Triple
T10773337
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Grothendieck duality |
E254134
|
entity |
| Predicate | relatedConcept |
P37
|
FINISHED |
| Object | Verdier duality |
E620670
|
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: Verdier duality | Statement: [Grothendieck duality, relatedConcept, Verdier duality]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Verdier duality Context triple: [Grothendieck duality, relatedConcept, Verdier duality]
-
A.
Verdier duality
chosen
Verdier duality is a powerful generalization of Poincaré duality formulated in the language of derived categories and sheaf theory, providing a duality functor that relates cohomology with compact support to ordinary cohomology on possibly singular or non-compact spaces.
-
B.
Grothendieck duality
Grothendieck duality is a foundational theory in algebraic geometry that generalizes classical Serre duality to a broad categorical and sheaf-theoretic framework for studying duality on schemes and morphisms.
-
C.
Serre duality
Serre duality is a fundamental theorem in algebraic geometry that generalizes classical duality for Riemann surfaces to higher-dimensional projective varieties, relating cohomology groups of coherent sheaves via a dualizing sheaf.
-
D.
Poincaré duality
Poincaré duality is a fundamental theorem in algebraic topology that relates the homology and cohomology groups of an oriented closed manifold in complementary dimensions.
-
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 (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_69d6aa5f54f4819082d0bbcb6f8797e6 |
completed | April 8, 2026, 7:19 p.m. |
| NER | Named-entity recognition | batch_69d7329b27748190bd0e2569c7972fd1 |
completed | April 9, 2026, 5:01 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69de238559b48190abc759e744ab0f8e |
completed | April 14, 2026, 11:22 a.m. |
Created at: April 8, 2026, 9:16 p.m.