Triple
T7685001
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Alexandrov–Hausdorff theorem |
E174093
|
entity |
| Predicate | relatesTo |
P37
|
FINISHED |
| Object |
Souslin operation
The Souslin operation is a set-theoretic construction that generates complex sets (notably analytic sets) from families of subsets of a topological space, playing a central role in descriptive set theory.
|
E681625
|
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: Souslin operation | Statement: [Alexandrov–Hausdorff theorem, relatesTo, Souslin operation]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Souslin operation Context triple: [Alexandrov–Hausdorff theorem, relatesTo, Souslin operation]
-
A.
Stone–Čech compactification
The Stone–Čech compactification is a construction in topology that associates to any topological space a universal, maximally extensive compact Hausdorff space into which it densely embeds.
-
B.
Cantor’s theorem
Cantor’s theorem is a fundamental result in set theory stating that the power set of any set has a strictly greater cardinality than the set itself, implying there is no largest infinity.
-
C.
Ky Fan’s lemma
Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
-
D.
continuum hypothesis
The continuum hypothesis is a central conjecture in set theory proposing a specific relationship between the sizes of the set of real numbers and the set of natural numbers, famously shown to be independent of the standard axioms of mathematics.
-
E.
Carathéodory’s extension theorem
Carathéodory’s extension theorem is a fundamental result in measure theory that guarantees a unique extension of a pre-measure defined on an algebra of sets to a complete measure on the generated σ-algebra.
- 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: Souslin operation Triple: [Alexandrov–Hausdorff theorem, relatesTo, Souslin operation]
Generated description
The Souslin operation is a set-theoretic construction that generates complex sets (notably analytic sets) from families of subsets of a topological space, playing a central role in descriptive set theory.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Souslin operation Target entity description: The Souslin operation is a set-theoretic construction that generates complex sets (notably analytic sets) from families of subsets of a topological space, playing a central role in descriptive set theory.
-
A.
Stone–Čech compactification
The Stone–Čech compactification is a construction in topology that associates to any topological space a universal, maximally extensive compact Hausdorff space into which it densely embeds.
-
B.
Cantor’s theorem
Cantor’s theorem is a fundamental result in set theory stating that the power set of any set has a strictly greater cardinality than the set itself, implying there is no largest infinity.
-
C.
Ky Fan’s lemma
Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
-
D.
continuum hypothesis
The continuum hypothesis is a central conjecture in set theory proposing a specific relationship between the sizes of the set of real numbers and the set of natural numbers, famously shown to be independent of the standard axioms of mathematics.
-
E.
Carathéodory’s extension theorem
Carathéodory’s extension theorem is a fundamental result in measure theory that guarantees a unique extension of a pre-measure defined on an algebra of sets to a complete measure on the generated σ-algebra.
- 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_69c6995840408190a19de6c51090f46f |
completed | March 27, 2026, 2:51 p.m. |
| NER | Named-entity recognition | batch_69c7022118908190a3a93cfda79be0a4 |
completed | March 27, 2026, 10:18 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c8a25c2a308190908ffdd2f0b7262f |
completed | March 29, 2026, 3:54 a.m. |
| NEDg | Description generation | batch_69c8a37c995881908c71791c6cc002f3 |
completed | March 29, 2026, 3:58 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69c8a3fe63a4819086bcb5f80cdbd30b |
completed | March 29, 2026, 4:01 a.m. |
Created at: March 27, 2026, 4:02 p.m.