Triple
T22328837
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Kähler identities |
E551970
|
entity |
| Predicate | relates |
P37
|
FINISHED |
| Object | Lefschetz operator |
—
|
NE NERFINISHED |
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: Lefschetz operator | Statement: [Kähler identities, relates, Lefschetz operator]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lefschetz operator Context triple: [Kähler identities, relates, Lefschetz operator]
-
A.
Lefschetz operator
chosen
The Lefschetz operator is a linear operator in Kähler geometry that acts on differential forms by wedging with the Kähler form, playing a central role in the Hard Lefschetz theorem and Hodge theory.
-
B.
Lefschetz
Lefschetz is a surname most notably associated with Solomon Lefschetz, a pioneering mathematician in algebraic topology and geometry.
-
C.
Lefschetz decomposition
Lefschetz decomposition is a structural breakdown of the derived category of coherent sheaves on an algebraic variety into a sequence of subcategories reflecting the geometry of a Lefschetz-type fibration or embedding.
-
D.
Lefschetz number
The Lefschetz number is a topological invariant, computed from the traces of induced maps on homology, that predicts the existence and number of fixed points of a continuous self-map on a topological space.
-
E.
Lefschetz duality
Lefschetz duality is a generalization of Poincaré duality that relates the homology of a compact manifold with boundary to the cohomology of the manifold relative to its boundary.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (2 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. |
Created at: April 16, 2026, 8:43 p.m.