I would like to take a look at the default search centers page layout file of Sharepoint in the 15 hive. Anyone have any idea where it is located or how I can find it?
The page you are looking for is in this folder directory,
File is named as
Depending on the version (online/on premise) but if you goto the site settings (make sure you are top level) then site collection then Site Collection Administration then search settings it will tell you the Site Collection Search Results Page etc.
Hope this helps.