Triple

T7251387
Position Surface form Disambiguated ID Type / Status
Subject Poincaré–Birkhoff fixed-point theorem E157608 entity
Predicate alsoKnownAs P39 FINISHED
Object Poincaré–Birkhoff twist theorem E157608 NE FINISHED

How this triple was built (2 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: Poincaré–Birkhoff twist theorem | Statement: [Poincaré–Birkhoff fixed-point theorem, alsoKnownAs, Poincaré–Birkhoff twist theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Poincaré–Birkhoff twist theorem
Context triple: [Poincaré–Birkhoff fixed-point theorem, alsoKnownAs, Poincaré–Birkhoff twist theorem]
  • A. Poincaré–Birkhoff fixed-point theorem chosen
    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. Poincaré–Bendixson theorem
    The Poincaré–Bendixson theorem is a fundamental result in the qualitative theory of dynamical systems that characterizes the possible long-term behaviors of trajectories in two-dimensional continuous flows, ruling out chaotic dynamics in the plane.
  • C. 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.
  • D. 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.
  • E. Bendixson–Dulac criterion
    The Bendixson–Dulac criterion is a result in the qualitative theory of planar dynamical systems that provides conditions under which a system has no periodic orbits in a given region.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69c6882d81d4819085f7ff862951ee4f completed March 27, 2026, 1:37 p.m.
NER Named-entity recognition batch_69c6ea791fec8190aee56ab4503770be completed March 27, 2026, 8:37 p.m.
NED1 Entity disambiguation (via context triple) batch_69c7db1278b08190bab9f01287040492 completed March 28, 2026, 1:43 p.m.
Created at: March 27, 2026, 2:56 p.m.