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.