Triple

T23234994
Position Surface form Disambiguated ID Type / Status
Subject Lie algebroid E581260 entity
Predicate relatedConcept P37 FINISHED
Object Courant algebroid
A Courant algebroid is a geometric structure generalizing Lie algebroids that combines a vector bundle with a bracket, anchor map, and bilinear form, and plays a central role in generalized complex geometry and string theory.
E1576271 NE FINISHED

How this triple was built (4 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: Courant algebroid | Statement: [Lie algebroid, relatedConcept, Courant algebroid]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Courant algebroid
Context triple: [Lie algebroid, relatedConcept, Courant algebroid]
  • A. 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.
  • 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. Poisson geometry
    Poisson geometry is the branch of differential geometry that studies manifolds equipped with a Poisson bracket, generalizing classical Hamiltonian mechanics and symplectic geometry.
  • D. Jacobi bracket
    The Jacobi bracket is a bilinear operation generalizing the Poisson bracket in differential geometry, central to the theory of Jacobi manifolds and 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. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Courant algebroid
Triple: [Lie algebroid, relatedConcept, Courant algebroid]
Generated description
A Courant algebroid is a geometric structure generalizing Lie algebroids that combines a vector bundle with a bracket, anchor map, and bilinear form, and plays a central role in generalized complex geometry and string theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Courant algebroid
Target entity description: A Courant algebroid is a geometric structure generalizing Lie algebroids that combines a vector bundle with a bracket, anchor map, and bilinear form, and plays a central role in generalized complex geometry and string theory.
  • A. 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.
  • 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. Poisson geometry
    Poisson geometry is the branch of differential geometry that studies manifolds equipped with a Poisson bracket, generalizing classical Hamiltonian mechanics and symplectic geometry.
  • D. Jacobi bracket
    The Jacobi bracket is a bilinear operation generalizing the Poisson bracket in differential geometry, central to the theory of Jacobi manifolds and 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. chosen

Provenance (5 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_69e2460556f88190be1744a84a84173f completed April 17, 2026, 2:39 p.m.
NER Named-entity recognition batch_69f192e8c7548190b53434eeb2620a6e completed April 29, 2026, 5:11 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0c3f59de808190afb414450ac32d0d completed May 19, 2026, 10:45 a.m.
NEDg Description generation batch_6a0c4008c4a881908ad49e733b549036 completed May 19, 2026, 10:48 a.m.
NED2 Entity disambiguation (via description) batch_6a0c40bece448190bb9fd1a3058a1f06 completed May 19, 2026, 10:51 a.m.
Created at: April 17, 2026, 4:09 p.m.