Triple

T1796817
Position Surface form Disambiguated ID Type / Status
Subject Mathematical Games E39621 entity
Predicate notableTopic P494 FINISHED
Object Penrose tilings
Penrose tilings are non-periodic tilings of the plane that use a small set of shapes to create patterns with fivefold symmetry and no translational repetition, widely studied in mathematics and physics.
E201323 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: Penrose tilings | Statement: [Mathematical Games, notableTopic, Penrose tilings]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Penrose tilings
Context triple: [Mathematical Games, notableTopic, Penrose tilings]
  • A. Kepler–Poinsot polyhedra
    The Kepler–Poinsot polyhedra are the four regular star polyhedra that extend the concept of Platonic solids into non-convex, self-intersecting forms.
  • B. Ulam spiral
    The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
  • C. Farey tessellation
    The Farey tessellation is a geometric partition of the hyperbolic plane into ideal triangles whose vertices correspond to rational numbers, closely linked to number theory and modular group actions.
  • D. Platonic solids
    Platonic solids are the five highly symmetrical, convex polyhedra (tetrahedron, cube, octahedron, dodecahedron, and icosahedron) that have identical regular polygonal faces and are fundamental in geometry and classical philosophy.
  • E. Archimedean solids
    Archimedean solids are a set of thirteen highly symmetric, semi-regular convex polyhedra characterized by identical vertices and faces composed of more than one type of regular polygon.
  • 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: Penrose tilings
Triple: [Mathematical Games, notableTopic, Penrose tilings]
Generated description
Penrose tilings are non-periodic tilings of the plane that use a small set of shapes to create patterns with fivefold symmetry and no translational repetition, widely studied in mathematics and physics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Penrose tilings
Target entity description: Penrose tilings are non-periodic tilings of the plane that use a small set of shapes to create patterns with fivefold symmetry and no translational repetition, widely studied in mathematics and physics.
  • A. Kepler–Poinsot polyhedra
    The Kepler–Poinsot polyhedra are the four regular star polyhedra that extend the concept of Platonic solids into non-convex, self-intersecting forms.
  • B. Ulam spiral
    The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
  • C. Farey tessellation
    The Farey tessellation is a geometric partition of the hyperbolic plane into ideal triangles whose vertices correspond to rational numbers, closely linked to number theory and modular group actions.
  • D. Platonic solids
    Platonic solids are the five highly symmetrical, convex polyhedra (tetrahedron, cube, octahedron, dodecahedron, and icosahedron) that have identical regular polygonal faces and are fundamental in geometry and classical philosophy.
  • E. Archimedean solids
    Archimedean solids are a set of thirteen highly symmetric, semi-regular convex polyhedra characterized by identical vertices and faces composed of more than one type of regular polygon.
  • 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_69a88632aa588190ba3978fde0db5bbd completed March 4, 2026, 7:21 p.m.
NER Named-entity recognition batch_69aa6566cd808190a67f33ad47d8ca8e completed March 6, 2026, 5:25 a.m.
NED1 Entity disambiguation (via context triple) batch_69adb5d6cee88190b26814134037aba6 completed March 8, 2026, 5:45 p.m.
NEDg Description generation batch_69adb8b626688190b4953d4549339dea completed March 8, 2026, 5:58 p.m.
NED2 Entity disambiguation (via description) batch_69adb9253fa08190bfb7d245208150c0 completed March 8, 2026, 6 p.m.
Created at: March 4, 2026, 7:32 p.m.