Breakage is broken merger, which doesn't merge, i.e. results in distinguishable states. Correctly implemented merger must produce indistinguishable states. If the substrate tries to implement merger, but fails, then the substrate is broken and doesn't implement computation.
>Implementation requires >= 1.
No, you require computation to work on a broken substrate, and that's an inadequate requirement. It's agreeable that your requirement isn't met and computation can't work on a broken substrate, but this doesn't imply that computation can't work on a working substrate.
We agree in intuition more than it seems you think we do. This paper is mapping the intuition to the philosophical discourse of substrate independence. Track its course from Putnam and Searle to Chalmers Shagrir and Anderson Piccinini, and you will see where it fits as a small contribution. The part we will keep on disagreeing though is calling whatever is inconvenient broken …
>Implementation requires >= 1.
No, you require computation to work on a broken substrate, and that's an inadequate requirement. It's agreeable that your requirement isn't met and computation can't work on a broken substrate, but this doesn't imply that computation can't work on a working substrate.