Triple

T3037537
Position Surface form Disambiguated ID Type / Status
Subject Andrei Kolmogorov E83045 entity
Predicate notableWork P4 FINISHED
Object 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.
E320432 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: Kolmogorov–Arnold–Moser theory | Statement: [Andrei Kolmogorov, notableWork, Kolmogorov–Arnold–Moser theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Kolmogorov–Arnold–Moser theory
Context triple: [Andrei Kolmogorov, notableWork, Kolmogorov–Arnold–Moser theory]
  • A. Poincaré–Birkhoff fixed-point theorem
    The Poincaré–Birkhoff fixed-point theorem is a fundamental result in dynamical systems and topology that guarantees the existence of at least two fixed points for certain area-preserving twist maps of an annulus.
  • B. 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.
  • C. 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.
  • D. 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.
  • E. Poincaré recurrence theorem
    The Poincaré recurrence theorem is a fundamental result in dynamical systems and ergodic theory stating that certain systems will, after a sufficiently long but finite time, return arbitrarily close to their initial state.
  • 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: Kolmogorov–Arnold–Moser theory
Triple: [Andrei Kolmogorov, notableWork, Kolmogorov–Arnold–Moser theory]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Kolmogorov–Arnold–Moser theory
Target entity description: 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.
  • A. Poincaré–Birkhoff fixed-point theorem
    The Poincaré–Birkhoff fixed-point theorem is a fundamental result in dynamical systems and topology that guarantees the existence of at least two fixed points for certain area-preserving twist maps of an annulus.
  • B. 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.
  • C. 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.
  • D. 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.
  • E. Poincaré recurrence theorem
    The Poincaré recurrence theorem is a fundamental result in dynamical systems and ergodic theory stating that certain systems will, after a sufficiently long but finite time, return arbitrarily close to their initial state.
  • 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_69ad8b2298908190a7cb4e9bdbf064d0 completed March 8, 2026, 2:43 p.m.
NER Named-entity recognition batch_69ad9b2cd4988190b52fe3616ecbe9ef completed March 8, 2026, 3:52 p.m.
NED1 Entity disambiguation (via context triple) batch_69b1dec8778c8190a5e06a29a0218404 completed March 11, 2026, 9:29 p.m.
NEDg Description generation batch_69b1e2c4aaa88190bb5e39c51d0583f0 completed March 11, 2026, 9:46 p.m.
NED2 Entity disambiguation (via description) batch_69b1e3228f488190b13c948c6c5d13d0 completed March 11, 2026, 9:48 p.m.
Created at: March 8, 2026, 3:01 p.m.