Kakutani skyscraper construction
E665941
Kakutani skyscraper construction is a method in ergodic theory for building measure-preserving transformations by stacking intervals into “skyscrapers” to analyze and classify dynamical systems.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Kakutani skyscraper construction canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7449403 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Kakutani skyscraper construction Context triple: [Kakutani equivalence in ergodic theory, relatedTo, Kakutani skyscraper construction]
-
A.
Kenzo Tange building
The Yamanashi Press and Broadcasting Center is a modernist concrete building in Kōfu, Japan, designed by renowned architect Kenzo Tange and noted for its bold, sculptural form and Metabolist influences.
-
B.
Fuji Television Building
The Fuji Television Building is a landmark futuristic headquarters of Fuji TV in Tokyo, renowned for its striking modernist architecture featuring a prominent spherical observation deck.
-
C.
Umeda Sky Building
Umeda Sky Building is a landmark high-rise complex in Osaka, Japan, known for its striking twin-tower design connected by a rooftop observatory with panoramic city views.
-
D.
Namba Parks Tower
Namba Parks Tower is a high-rise office and commercial building in Osaka, Japan, integrated into the Namba Parks complex known for its distinctive terraced rooftop gardens and mixed-use urban design.
-
E.
Kobe Harborland Center Building
Kobe Harborland Center Building is a commercial high-rise complex in Kobe, Japan, featuring offices, shops, and entertainment facilities within the Kobe Harborland waterfront district.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Kakutani skyscraper construction Target entity description: Kakutani skyscraper construction is a method in ergodic theory for building measure-preserving transformations by stacking intervals into “skyscrapers” to analyze and classify dynamical systems.
-
A.
Kenzo Tange building
The Yamanashi Press and Broadcasting Center is a modernist concrete building in Kōfu, Japan, designed by renowned architect Kenzo Tange and noted for its bold, sculptural form and Metabolist influences.
-
B.
Fuji Television Building
The Fuji Television Building is a landmark futuristic headquarters of Fuji TV in Tokyo, renowned for its striking modernist architecture featuring a prominent spherical observation deck.
-
C.
Umeda Sky Building
Umeda Sky Building is a landmark high-rise complex in Osaka, Japan, known for its striking twin-tower design connected by a rooftop observatory with panoramic city views.
-
D.
Namba Parks Tower
Namba Parks Tower is a high-rise office and commercial building in Osaka, Japan, integrated into the Namba Parks complex known for its distinctive terraced rooftop gardens and mixed-use urban design.
-
E.
Kobe Harborland Center Building
Kobe Harborland Center Building is a commercial high-rise complex in Kobe, Japan, featuring offices, shops, and entertainment facilities within the Kobe Harborland waterfront district.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
construction in ergodic theory
ⓘ
method in dynamical systems ⓘ |
| appliedIn |
classification of measure-preserving transformations
ⓘ
ergodic decomposition problems ⓘ symbolic dynamics via tower representations ⓘ |
| assumes |
measurable transformation
ⓘ
sigma-finite measure space ⓘ |
| constructionStep |
define a transformation that moves points up the tower
ⓘ
define return times to the base set ⓘ identify the top of each column with the base via the induced map ⓘ partition a base set into subintervals or subsets ⓘ stack copies of the base according to return times ⓘ |
| domain |
probability space
ⓘ
standard measure space ⓘ |
| field |
dynamical systems
ⓘ
ergodic theory ⓘ measure theory ⓘ |
| historicalContext | introduced in mid-20th century ergodic theory ⓘ |
| mathematicalArea |
analysis
ⓘ
probability theory on dynamical systems ⓘ pure mathematics ⓘ |
| namedAfter | Shizuo Kakutani ⓘ |
| output |
measure-preserving transformation on a tower
ⓘ
skyscraper representation of a transformation ⓘ |
| property |
preserves the underlying measure by construction
ⓘ
represents transformations as stacks of intervals or sets ⓘ |
| purpose |
to analyze dynamical systems
ⓘ
to build measure-preserving transformations ⓘ to classify measure-preserving transformations ⓘ |
| relatedTo |
Kakutani equivalence
ⓘ
linked to:
Kakutani equivalence in ergodic theory
Rokhlin lemma ⓘ
linked to:
Kakutani–Rokhlin towers
cutting and stacking construction ⓘ induced transformations in ergodic theory ⓘ |
| usedFor |
comparing measure-preserving systems up to Kakutani equivalence
ⓘ
constructing examples of ergodic transformations ⓘ constructing examples of non-isomorphic but Kakutani equivalent systems ⓘ studying orbit structure of transformations ⓘ |
| usesConcept |
Poincaré recurrence
ⓘ
linked to:
Poincaré recurrence theorem
Rokhlin tower ⓘ induced transformation ⓘ interval partition ⓘ measure-preserving transformation ⓘ return time ⓘ tower decomposition ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Kakutani skyscraper construction Description of subject: Kakutani skyscraper construction is a method in ergodic theory for building measure-preserving transformations by stacking intervals into “skyscrapers” to analyze and classify dynamical systems.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.