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.