Triple

T14265439
Position Surface form Disambiguated ID Type / Status
Subject Wacław Sierpiński E353630 entity
Predicate notableIdea P4 FINISHED
Object Sierpiński graph
The Sierpiński graph is a self-similar, fractal-like graph structure closely related to the Sierpiński triangle and studied in graph theory and fractal geometry.
E1090237 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: Sierpiński graph | Statement: [Wacław Sierpiński, notableIdea, Sierpiński graph]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Sierpiński graph
Context triple: [Wacław Sierpiński, notableIdea, Sierpiński graph]
  • A. Sierpiński carpet
    The Sierpiński carpet is a classic two-dimensional fractal formed by repeatedly removing central squares from a larger square, resulting in a highly intricate, self-similar pattern with zero area but infinite perimeter.
  • B. Menger sponge
    The Menger sponge is a classic three-dimensional fractal object characterized by infinite surface area and zero volume, constructed by recursively removing cubes from a larger cube.
  • C. Cayley graph
    A Cayley graph is a graphical representation of a group where vertices correspond to group elements and edges represent multiplication by chosen generators, widely used in group theory and geometric group theory.
  • D. 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.
  • E. Szekeres snark
    The Szekeres snark is a famous cubic graph in graph theory that serves as a counterexample in edge-coloring problems and helped advance the study of snark graphs.
  • 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: Sierpiński graph
Triple: [Wacław Sierpiński, notableIdea, Sierpiński graph]
Generated description
The Sierpiński graph is a self-similar, fractal-like graph structure closely related to the Sierpiński triangle and studied in graph theory and fractal geometry.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Sierpiński graph
Target entity description: The Sierpiński graph is a self-similar, fractal-like graph structure closely related to the Sierpiński triangle and studied in graph theory and fractal geometry.
  • A. Sierpiński carpet
    The Sierpiński carpet is a classic two-dimensional fractal formed by repeatedly removing central squares from a larger square, resulting in a highly intricate, self-similar pattern with zero area but infinite perimeter.
  • B. Menger sponge
    The Menger sponge is a classic three-dimensional fractal object characterized by infinite surface area and zero volume, constructed by recursively removing cubes from a larger cube.
  • C. Cayley graph
    A Cayley graph is a graphical representation of a group where vertices correspond to group elements and edges represent multiplication by chosen generators, widely used in group theory and geometric group theory.
  • D. 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.
  • E. Szekeres snark
    The Szekeres snark is a famous cubic graph in graph theory that serves as a counterexample in edge-coloring problems and helped advance the study of snark graphs.
  • 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_69d8278c43e08190824146f4632b89a5 completed April 9, 2026, 10:26 p.m.
NER Named-entity recognition batch_69de6357a8188190ba518a486521052b completed April 14, 2026, 3:55 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd326551b08190ae8fe220a6422339 completed May 8, 2026, 12:46 a.m.
NEDg Description generation batch_69fd3417e8e88190b099bfe4ba30f364 completed May 8, 2026, 12:53 a.m.
NED2 Entity disambiguation (via description) batch_69fd37df3dfc8190a594abb2c14e11bb completed May 8, 2026, 1:09 a.m.
Created at: April 10, 2026, 1:09 a.m.