Triple

T12026933
Position Surface form Disambiguated ID Type / Status
Subject Connes–Moscovici index theorem E286301 entity
Predicate involves P1256 FINISHED
Object Godbillon–Vey class E911357 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: Godbillon–Vey class | Statement: [Connes–Moscovici index theorem, involves, Godbillon–Vey class]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Godbillon–Vey class
Context triple: [Connes–Moscovici index theorem, involves, Godbillon–Vey class]
  • A. Godbillon–Vey invariant chosen
    The Godbillon–Vey invariant is a characteristic class in differential topology that assigns a real number to certain codimension-one foliations of manifolds, capturing subtle geometric and dynamical properties of their leaf structure.
  • B. Thurston’s classification of surface diffeomorphisms
    Thurston’s classification of surface diffeomorphisms is a foundational theorem in low-dimensional topology that categorizes self-maps of surfaces into periodic, reducible, or pseudo-Anosov types, profoundly influencing the study of 3-manifolds and dynamical systems.
  • C. Kontsevich–Zorich cocycle
    The Kontsevich–Zorich cocycle is a dynamical system arising from the action of the Teichmüller geodesic flow on the Hodge bundle over moduli spaces of Riemann surfaces, central to understanding deviations of ergodic averages and Lyapunov exponents in flat surface dynamics.
  • D. 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.
  • E. Euler class
    The Euler class is a topological characteristic class associated with oriented real vector bundles, capturing obstruction information such as the existence of nowhere-vanishing sections.
  • 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_69d6ab4669e48190b59246358b0383ab completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d903f02638819091e0cc0e93fa5ea7 completed April 10, 2026, 2:06 p.m.
NED1 Entity disambiguation (via context triple) batch_69f48b8111b88190a42a8904a2d26862 completed May 1, 2026, 11:16 a.m.
Created at: April 8, 2026, 9:47 p.m.