Triple
T12026889
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | noncommutative geometry |
E286300
|
entity |
| Predicate | keyConcept |
P531
|
FINISHED |
| Object |
Connes–Chern character
The Connes–Chern character is a fundamental map in noncommutative geometry that connects K-theory of noncommutative algebras to cyclic cohomology, generalizing the classical Chern character from vector bundles to operator algebras.
|
E391904
|
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: Connes–Chern character | Statement: [noncommutative geometry, keyConcept, Connes–Chern character]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Connes–Chern character Context triple: [noncommutative geometry, keyConcept, Connes–Chern character]
-
A.
Connes–Moscovici index theorem
The Connes–Moscovici index theorem is a fundamental result in noncommutative geometry that generalizes the classical Atiyah–Singer index theorem to the setting of foliations and noncommutative spaces.
-
B.
Cheeger–Simons differential characters
Cheeger–Simons differential characters are geometric invariants that refine ordinary cohomology by incorporating both integral cohomology classes and differential form data, providing a model for differential cohomology theories.
-
C.
Chern character
The Chern character is a fundamental homomorphism from K-theory to cohomology that translates vector bundles into characteristic classes, playing a central role in index theory and algebraic topology.
-
D.
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.
-
E.
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.
- 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: Connes–Chern character Triple: [noncommutative geometry, keyConcept, Connes–Chern character]
Generated description
The Connes–Chern character is a fundamental map in noncommutative geometry that connects K-theory of noncommutative algebras to cyclic cohomology, generalizing the classical Chern character from vector bundles to operator algebras.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Connes–Chern character Target entity description: The Connes–Chern character is a fundamental map in noncommutative geometry that connects K-theory of noncommutative algebras to cyclic cohomology, generalizing the classical Chern character from vector bundles to operator algebras.
-
A.
Connes–Moscovici index theorem
The Connes–Moscovici index theorem is a fundamental result in noncommutative geometry that generalizes the classical Atiyah–Singer index theorem to the setting of foliations and noncommutative spaces.
-
B.
Cheeger–Simons differential characters
Cheeger–Simons differential characters are geometric invariants that refine ordinary cohomology by incorporating both integral cohomology classes and differential form data, providing a model for differential cohomology theories.
-
C.
Chern character
chosen
The Chern character is a fundamental homomorphism from K-theory to cohomology that translates vector bundles into characteristic classes, playing a central role in index theory and algebraic topology.
-
D.
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.
-
E.
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.
- F. None of above.
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_69d6ab4669e48190b59246358b0383ab |
completed | April 8, 2026, 7:23 p.m. |
| NER | Named-entity recognition | batch_69d903f02638819091e0cc0e93fa5ea7 |
completed | April 10, 2026, 2:06 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f48b8111b88190a42a8904a2d26862 |
completed | May 1, 2026, 11:16 a.m. |
| NEDg | Description generation | batch_69f48fc7a8848190a06b34cc45db4789 |
completed | May 1, 2026, 11:34 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69f495f069c48190a6e5856c272420c0 |
completed | May 1, 2026, noon |
Created at: April 8, 2026, 9:47 p.m.