At fixed totals and order, pair counts forced 234 to 239 consecutive sets in one mouse table with six axons

We tested how much a group-order score adds after pairwise wiring is known. We used the Figure 5a mouse muscle source table from Meirovitch and colleagues. It has 297 target rows and six axon columns. We fixed the published order, each axon count and the target input counts. Those totals alone allowed zero to 297 consecutive input sets. Adding all 15 pair counts forced 234 to 239; the observed count was 235. Integer model tables attain both bounds. A path identity and three rare pair counts give a short proof. We also tested the 52 targets with three or four inputs. Their own pair counts and degrees fixed exactly 37 consecutive sets. We checked 359 alternative orders after removal of reversal. Each had a certified upper bound of at most 221 under the primary margins. The published order had at least 234 in every allowed table. Thus the group score and its best order follow closely from pairwise structure under these constraints. This result concerns one finite table and does not assume independent rows. It does not show that activity caused the pattern. The source omits single-input targets. We used no matched axon activity. The package has independent code, aggregate facts, exact certificates, integer witnesses, figures, source hashes and repeat instructions. Original source rows remain external under their source terms.

neuromuscular junction · connectome · axon order · co-innervation · pair counts · integer programming · exact certificate · structure and function