Triple

T11219432
Position Surface form Disambiguated ID Type / Status
Subject Milnor–Thurston kneading theory E265519 entity
Predicate relatedTo P37 FINISHED
Object Sharkovsky ordering
Sharkovsky ordering is a specific total ordering of the natural numbers used in one-dimensional dynamical systems to characterize the coexistence and implications of periodic orbits.
E911356 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: Sharkovsky ordering | Statement: [Milnor–Thurston kneading theory, relatedTo, Sharkovsky ordering]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Sharkovsky ordering
Context triple: [Milnor–Thurston kneading theory, relatedTo, Sharkovsky ordering]
  • A. Ulam sequence
    The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
  • B. Smale horseshoe
    The Smale horseshoe is a fundamental example in dynamical systems theory that illustrates chaotic behavior through a specific stretching-and-folding map of a square into a horseshoe-shaped region.
  • C. Denjoy–Young–Saks theorem
    The Denjoy–Young–Saks theorem is a result in real analysis that classifies the possible behaviors of the derivative of a real function at almost every point on the real line.
  • D. 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.
  • E. Erdős–Szekeres theorem
    The Erdős–Szekeres theorem is a fundamental result in combinatorial geometry that guarantees the existence of large convex polygons within sufficiently large sets of points in the plane in general position.
  • 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: Sharkovsky ordering
Triple: [Milnor–Thurston kneading theory, relatedTo, Sharkovsky ordering]
Generated description
Sharkovsky ordering is a specific total ordering of the natural numbers used in one-dimensional dynamical systems to characterize the coexistence and implications of periodic orbits.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Sharkovsky ordering
Target entity description: Sharkovsky ordering is a specific total ordering of the natural numbers used in one-dimensional dynamical systems to characterize the coexistence and implications of periodic orbits.
  • A. Ulam sequence
    The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
  • B. Smale horseshoe
    The Smale horseshoe is a fundamental example in dynamical systems theory that illustrates chaotic behavior through a specific stretching-and-folding map of a square into a horseshoe-shaped region.
  • C. Denjoy–Young–Saks theorem
    The Denjoy–Young–Saks theorem is a result in real analysis that classifies the possible behaviors of the derivative of a real function at almost every point on the real line.
  • D. 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.
  • E. Erdős–Szekeres theorem
    The Erdős–Szekeres theorem is a fundamental result in combinatorial geometry that guarantees the existence of large convex polygons within sufficiently large sets of points in the plane in general position.
  • 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_69d6aac59460819089b9848b27f57848 completed April 8, 2026, 7:21 p.m.
NER Named-entity recognition batch_69d7e8eb84c48190b4f3bede254afde2 completed April 9, 2026, 5:59 p.m.
NED1 Entity disambiguation (via context triple) batch_69e4976f38788190855aed6338d819b7 completed April 19, 2026, 8:50 a.m.
NEDg Description generation batch_69e49d37989881909c7e75ddfff06726 completed April 19, 2026, 9:15 a.m.
NED2 Entity disambiguation (via description) batch_69e49f41a1f8819087cc15527dc7ff63 completed April 19, 2026, 9:24 a.m.
Created at: April 8, 2026, 9:30 p.m.