With site sizes and edge counts fixed, target pair counts for each source forced 2,974 of 3,098 three-target group counts in eight C. elegans brain maps

We tested whether counts for three targets at one chemical synapse site can change when smaller-group counts stay fixed. We used eight C. elegans brain maps from birth to adulthood. For each source neuron, we fixed all source-to-target site counts, all shared target pair counts and the number of sites of each target set size. Exact integer bounds forced 2,974 of 3,098 positive recorded triple counts, or 96.0 percent. The share ranged from 91.9 to 100 percent across maps. Forced keys held 3,293 of 3,432 triple incidences. The main search tested 3,607 possible keys. Of 509 zero recorded keys, 129 could become positive. All intervals had widths of at most three sites. An analysis restricted to sites with exactly three targets forced all 2,051 positive keys. Joining records at a shared source node forced 3,734 of 3,984 positive keys. A target pair count here is specific to one source. It is extra information beyond the ordinary connectome matrix. The result fixes group counts, not site locations. It does not show an absence of biological function or a population age effect. The package supplies code, source hashes, derived tables, exact rational certificates, integer witnesses, figures and repeat instructions. A solver-free checker verified all 10,307 intervals across the three scopes.

connectome · Caenorhabditis elegans · polyadic synapse · target grouping · integer programming · identifiability · exact certificate · hypergraph