compact Groups” (with Raoul Bott) is a seminal mathematical paper that develops the theory of equivariant index for elliptic operators under compact Lie group actions, laying key foundations for modern index theory and representation theory.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: “Elliptic Operators and Compact Groups” (with Raoul Bott) Target entity description: “Elliptic Operators and Compact Groups” (with Raoul Bott) is a seminal mathematical paper that develops the theory of equivariant index for elliptic operators under compact Lie group actions, laying key foundations for modern index theory and representation theory.
-
A.
Atiyah–Singer index theorem
The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
-
B.
Chern–Weil theory
Chern–Weil theory is a framework in differential geometry that constructs characteristic classes of vector bundles from curvature forms, linking topology and geometry through invariant polynomials.
-
C.
L’intégration dans les groupes topologiques et ses applications
L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
-
D.
The Poincaré-Birkhoff-Witt theorem in ring theory
"The Poincaré-Birkhoff-Witt theorem in ring theory" is a mathematical work, attributed here to N. G. de Bruijn, that studies and applies the Poincaré–Birkhoff–Witt theorem in the context of associative and Lie-theoretic ring structures.
-
E.
Produits tensoriels topologiques et espaces nucléaires
"Produits tensoriels topologiques et espaces nucléaires" is a foundational 1953 doctoral thesis in functional analysis that introduced and developed the theory of nuclear spaces and topological tensor products.
- 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.