Triple

T7419954
Position Surface form Disambiguated ID Type / Status
Subject Kovalevskaya top E171219 entity
Predicate hasIntegralOfMotion P35803 FINISHED
Object Kovalevskaya integral
The Kovalevskaya integral is an additional conserved quantity that makes the motion of the Kovalevskaya top exactly integrable in classical rigid body dynamics.
E662759 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: Kovalevskaya integral | Statement: [Kovalevskaya top, hasIntegralOfMotion, Kovalevskaya integral]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Kovalevskaya integral
Context triple: [Kovalevskaya top, hasIntegralOfMotion, Kovalevskaya integral]
  • A. Kovalevskaya top
    The Kovalevskaya top is a famous integrable case of the motion of a rigid body about a fixed point in classical mechanics, discovered and analyzed by mathematician Sofia Kovalevskaya.
  • B. Jacobi integral
    The Jacobi integral is a conserved quantity in celestial mechanics and dynamical systems that simplifies the analysis of motion in rotating reference frames, particularly in the restricted three-body problem.
  • C. Liouville–Arnold theorem
    The Liouville–Arnold theorem is a fundamental result in Hamiltonian mechanics that guarantees the integrability of a system with sufficiently many conserved quantities and describes its motion as quasi-periodic on invariant tori in phase space.
  • D. Kolmogorov–Arnold–Moser theory
    Kolmogorov–Arnold–Moser theory is a fundamental result in dynamical systems that explains the persistence of quasi-periodic motions in nearly integrable Hamiltonian systems under small perturbations.
  • E. Cauchy–Kovalevskaya theorem
    The Cauchy–Kovalevskaya theorem is a fundamental result in partial differential equations that guarantees the existence and uniqueness of analytic solutions to certain initial value problems under appropriate analyticity conditions.
  • 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: Kovalevskaya integral
Triple: [Kovalevskaya top, hasIntegralOfMotion, Kovalevskaya integral]
Generated description
The Kovalevskaya integral is an additional conserved quantity that makes the motion of the Kovalevskaya top exactly integrable in classical rigid body dynamics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Kovalevskaya integral
Target entity description: The Kovalevskaya integral is an additional conserved quantity that makes the motion of the Kovalevskaya top exactly integrable in classical rigid body dynamics.
  • A. Kovalevskaya top
    The Kovalevskaya top is a famous integrable case of the motion of a rigid body about a fixed point in classical mechanics, discovered and analyzed by mathematician Sofia Kovalevskaya.
  • B. Jacobi integral
    The Jacobi integral is a conserved quantity in celestial mechanics and dynamical systems that simplifies the analysis of motion in rotating reference frames, particularly in the restricted three-body problem.
  • C. Liouville–Arnold theorem
    The Liouville–Arnold theorem is a fundamental result in Hamiltonian mechanics that guarantees the integrability of a system with sufficiently many conserved quantities and describes its motion as quasi-periodic on invariant tori in phase space.
  • D. Kolmogorov–Arnold–Moser theory
    Kolmogorov–Arnold–Moser theory is a fundamental result in dynamical systems that explains the persistence of quasi-periodic motions in nearly integrable Hamiltonian systems under small perturbations.
  • E. Cauchy–Kovalevskaya theorem
    The Cauchy–Kovalevskaya theorem is a fundamental result in partial differential equations that guarantees the existence and uniqueness of analytic solutions to certain initial value problems under appropriate analyticity conditions.
  • 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_69c68a625d048190af70eb8b63bec5a0 completed March 27, 2026, 1:47 p.m.
NER Named-entity recognition batch_69c6f4ec85488190a1f7fb913e0fbe35 completed March 27, 2026, 9:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69c81ef7fc808190a564ab4d9d97ab37 completed March 28, 2026, 6:33 p.m.
NEDg Description generation batch_69c81f9b565881909bebcc3112037f52 completed March 28, 2026, 6:36 p.m.
NED2 Entity disambiguation (via description) batch_69c8207912f4819086e99ed441bee805 completed March 28, 2026, 6:39 p.m.
Created at: March 27, 2026, 3:11 p.m.