You're certainly right that formal definitions are important. However, on this forum, I think informality can be appropriate. Though there are variations and in

You're certainly right that formal definitions are important. However, on this forum, I think informality can be appropriate. Though there are variations and inconsistencies, in the theoretical cryptography community, second preimage resistance is most often formalized as "universal one-wayness" and preimage resistance is formalized as "one-wayness." I did however was careless when I claimed that shrinking by 1 bit suffices for preimage resistance. The hash function needs to shrink by at least log(n) bits to rule out computationally-bounded adversaries finding preimages. Also, apologies for the formatting of my OP - I don't post here often.