my grandfather's axe

When I was an undergrad in the seminary, we studied epistemology in year two. One of the questions posed was about an item's identity, and the thought experiment, as I remember it, was called "My Grandfather's Axe".

It goes like this: My grandfather bought an axe as a young man. Through the course of his life, he changed the handle four times, and the head once. When my father got it, he changed the handle twice and the head once. Now I have it, and I've changed the head once and I'm on my second handle.

The question is, is it still my grandfather's axe? And if not, when did it stop being my grandfather's axe? In my family, it's still my grandfather's axe, and woe betide the upstart who says otherwise.

I built the Yellow Maserati from a frame I bought online. Initially all the parts except the fork and headset were cannibalized from a Giant bike that was my first bike as an adult (the carbon fork had developed a crack, which cave me the excuse to buy the frame and fork).

But I've replaced every part... and I mean EVERY part... except the frame, fork, and headset, and the cyclocross brake levers on the tops of the handlebars. New wheels, replacement cranks and bottom bracket, even new bottle cages. I've replaced the shifting system twice. Is it still the same bike?

I'd say what keeps the bike's identity is the frame. No matter what you hang on the frame, if it's still the same frame, it's still the same bike. And that IS the single highest-cost item on this bike, if that makes any difference (a discussion on my bike club's Facebook page about wheels reminds me that, on some bikes, the wheelset may be of higher cost than the frame... and even some higher-end shifting systems might cost more than the frames on which they are hung, although that's a rarefied biking atmosphere into which I will probably never venture).

Is it still the same frame if it's repainted? How about if it's repaired, especially if it's repaired badly and the ride quality is fundamentally changed? Frames are not modular, so one doesn't change part of a frame, or you would run down an even deeper and more convoluted rabbit hole of how much of a frame one could replace before it's not the same bike.

I'm waiting for a bearing to come in to fix the steerer. It's a tiny part, but it got me wondering.