Triple
T6801415
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Poincaré duality |
E156194
|
entity |
| Predicate | relatedConcept |
P37
|
FINISHED |
| Object | Hodge theory |
E129504
|
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: Hodge theory | Statement: [Poincaré duality, relatedConcept, Hodge theory]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hodge theory Context triple: [Poincaré duality, relatedConcept, Hodge theory]
-
A.
Hodge theory
chosen
Hodge theory is a branch of mathematics that studies the relationship between differential forms, cohomology, and complex geometry, particularly on complex manifolds.
-
B.
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.
-
C.
Hodge–Riemann bilinear relations
The Hodge–Riemann bilinear relations are fundamental positivity and orthogonality conditions on the intersection form in Hodge theory that underpin results such as the hard Lefschetz theorem and the Hodge index theorem.
-
D.
Hodge filtration
The Hodge filtration is a decreasing sequence of complex subspaces on the cohomology of a complex algebraic variety that encodes its Hodge decomposition and mixed Hodge structure.
-
E.
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.
- 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_69c68826e6a48190a3d220b541e639de |
completed | March 27, 2026, 1:37 p.m. |
| NER | Named-entity recognition | batch_69c6d2e595188190a0bb4b595df3adb2 |
completed | March 27, 2026, 6:56 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c723d211508190a31747b2d67ed42e |
completed | March 28, 2026, 12:41 a.m. |
Created at: March 27, 2026, 2:16 p.m.