Triple

T22329103
Position Surface form Disambiguated ID Type / Status
Subject de Rham cohomology E551975 entity
Predicate relatedConcept P37 FINISHED
Object Čech–de Rham complex
The Čech–de Rham complex is a double complex that combines Čech cochains with differential forms to compute de Rham cohomology via open covers.
E1531325 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: Čech–de Rham complex | Statement: [de Rham cohomology, relatedConcept, Čech–de Rham complex]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Čech–de Rham complex
Context triple: [de Rham cohomology, relatedConcept, Čech–de Rham complex]
  • A. de Rham cohomology
    de Rham cohomology is a cohomology theory for smooth manifolds that uses differential forms to capture their global topological and geometric properties.
  • B. 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.
  • C. 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.
  • D. Alexander–Spanier cohomology
    Alexander–Spanier cohomology is a cohomology theory in algebraic topology defined using cochains on all finite subsets of a space, notable for its generality and close relationship to Čech and singular cohomology.
  • E. 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.
  • 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: Čech–de Rham complex
Triple: [de Rham cohomology, relatedConcept, Čech–de Rham complex]
Generated description
The Čech–de Rham complex is a double complex that combines Čech cochains with differential forms to compute de Rham cohomology via open covers.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Čech–de Rham complex
Target entity description: The Čech–de Rham complex is a double complex that combines Čech cochains with differential forms to compute de Rham cohomology via open covers.
  • A. de Rham cohomology
    de Rham cohomology is a cohomology theory for smooth manifolds that uses differential forms to capture their global topological and geometric properties.
  • B. 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.
  • C. 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.
  • D. Alexander–Spanier cohomology
    Alexander–Spanier cohomology is a cohomology theory in algebraic topology defined using cochains on all finite subsets of a space, notable for its generality and close relationship to Čech and singular cohomology.
  • E. 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.
  • 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_69e11e482f788190b78d1588fc26d606 completed April 16, 2026, 5:37 p.m.
NER Named-entity recognition batch_69f1576ab52c819087563cd778d6bc5e completed April 29, 2026, 12:57 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0ad523ecec8190a85eb932288965fb completed May 18, 2026, 9 a.m.
NEDg Description generation batch_6a0ad992b43c8190b0e409d64db83308 completed May 18, 2026, 9:19 a.m.
NED2 Entity disambiguation (via description) batch_6a0adac48bec8190989dd7c5e28d283a completed May 18, 2026, 9:24 a.m.
Created at: April 16, 2026, 8:43 p.m.