Triple

T10991959
Position Surface form Disambiguated ID Type / Status
Subject Hirzebruch–Riemann–Roch theorem E259772 entity
Predicate relatesConcept P463 FINISHED
Object Chern classes E240803 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: Chern classes | Statement: [Hirzebruch–Riemann–Roch theorem, relatesConcept, Chern classes]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Chern classes
Context triple: [Hirzebruch–Riemann–Roch theorem, relatesConcept, Chern classes]
  • A. Chern classes chosen
    Chern classes are fundamental topological invariants in differential and algebraic geometry that classify complex vector bundles and capture their curvature and twisting properties.
  • B. Characteristic Classes
    Characteristic Classes is a foundational mathematical text in differential topology and geometry that systematically develops the theory of characteristic classes for vector bundles and fiber bundles.
  • 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. Stiefel–Whitney classes
    Stiefel–Whitney classes are characteristic classes in algebraic topology that assign cohomology invariants to real vector bundles, capturing their topological and orientability properties.
  • E. Chern–Weil theory
    Chern–Weil theory is a framework in differential geometry that constructs characteristic classes of vector bundles from curvature forms, linking topology and geometry through invariant polynomials.
  • 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_69d6aa8a6a548190a750f944ccdc8064 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d795d1e918819090c71f5a077fa15a completed April 9, 2026, 12:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69e34504ebec8190a78e4795765b0c24 completed April 18, 2026, 8:47 a.m.
Created at: April 8, 2026, 9:24 p.m.