Triple

T7251386
Position Surface form Disambiguated ID Type / Status
Subject Poincaré–Birkhoff fixed-point theorem E157608 entity
Predicate alsoKnownAs P39 FINISHED
Object Poincaré–Birkhoff 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 theorem | Statement: [Poincaré–Birkhoff fixed-point theorem, alsoKnownAs, Poincaré–Birkhoff theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Poincaré–Birkhoff theorem
Context triple: [Poincaré–Birkhoff fixed-point theorem, alsoKnownAs, Poincaré–Birkhoff 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. Poincaré–Hopf theorem
    The Poincaré–Hopf theorem is a fundamental result in differential topology that relates the sum of the indices of a vector field’s isolated zeros on a compact manifold to the manifold’s Euler characteristic.
  • 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. 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.
  • 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_69c7d3a7502081909d2a97a60cc445ae completed March 28, 2026, 1:12 p.m.
Created at: March 27, 2026, 2:56 p.m.