I would however like to make one observation:
They're looking for both, actually, as well as quite a few other things -- probably because the more requirements they add, the more ways they can reject an application for addressing 99% of their topic, because it didn't cover a 1% side-issue they threw in.
Here are some examples of where they specifically require submissions to address biological issues:
[Applicants must provide] empirical correlation to the real world of biochemistry and molecular biology - not just mathematical or computer modelsAnd so on.[must address] The ability of the genome to convey instructions, deliver orders, and actually produce the needed biological end-products
[must address] The bizarre concentration of singlehanded optical isomers (homochirality of enantiomers) in living things
By "mechanism," the Foundation means a scenario of sequential, cause-and-effect (or at least "functionally dependent"), empirically correlated events explaining how genetic prescriptive information (instruction) arose naturally within Nature sufficient to give rise to current life.
Any scientific life-origins theory must connect with "life" as we observe it
The hypothetical mechanism must demonstrate correspondence with "the real world" of biochemistry
Parallel computer models must similarly have direct empirical correlation with naturally occurring environmental, chemical, biochemical, and molecular biological scenarios.
model addresses biochemical problems such as the instability and difficulty with which ribonucleotides are made and activated; exclusively 3'5' beta-D-ribonucleotide phosphodiester linkages are established rather than 2'5' or 5'5'; deleterious cross-reactions are avoided; hydrolysis is prevented; and other issues of prebiotic plausibility
Not only are submissions required to in effect explain all modern biology, but they are also required to be so comprehensive as to strike silent all possible concern about evolvability of any complex biological system whatsoever:
submission silences arguments of all-or-none "irreducible complexity" in evolving molecular machines and larger biosystemsAnd not only that, but the submission must be able to convince fans of "apparent design" that they are mistaken when they perceive "design" in any biological system (which needless to say goes vastly beyond merely demonstrating how life could have begun):
submission demonstrates that the "appearance or inference of design" in biosystems is only apparent rather than realAs I said earlier, the sponsors of the "prize" want to set the bar so high and difficult that they never have to pay out.
Math Links: I don't know how many of these links are publicly available. Some are.