Triple

T10732794
Position Surface form Disambiguated ID Type / Status
Subject Serre duality E253115 entity
Predicate uses P98 FINISHED
Object Serre duality pairing E253115 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: Serre duality pairing | Statement: [Serre duality, uses, Serre duality pairing]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Serre duality pairing
Context triple: [Serre duality, uses, Serre duality pairing]
  • A. Serre duality chosen
    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.
  • B. 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.
  • C. Verdier duality
    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.
  • D. 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.
  • E. Kronecker pairing
    The Kronecker pairing is a fundamental bilinear map in algebraic topology that evaluates cohomology classes on homology classes, linking the two via an integer (or field) value.
  • 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_69d6aa5d8be481909a43218b2bfdbe95 completed April 8, 2026, 7:19 p.m.
NER Named-entity recognition batch_69d7101ff9808190a27fcc06da097ea3 completed April 9, 2026, 2:34 a.m.
NED1 Entity disambiguation (via context triple) batch_69de22bb62e481909544c87801012df3 completed April 14, 2026, 11:19 a.m.
Created at: April 8, 2026, 9:14 p.m.