One second to compute the largest Fibonacci number I can

Most of us are familiar with the Fibonacci sequence. What's the largest Fibonacci number you can compute in 1 second?
I'm not setting any world records, here; I don't own a supercomputer.

You can criticise my code here: https://github.com/SheafificationOfG/...

Addenda:
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At 7:59, the e_{01}s in the bottom row are incorrect... [in my defense, the Fibonacci transition matrix is symmetric]. Thanks ‪@andykhang404‬!
At 13:57 (as of 2024-09-16), the GitHub link has been moved! See above.
At 14:44, the formula for the coefficient of the product polynomial is incorrect; every instance of (N-1) should be replaced with an n in the summation on the right hand side... This error repeats at 15:14. Embarrassing! Thanks ‪@henryroyer7691‬!

Timestamps:
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00:00 - Introduction
01:06 - Recursion
02:35 - Memoisation
03:39 - "Linear" nonrecursive algorithm
04:31 - Matrix-based algorithm
05:57 - Things add up
08:20 - Fast exponentiation algorithm
10:07 - Grade-school multiplication
11:45 - Multiplication through division
14:38 - Discreet improvements
17:27 - Fast and Furious (wysi)
19:36 - Golden medallist
22:10 - Thx 4 watching
22:38 - The ugly truth