But improvisation is also a part of cooking. Maybe we couldn't find saffron for our paella - does that make it no longer paella? Maybe we never really liked our grandmother's meatballs and start making them differently - have we broken with tradition?
Afterall, every recipe evolved from improvisation at some point. As people moved around and environments changed, cooks all over the world had to make do with the ingredients they could find. They made little tweaks over the years until now we have a dishes like gumbo and falafel and Yorkshire pudding.
And this is all without counting the improvisation that comes when a cook is alone in the kitchen, tasting and seasoning as they go! A dish is very rarely exactly the same twice in a row.
Authenticity...what does that really mean?