Triple

T7871938
Position Surface form Disambiguated ID Type / Status
Subject Jacobi bracket E182756 entity
Predicate relatedTo P37 FINISHED
Object Poisson manifold E697763 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: Poisson manifold | Statement: [Jacobi bracket, relatedTo, Poisson manifold]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Poisson manifold
Context triple: [Jacobi bracket, relatedTo, Poisson manifold]
  • A. Poisson geometry chosen
    Poisson geometry is the branch of differential geometry that studies manifolds equipped with a Poisson bracket, generalizing classical Hamiltonian mechanics and symplectic geometry.
  • B. Jacobi manifold
    A Jacobi manifold is a smooth manifold equipped with a Lie bracket on its space of smooth functions that satisfies a generalized Leibniz rule, extending the notion of Poisson manifolds.
  • C. Lie algebroid
    A Lie algebroid is a geometric structure that generalizes Lie algebras and tangent bundles, encoding infinitesimal symmetries on manifolds via a vector bundle with a Lie bracket and an anchor map.
  • D. Poisson bracket
    The Poisson bracket is a fundamental mathematical operator in classical mechanics and symplectic geometry that encodes the time evolution and mutual relationships of dynamical variables in Hamiltonian systems.
  • E. Carathéodory–Jacobi–Lie theorem
    The Carathéodory–Jacobi–Lie theorem is a fundamental result in symplectic geometry and Hamiltonian mechanics that provides canonical local coordinates adapted to a given set of commuting functions.
  • 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_69ca82894d9081908a832bfce71a4714 completed March 30, 2026, 2:02 p.m.
NER Named-entity recognition batch_69cb39a5950481908399211c5dfe2569 completed March 31, 2026, 3:04 a.m.
NED1 Entity disambiguation (via context triple) batch_69cbdf844f24819091cb8757d29a4a3f completed March 31, 2026, 2:51 p.m.
Created at: March 30, 2026, 4:56 p.m.