After some back and forth with AI, I think I understand: 1. The Exponential Time Hypothesis being false shows that 3SAT specifically is sub-exponential time 2. Any NP complete problem can be changed into 3SAT in polynomial time

Put these two together and you would think that they would mean that any NP complete problem can be solved in sub-exponential time. But this isn't necessarily true because changing the NP complete problem into 3SAT can increase the number of variables, which can theoretically negate the sub-exponential time.

P=NP -> 3SAT has a polynomial time algorithm

P=/=NP -> 3SAT has no polynomial-time algorithm

ETH is true -> 3SAT has no subexponential time algorithm

ETH is false -> 3SAT has a subexponential time algorithm

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ETH true -> P=/=NP

ETH false (!!!) -> P ?= NP remain unsolved

The algorithm's runtime is in faster growing than O(exp(n^a)) for any a < 1. It's not subexponential in the sense that factoring is, which I believe has a secondary exponent of 1/3 under the best algorithms.

It's still a big result, but it's mostly theoretical. It might help explain, structurally, why most SAT instances are far easier than an exponential model would indicate.

For example, a 2^√n subexponential algorithm then used on an input after a n^2 polynomial reduction from some other NP-complete language incurs a total running time of 2^√(n^2) = 2^n, which again is exponential.