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.