Triple
T15402647
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Erich Kähler |
E368361
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Kähler differentials
Kähler differentials are a fundamental construction in algebraic geometry and commutative algebra that generalize the notion of differential forms to arbitrary commutative rings and schemes, enabling the study of infinitesimal behavior and smoothness.
|
E1155253
|
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: Kähler differentials | Statement: [Erich Kähler, knownFor, Kähler differentials]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Kähler differentials Context triple: [Erich Kähler, knownFor, Kähler differentials]
-
A.
Differential Forms in Algebraic Topology
Differential Forms in Algebraic Topology is a foundational graduate-level textbook that develops algebraic topology using the language of differential forms, bridging differential geometry and topological methods.
-
B.
Kähler identities
Kähler identities are fundamental commutation relations in Kähler geometry that link the Lefschetz operator, its adjoint, and the Dolbeault operators, playing a key role in Hodge theory and complex differential geometry.
-
C.
Kähler form
A Kähler form is a closed, positive-definite (1,1)-form that defines the compatible symplectic and Hermitian structure on a Kähler manifold.
-
D.
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.
-
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: Kähler differentials Triple: [Erich Kähler, knownFor, Kähler differentials]
Generated description
Kähler differentials are a fundamental construction in algebraic geometry and commutative algebra that generalize the notion of differential forms to arbitrary commutative rings and schemes, enabling the study of infinitesimal behavior and smoothness.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Kähler differentials Target entity description: Kähler differentials are a fundamental construction in algebraic geometry and commutative algebra that generalize the notion of differential forms to arbitrary commutative rings and schemes, enabling the study of infinitesimal behavior and smoothness.
-
A.
Differential Forms in Algebraic Topology
Differential Forms in Algebraic Topology is a foundational graduate-level textbook that develops algebraic topology using the language of differential forms, bridging differential geometry and topological methods.
-
B.
Kähler identities
Kähler identities are fundamental commutation relations in Kähler geometry that link the Lefschetz operator, its adjoint, and the Dolbeault operators, playing a key role in Hodge theory and complex differential geometry.
-
C.
Kähler form
A Kähler form is a closed, positive-definite (1,1)-form that defines the compatible symplectic and Hermitian structure on a Kähler manifold.
-
D.
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.
-
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
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_69d85a16c68c819099c1b547fbc87b32 |
completed | April 10, 2026, 2:01 a.m. |
| NER | Named-entity recognition | batch_69e03e8ea0ac8190a5c68b1951ad3db1 |
completed | April 16, 2026, 1:42 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69ff13584f8881908b2527c51f85ae28 |
completed | May 9, 2026, 10:58 a.m. |
| NEDg | Description generation | batch_69ff145ac8e081908b075cee67e82aa3 |
completed | May 9, 2026, 11:02 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69ff1509e5a48190b69f1a44d793e07d |
completed | May 9, 2026, 11:05 a.m. |
Created at: April 10, 2026, 3:19 a.m.