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.