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.