Triple

T7251385
Position Surface form Disambiguated ID Type / Status
Subject Poincaré–Birkhoff fixed-point theorem E157608 entity
Predicate influenceOn P1994 FINISHED
Object KAM theory E320432 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: KAM theory | Statement: [Poincaré–Birkhoff fixed-point theorem, influenceOn, KAM theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: KAM theory
Context triple: [Poincaré–Birkhoff fixed-point theorem, influenceOn, KAM theory]
  • A. Kolmogorov–Arnold–Moser theory chosen
    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. Milnor–Thurston kneading theory
    Milnor–Thurston kneading theory is a mathematical framework in one-dimensional dynamical systems that encodes the combinatorial behavior of interval maps to study their dynamics and entropy.
  • C. 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.
  • D. Kakutani equivalence in ergodic theory
    Kakutani equivalence in ergodic theory is a notion of equivalence between measure-preserving dynamical systems based on the isomorphism of their induced transformations on subsets of positive measure.
  • E. Young tower construction in nonuniformly hyperbolic dynamics
    "Young tower construction in nonuniformly hyperbolic dynamics" is a foundational work in dynamical systems that introduced a powerful tower-based method for analyzing statistical properties such as decay of correlations and limit theorems in nonuniformly hyperbolic systems.
  • 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.