Triple
T5837401
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hodge theory |
E129504
|
entity |
| Predicate | relatedTo |
P37
|
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: [Hodge theory, relatedTo, Dolbeault cohomology]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Dolbeault cohomology Context triple: [Hodge theory, relatedTo, 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_69c0084af79c81908af128ccc29983d0 |
completed | March 22, 2026, 3:18 p.m. |
| NER | Named-entity recognition | batch_69c034a48750819099ae917ae2b54e6d |
completed | March 22, 2026, 6:27 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c0bfce88f88190bbc78ce9c7c3c107 |
completed | March 23, 2026, 4:21 a.m. |
Created at: March 22, 2026, 3:54 p.m.