Triple

T13443970
Position Surface form Disambiguated ID Type / Status
Subject Kolmogorov–Arnold–Moser theory E320432 entity
Predicate relatedTo P37 FINISHED
Object Nekhoroshev theory
Nekhoroshev theory is a result in Hamiltonian dynamical systems that provides exponentially long stability estimates for nearly integrable systems under small perturbations.
E1041765 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: Nekhoroshev theory | Statement: [Kolmogorov–Arnold–Moser theory, relatedTo, Nekhoroshev theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Nekhoroshev theory
Context triple: [Kolmogorov–Arnold–Moser theory, relatedTo, Nekhoroshev theory]
  • A. 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.
  • B. 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.
  • C. Liouville's theorem in Hamiltonian mechanics
    Liouville's theorem in Hamiltonian mechanics states that the phase-space volume occupied by an ensemble of systems evolving under Hamiltonian dynamics is conserved over time, implying incompressible flow in phase space.
  • D. 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.
  • E. 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.
  • 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: Nekhoroshev theory
Triple: [Kolmogorov–Arnold–Moser theory, relatedTo, Nekhoroshev theory]
Generated description
Nekhoroshev theory is a result in Hamiltonian dynamical systems that provides exponentially long stability estimates for nearly integrable systems under small perturbations.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Nekhoroshev theory
Target entity description: Nekhoroshev theory is a result in Hamiltonian dynamical systems that provides exponentially long stability estimates for nearly integrable systems under small perturbations.
  • A. 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.
  • B. 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.
  • C. Liouville's theorem in Hamiltonian mechanics
    Liouville's theorem in Hamiltonian mechanics states that the phase-space volume occupied by an ensemble of systems evolving under Hamiltonian dynamics is conserved over time, implying incompressible flow in phase space.
  • D. Painlevé conjecture in celestial mechanics
    The Painlevé conjecture in celestial mechanics is a hypothesis about the possible occurrence of non-collision singularities—where bodies in an N-body gravitational system exhibit infinite behavior in finite time without actually colliding.
  • 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_69d80761e6cc8190a90c844589998ecc completed April 9, 2026, 8:09 p.m.
NER Named-entity recognition batch_69dbaee881888190811ddf01bc699864 completed April 12, 2026, 2:40 p.m.
NED1 Entity disambiguation (via context triple) batch_69f739965ef081909e85881ce805bbb5 completed May 3, 2026, 12:03 p.m.
NEDg Description generation batch_69f740e536d48190af369b38aa42438d completed May 3, 2026, 12:34 p.m.
NED2 Entity disambiguation (via description) batch_69f741b72d08819087808bf9bcffa0a1 completed May 3, 2026, 12:38 p.m.
Created at: April 9, 2026, 9:40 p.m.