Triple

T13614780
Position Surface form Disambiguated ID Type / Status
Subject Differential Analysis on Complex Manifolds E325283 entity
Predicate topic P261 FINISHED
Object Dolbeault cohomology E551971 NE FINISHED

How this triple was built (2 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: Dolbeault cohomology | Statement: [Differential Analysis on Complex Manifolds, topic, Dolbeault cohomology]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Dolbeault cohomology
Context triple: [Differential Analysis on Complex Manifolds, topic, Dolbeault cohomology]
  • A. Dolbeault cohomology classes chosen
    Dolbeault cohomology classes are equivalence classes of differential forms on a complex manifold defined using the ∂̄-operator, encoding the manifold’s complex-analytic and geometric structure.
  • B. Differential Analysis on Complex Manifolds
    "Differential Analysis on Complex Manifolds" is a foundational mathematical monograph that systematically develops the theory of differential and complex geometry on complex manifolds.
  • C. Hodge decomposition
    Hodge decomposition is a fundamental result in differential geometry and Hodge theory that expresses differential forms on a Riemannian manifold uniquely as sums of exact, co-exact, and harmonic components.
  • D. Deligne cohomology
    Deligne cohomology is a refined cohomology theory in algebraic geometry that combines singular cohomology and differential forms to capture both topological and arithmetic information about complex algebraic varieties.
  • E. Hodge theory
    Hodge theory is a branch of mathematics that studies the relationship between differential forms, cohomology, and complex geometry, particularly on complex manifolds.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d8076aae28819092cf636190ee5529 completed April 9, 2026, 8:09 p.m.
NER Named-entity recognition batch_69dbb0ad0a7c81909c7972187202db96 completed April 12, 2026, 2:48 p.m.
NED1 Entity disambiguation (via context triple) batch_69f77f9cbc388190972e949324144d2f completed May 3, 2026, 5:02 p.m.
Created at: April 9, 2026, 9:50 p.m.