Triple

T14265464
Position Surface form Disambiguated ID Type / Status
Subject Stefan Mazurkiewicz E353631 entity
Predicate notableWork P4 FINISHED
Object 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.
E1090239 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 theorem | Statement: [Stefan Mazurkiewicz, notableWork, Mazurkiewicz–Sierpiński theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Mazurkiewicz–Sierpiński theorem
Context triple: [Stefan Mazurkiewicz, notableWork, Mazurkiewicz–Sierpiński theorem]
  • A. Szekeres–Lindström theorem
    The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
  • B. Alexandrov–Hausdorff theorem
    The Alexandrov–Hausdorff theorem is a result in descriptive set theory that characterizes analytic sets as continuous images of Baire space, playing a key role in the study of definable sets in Polish spaces.
  • C. Knaster–Kuratowski–Mazurkiewicz lemma
    The Knaster–Kuratowski–Mazurkiewicz lemma is a fundamental result in combinatorial topology that guarantees the existence of a point common to a family of closed sets covering a simplex under certain intersection conditions, and underlies several fixed-point theorems.
  • D. 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.
  • E. Jarník–Besicovitch theorem
    The Jarník–Besicovitch theorem is a fundamental result in metric number theory that determines the Hausdorff dimension of sets of real numbers that are very well approximable by rationals.
  • 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 theorem
Triple: [Stefan Mazurkiewicz, notableWork, Mazurkiewicz–Sierpiński theorem]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Mazurkiewicz–Sierpiński theorem
Target entity description: 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.
  • A. Szekeres–Lindström theorem
    The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
  • B. Alexandrov–Hausdorff theorem
    The Alexandrov–Hausdorff theorem is a result in descriptive set theory that characterizes analytic sets as continuous images of Baire space, playing a key role in the study of definable sets in Polish spaces.
  • C. Knaster–Kuratowski–Mazurkiewicz lemma
    The Knaster–Kuratowski–Mazurkiewicz lemma is a fundamental result in combinatorial topology that guarantees the existence of a point common to a family of closed sets covering a simplex under certain intersection conditions, and underlies several fixed-point theorems.
  • D. 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.
  • E. Jarník–Besicovitch theorem
    The Jarník–Besicovitch theorem is a fundamental result in metric number theory that determines the Hausdorff dimension of sets of real numbers that are very well approximable by rationals.
  • 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.