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What's the problem with adding more tape as needed? You don't need a literally infinite tape to have infinite tape from the machine's POV.

Linux already overcommits memory so much you can imaging it's infinite, the big show-stopper is the 64 bit integers used to track it. We'd need infinite pointer sizes before we could meaningfully use infinite tape.

Good thing is there is no halting problem when using 64bit pointers.

Turing machines don't have pointers, just offsets from the current position. Since you can't move infinite steps, you can still use finite offsets.

GP probably meant something among the lines of: "What is the most nested turing complete system ever built"

You are correct, this is what I meant.

I've found "self-interpreter" implementations that aim to be short

https://arxiv.org/html/cs/0311032

https://codegolf.stackexchange.com/questions/585/self-interp...

But I haven't found anyone yet that optimized for actual number of recursive implementations on a real machine.

Can you prove that statement in finite time?