Triple

T7648138
Position Surface form Disambiguated ID Type / Status
Subject Alexandrov compactification E173177 entity
Predicate relatedConcept P37 FINISHED
Object Freudenthal compactification
The Freudenthal compactification is a topological construction that extends a non-compact, locally compact space by adding a boundary of “ends” to obtain a compact space that more finely captures its asymptotic structure than the one-point (Alexandrov) compactification.
E679314 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: Freudenthal compactification | Statement: [Alexandrov compactification, relatedConcept, Freudenthal compactification]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Freudenthal compactification
Context triple: [Alexandrov compactification, relatedConcept, Freudenthal compactification]
  • A. Alexandrov compactification
    The Alexandrov compactification is a topological construction that adds a single “point at infinity” to a non-compact space to make it compact.
  • B. Tychonoff theorem for products of compact spaces
    The Tychonoff theorem for products of compact spaces is a fundamental result in topology stating that any product of compact topological spaces is compact, a statement that is equivalent in strength to the axiom of choice.
  • C. Alexandrov–Hausdorff theorem
    The Alexandrov–Hausdorff theorem is a result in descriptive set theory that characterizes analytic sets as continuous images of Baire space, playing a key role in the study of definable sets in Polish spaces.
  • D. Hausdorff
    Hausdorff is a topological separation property requiring that any two distinct points in a space can be enclosed in disjoint open sets.
  • E. Alexandrov–Čech cohomology
    Alexandrov–Čech cohomology is a topological cohomology theory that computes invariants of spaces using inverse limits over open covers, closely related to and often coinciding with sheaf cohomology.
  • 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: Freudenthal compactification
Triple: [Alexandrov compactification, relatedConcept, Freudenthal compactification]
Generated description
The Freudenthal compactification is a topological construction that extends a non-compact, locally compact space by adding a boundary of “ends” to obtain a compact space that more finely captures its asymptotic structure than the one-point (Alexandrov) compactification.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Freudenthal compactification
Target entity description: The Freudenthal compactification is a topological construction that extends a non-compact, locally compact space by adding a boundary of “ends” to obtain a compact space that more finely captures its asymptotic structure than the one-point (Alexandrov) compactification.
  • A. Alexandrov compactification
    The Alexandrov compactification is a topological construction that adds a single “point at infinity” to a non-compact space to make it compact.
  • B. Tychonoff theorem for products of compact spaces
    The Tychonoff theorem for products of compact spaces is a fundamental result in topology stating that any product of compact topological spaces is compact, a statement that is equivalent in strength to the axiom of choice.
  • C. Alexandrov–Hausdorff theorem
    The Alexandrov–Hausdorff theorem is a result in descriptive set theory that characterizes analytic sets as continuous images of Baire space, playing a key role in the study of definable sets in Polish spaces.
  • D. Hausdorff
    Hausdorff is a topological separation property requiring that any two distinct points in a space can be enclosed in disjoint open sets.
  • E. Alexandrov–Čech cohomology
    Alexandrov–Čech cohomology is a topological cohomology theory that computes invariants of spaces using inverse limits over open covers, closely related to and often coinciding with sheaf cohomology.
  • 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_69c6995473348190a4f41d110d619a18 completed March 27, 2026, 2:51 p.m.
NER Named-entity recognition batch_69c6faf6328c8190bce0a3f8a17ef890 completed March 27, 2026, 9:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69c89ada2a54819098672d45ab56f784 completed March 29, 2026, 3:22 a.m.
NEDg Description generation batch_69c89b7c27988190b78be7f249bda554 completed March 29, 2026, 3:24 a.m.
NED2 Entity disambiguation (via description) batch_69c89c56d9688190bd14badc319f9c44 completed March 29, 2026, 3:28 a.m.
Created at: March 27, 2026, 3:58 p.m.