Triple

T14265465
Position Surface form Disambiguated ID Type / Status
Subject Stefan Mazurkiewicz E353631 entity
Predicate notableWork P4 FINISHED
Object Mazurkiewicz–Sierpiński paradox
The Mazurkiewicz–Sierpiński paradox is a result in set-theoretic geometry showing that a sphere can be decomposed and reassembled in a counterintuitive way, illustrating the existence of paradoxical decompositions similar to the Banach–Tarski paradox.
E1091124 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: Mazurkiewicz–Sierpiński paradox | Statement: [Stefan Mazurkiewicz, notableWork, Mazurkiewicz–Sierpiński paradox]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Mazurkiewicz–Sierpiński paradox
Context triple: [Stefan Mazurkiewicz, notableWork, Mazurkiewicz–Sierpiński paradox]
  • A. Banach–Tarski paradox
    The Banach–Tarski paradox is a theorem in set-theoretic geometry stating that a solid ball in 3‑dimensional space can be decomposed into finitely many non-measurable pieces and reassembled into two identical copies of the original ball, highlighting counterintuitive consequences of the axiom of choice.
  • B. Mazurkiewicz–Sierpiński theorem
    The Mazurkiewicz–Sierpiński theorem is a result in topology and measure theory that characterizes certain properties of measurable sets and mappings, particularly concerning continuous images of sets in Euclidean spaces.
  • C. Sierpiński set
    The Sierpiński set is a subset of the real numbers with the property that it intersects every uncountable closed subset of the reals in only countably many points, illustrating extreme pathological behavior in set theory and real analysis.
  • D. Banach–Mazur game
    The Banach–Mazur game is an infinite two-player topological game used to characterize properties such as Baire category and completeness in metric and topological spaces.
  • E. Steinhaus theorem
    The Steinhaus theorem is a fundamental result in measure theory stating that the difference set of any subset of the real numbers with positive Lebesgue measure contains an open interval around zero.
  • 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: Mazurkiewicz–Sierpiński paradox
Triple: [Stefan Mazurkiewicz, notableWork, Mazurkiewicz–Sierpiński paradox]
Generated description
The Mazurkiewicz–Sierpiński paradox is a result in set-theoretic geometry showing that a sphere can be decomposed and reassembled in a counterintuitive way, illustrating the existence of paradoxical decompositions similar to the Banach–Tarski paradox.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Mazurkiewicz–Sierpiński paradox
Target entity description: The Mazurkiewicz–Sierpiński paradox is a result in set-theoretic geometry showing that a sphere can be decomposed and reassembled in a counterintuitive way, illustrating the existence of paradoxical decompositions similar to the Banach–Tarski paradox.
  • A. Banach–Tarski paradox
    The Banach–Tarski paradox is a theorem in set-theoretic geometry stating that a solid ball in 3‑dimensional space can be decomposed into finitely many non-measurable pieces and reassembled into two identical copies of the original ball, highlighting counterintuitive consequences of the axiom of choice.
  • B. Mazurkiewicz–Sierpiński theorem
    The Mazurkiewicz–Sierpiński theorem is a result in topology and measure theory that characterizes certain properties of measurable sets and mappings, particularly concerning continuous images of sets in Euclidean spaces.
  • C. Sierpiński set
    The Sierpiński set is a subset of the real numbers with the property that it intersects every uncountable closed subset of the reals in only countably many points, illustrating extreme pathological behavior in set theory and real analysis.
  • D. Banach–Mazur game
    The Banach–Mazur game is an infinite two-player topological game used to characterize properties such as Baire category and completeness in metric and topological spaces.
  • E. Steinhaus theorem
    The Steinhaus theorem is a fundamental result in measure theory stating that the difference set of any subset of the real numbers with positive Lebesgue measure contains an open interval around zero.
  • 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_69fd3d150b188190a0858ab94f81d9a8 completed May 8, 2026, 1:32 a.m.
NEDg Description generation batch_69fd3e13914c81908f4dcda7f0f6a927 completed May 8, 2026, 1:36 a.m.
NED2 Entity disambiguation (via description) batch_69fd3ee3f66081909301276aeee05350 completed May 8, 2026, 1:39 a.m.
Created at: April 10, 2026, 1:09 a.m.