To take the next step — and we’re close to the finish line! — note that the proof doesn’t put any constraint on the upper value of K. If we choose some definite K1, the proof establishes the existence of a single 2-good pair, which we can label a1 and b1. If we choose K2, it proves the existence of a pair we’ll call a2 and b2; that pair may or may not produce a functionally different approximation of r. Maybe there’s just a single solution that repeats for every K?
AMD could always decide to release higher-end processor options at a later date, but the fact is that it makes little financial sense to try to build mini gaming PCs around socket AM5 processors right now. These need pairs of fast DDR5 sticks to maximize their performance, and prices for fast DDR5 sticks have shot into the stratosphere over the past year. It’s hard to make any kind of gaming PC make financial sense right now, but the frames-per-second-per-dollar you get from a desktop iGPU make them particularly unappealing. This may explain why the CPUs are targeting business desktops first.
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