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.