Triple
T16571017
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Bronisław Knaster |
E402583
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Knaster–Reichbach covering
The Knaster–Reichbach covering is a construction in set-theoretic topology used to extend homeomorphisms between dense subsets of Polish spaces to global homeomorphisms.
|
E1221301
|
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: Knaster–Reichbach covering | Statement: [Bronisław Knaster, notableWork, Knaster–Reichbach covering]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Knaster–Reichbach covering Context triple: [Bronisław Knaster, notableWork, Knaster–Reichbach covering]
-
A.
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.
-
B.
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.
-
C.
Cover’s theorem
Cover’s theorem is a result in statistical pattern recognition stating that data cast nonlinearly into a higher-dimensional space is more likely to be linearly separable than in a lower-dimensional space.
-
D.
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.
-
E.
Kuratowski’s closure-complement problem
Kuratowski’s closure-complement problem is a classic result in topology that determines the maximum number of distinct sets obtainable from a subset of a topological space by repeatedly applying closure and complement operations.
- 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: Knaster–Reichbach covering Triple: [Bronisław Knaster, notableWork, Knaster–Reichbach covering]
Generated description
The Knaster–Reichbach covering is a construction in set-theoretic topology used to extend homeomorphisms between dense subsets of Polish spaces to global homeomorphisms.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Knaster–Reichbach covering Target entity description: The Knaster–Reichbach covering is a construction in set-theoretic topology used to extend homeomorphisms between dense subsets of Polish spaces to global homeomorphisms.
-
A.
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.
-
B.
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.
-
C.
Cover’s theorem
Cover’s theorem is a result in statistical pattern recognition stating that data cast nonlinearly into a higher-dimensional space is more likely to be linearly separable than in a lower-dimensional space.
-
D.
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.
-
E.
Kuratowski’s closure-complement problem
Kuratowski’s closure-complement problem is a classic result in topology that determines the maximum number of distinct sets obtainable from a subset of a topological space by repeatedly applying closure and complement operations.
- 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_69d8838648088190acf97ef11fc3f61b |
completed | April 10, 2026, 4:58 a.m. |
| NER | Named-entity recognition | batch_69e35958d49c8190b995188240fb355b |
completed | April 18, 2026, 10:13 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a006ee8812c81908ef74636bf39d44a |
completed | May 10, 2026, 11:41 a.m. |
| NEDg | Description generation | batch_6a0070024cb4819092ee0ce1320f0905 |
completed | May 10, 2026, 11:46 a.m. |
| NED2 | Entity disambiguation (via description) | batch_6a00707959a081909fc04947624abbe5 |
completed | May 10, 2026, 11:48 a.m. |
Created at: April 10, 2026, 5:16 a.m.