Triple

T10946690
Position Surface form Disambiguated ID Type / Status
Subject Atiyah–Bott fixed-point theorem E258614 entity
Predicate usesConcept P531 FINISHED
Object Chern character E391904 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 character | Statement: [Atiyah–Bott fixed-point theorem, usesConcept, Chern character]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Chern character
Context triple: [Atiyah–Bott fixed-point theorem, usesConcept, Chern character]
  • A. Chern character chosen
    The Chern character is a fundamental homomorphism from K-theory to cohomology that translates vector bundles into characteristic classes, playing a central role in index theory and algebraic topology.
  • B. Chern
    Chern is a settlement in Russia that historically served as the administrative center of Chernsky Uyezd.
  • C. Chern classes
    Chern classes are fundamental topological invariants in differential and algebraic geometry that classify complex vector bundles and capture their curvature and twisting properties.
  • D. 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.
  • E. 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.
  • 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_69d6aa8769b4819082bfe5e61b9017f0 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d770eaaea08190b06e508600d8a305 completed April 9, 2026, 9:27 a.m.
NED1 Entity disambiguation (via context triple) batch_69e23c3c885081908edcece772b2e759 completed April 17, 2026, 1:57 p.m.
Created at: April 8, 2026, 9:23 p.m.