The existence of a pair of elements with spacing of less than 1 / K is the crux of the proof. The rest is just a bit of manipulation to relate these elements to a rational approximation of the starting number r.
Bringing along the newer Tensor G5 processor might have potentially helped with battery life, though. The battery life on Pixel 10a isn't bad by any means, but it isn't noticeably better than Pixel 9a, either. The cell size is the same, and Google still rates it for about 30 hours of usage, which you can easily get as long as you don't do too much YouTubing or other battery-intensive activities. My charges lasted closer to 24 hours, which is acceptable for a $500 phone but not remarkable.
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