Triple
T11365421
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Deligne cohomology |
E269189
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
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.
|
E921617
|
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: Cheeger–Simons differential characters | Statement: [Deligne cohomology, relatedTo, Cheeger–Simons differential characters]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Cheeger–Simons differential characters Context triple: [Deligne cohomology, relatedTo, Cheeger–Simons differential characters]
-
A.
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.
-
B.
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.
-
C.
Chern classes
Chern classes are fundamental topological invariants in differential and algebraic geometry that classify complex vector bundles and capture their curvature and twisting properties.
-
D.
Chern–Simons forms
Chern–Simons forms are secondary characteristic classes in differential geometry that arise from connections on principal bundles and play a central role in topological quantum field theories.
-
E.
Mayer–Vietoris sequence in de Rham cohomology
The Mayer–Vietoris sequence in de Rham cohomology is a long exact sequence that computes the de Rham cohomology of a manifold by relating it to the cohomology of an open cover and their intersection.
- 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: Cheeger–Simons differential characters Triple: [Deligne cohomology, relatedTo, Cheeger–Simons differential characters]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Cheeger–Simons differential characters Target entity description: 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.
-
A.
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.
-
B.
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.
-
C.
Chern classes
Chern classes are fundamental topological invariants in differential and algebraic geometry that classify complex vector bundles and capture their curvature and twisting properties.
-
D.
Chern–Simons forms
Chern–Simons forms are secondary characteristic classes in differential geometry that arise from connections on principal bundles and play a central role in topological quantum field theories.
-
E.
Mayer–Vietoris sequence in de Rham cohomology
The Mayer–Vietoris sequence in de Rham cohomology is a long exact sequence that computes the de Rham cohomology of a manifold by relating it to the cohomology of an open cover and their intersection.
- 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_69d6aacca1048190b39dbbc2174616fa |
completed | April 8, 2026, 7:21 p.m. |
| NER | Named-entity recognition | batch_69d7ea4589908190948a8225768e1eec |
completed | April 9, 2026, 6:04 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e55667d4908190b6290135eba41e54 |
completed | April 19, 2026, 10:25 p.m. |
| NEDg | Description generation | batch_69e562c6e7c8819098d22a6e0daa4a51 |
completed | April 19, 2026, 11:18 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69e56a472f0c819086c1cccaa5ca0ae7 |
completed | April 19, 2026, 11:50 p.m. |
Created at: April 8, 2026, 9:33 p.m.