Triple

T10269803
Position Surface form Disambiguated ID Type / Status
Subject Chern classes E240803 entity
Predicate usedFor P98 FINISHED
Object Gauss–Bonnet–Chern theorem E159880 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: Gauss–Bonnet–Chern theorem | Statement: [Chern classes, usedFor, Gauss–Bonnet–Chern theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Gauss–Bonnet–Chern theorem
Context triple: [Chern classes, usedFor, Gauss–Bonnet–Chern theorem]
  • A. Gauss–Bonnet theorem (early form)
    The Gauss–Bonnet theorem (early form) is an early version of the fundamental result in differential geometry that links the total curvature of a surface to its topological characteristics, originally developed by Carl Friedrich Gauss.
  • B. Hopf conjecture (on Euler characteristic and curvature)
    The Hopf conjecture on Euler characteristic and curvature is an open problem in differential geometry proposing a deep link between the sign of a manifold’s Euler characteristic and the sign of its sectional curvature, especially for even-dimensional manifolds with positive or negative curvature.
  • C. Hirzebruch signature theorem
    The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
  • D. Chern–Weil theory chosen
    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. Atiyah–Bott fixed-point theorem
    The Atiyah–Bott fixed-point theorem is a fundamental result in equivariant cohomology that expresses global invariants, such as indices of elliptic operators, in terms of local data at the fixed points of a group action.
  • 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_69d381a94c1881908fc38fc263d9b9c2 completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d4d270fb088190ba43b6f24e881b94 completed April 7, 2026, 9:46 a.m.
NED1 Entity disambiguation (via context triple) batch_69d71ceeeec88190a36a5e67dc44cfe1 completed April 9, 2026, 3:28 a.m.
Created at: April 6, 2026, 11:35 a.m.