> The sequence `⌊.+` is an inner product chosen specifically to achieve this effect, with addition where multiplication would normally be, and ⌊ (min) where multiplication would normally be.

Sorry, it is early for me too. I am wondering if there is a mistake here. Do you mean that addition is where multiplication would be and min is where addition would be?

The regular inner product would be

  C_ij := \sum_k A_ik B_kj

and the modified one is

  C_ij := \min_k (A_ik + B_kj)

?