Triple

T12071204
Position Surface form Disambiguated ID Type / Status
Subject Zermelo recurrence objection E287425 entity
Predicate usesConcept P531 FINISHED
Object Poincaré recurrence theorem E156189 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 recurrence theorem | Statement: [Zermelo recurrence objection, usesConcept, Poincaré recurrence theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Poincaré recurrence theorem
Context triple: [Zermelo recurrence objection, usesConcept, Poincaré recurrence theorem]
  • A. Poincaré recurrence theorem chosen
    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.
  • B. 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.
  • C. 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.
  • D. Poincaré separation theorem
    The Poincaré separation theorem is a result in linear algebra and spectral theory that characterizes how the eigenvalues of a symmetric matrix relate to those of its principal submatrices, closely connected to eigenvalue interlacing phenomena.
  • E. ergodic theorem
    The ergodic theorem is a fundamental result in dynamical systems and probability theory that links long-term time averages of a system’s evolution to ensemble or space averages, underpinning the statistical behavior of many physical and stochastic processes.
  • 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_69d6ab4846e081908ee7bbd66a6d3459 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d9045a507081909070ea37173d6f97 completed April 10, 2026, 2:08 p.m.
NED1 Entity disambiguation (via context triple) batch_69f5f65ccc788190942e16c56f2a495f completed May 2, 2026, 1:04 p.m.
Created at: April 8, 2026, 9:48 p.m.