Triple

T12797583
Position Surface form Disambiguated ID Type / Status
Subject Algebraic Topology E305928 entity
Predicate developsConcept P201 FINISHED
Object Poincaré duality E156194 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: Poincaré duality | Statement: [Algebraic Topology, developsConcept, Poincaré duality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Poincaré duality
Context triple: [Algebraic Topology, developsConcept, Poincaré duality]
  • A. Poincaré duality chosen
    Poincaré duality is a fundamental theorem in algebraic topology that relates the homology and cohomology groups of an oriented closed manifold in complementary dimensions.
  • B. 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.
  • C. Pontryagin classes
    Pontryagin classes are characteristic classes associated with real vector bundles that capture topological information about the bundle’s curvature and play a central role in differential topology and geometry.
  • D. 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.
  • E. 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.
  • 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_69d7bdf366888190a8cccb982606889c completed April 9, 2026, 2:55 p.m.
NER Named-entity recognition batch_69d96e6db68481909a2ca8da1287f3e0 completed April 10, 2026, 9:41 p.m.
NED1 Entity disambiguation (via context triple) batch_69f6850d6ebc8190aaffcac09f4b15eb completed May 2, 2026, 11:13 p.m.
Created at: April 9, 2026, 5:30 p.m.