What is the bare minimum quantity of classic automobile that needs to survive, to be authentic when restored?

A chassis and engine number would be a good start. Sometimes with with older cars even the rear axel can have a serial number. You give no indication as to what if any vehicle or age you are referring so it is more difficult to give a definitive answer.

From my point of view if part of the chassis exists and is repaired/rebuilt, then it is can be considered the Original chassis if you know the chassis number. Very often older vehicles were fitted with bodies by other manufacturers/Coach builders and therefore had their own body/build numbers.

This is an ancient paradox:

http://en.wikipedia.org/wiki/Ship_of_Theseus

Boyd Coddington of American Hotrod was prosecuted for registering 'new' cars as old so avoiding laws on pollution etc.

And of course, the many parts of an old car could spawn new versions, all with a claim to originality

In the UK, rebuilt cars are subject to a vehicle identity check, points are given for original items, chassis/body engine axle etc, requiring a minimum score to retain the original registration or the 'stigma' of a Q plate

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