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.