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It's an old track/path frame
You do know that's tautology, don't you? Path cycling is done on circuits closed to other traffic, and eventually became track cycling when circuits were built specifically for bicycles. A dual purpose bike is Road & Path, as is a cycling club which participates in both disciplines, although I think the only active one still designated as such is Redditch R&P CC
Yes! Nice bike. Seems like you have room for wider tyres, even with mudguards (which is rare). Are those 23s? Would love to fit 28c at the front of my track frame, but the clearances are too tight.