Impagliazzo, Paturi and Calabro, Impagliazzo, Paturi introduced Exponential-Time Hypothesis (ETH) and Strongly Exponential-Time Hypothesis (SETH). Roughly, SETH says that there is no algorithm which solves SAT in time $1.99^n$.
I was wondering what would that mean to break SETH. We definitely need to find an algorithm which solves SAT in fewer than $2^n$ steps, but I don't quite understand what computational model we should use. As far as I know, results based on SETH (see, e.g., Cygan, Dell, Lokshtanov, Marx, Nederlof, Okamoto, Paturi, Saurabh, Wahlstrom) don't need to make assumptions about the underlying model of computation.
Assume, for example, that we found an algorithm which solves SAT in time $1.5^n$ using space $1.5^n$. Does it automatically imply that we can find a Turing Machine which solves this problem in time $1.99^n$? Does it break SETH?