Fixed partners and cell totals forced a negative density slope on choice similarity in 103 I-to-E pairs from one mouse parietal cortex

We tested whether extra synapses were needed for a negative relation between choice similarity and synapse density in one mouse parietal cortex. Prior SCI reports found different results for count and density scores. We extended that work in 103 inhibitory-to-excitatory pairs with 156 synapses. Density was count divided by measured axon-dendrite overlap. A calculation with one synapse per observed pair gave 78.8% of the recorded slope. We kept partners and each cell's count totals fixed. Complete enumeration gave 17,151 feasible tables. Every table had a negative slope. The full slope could range only from -0.050254 to -0.006548 per micrometre per similarity unit; the recorded slope was -0.028219. A rational dual certificate confirmed the negative upper bound without a probability model. The sign remained forced after each of nine sources or 66 targets was removed. Under an overlap-weighted conditional Poisson reference, the recorded extra-count slope had an exact lower-tail probability of 0.138732. Equal pair weights gave 0.514761. The partner-fixed E-to-I panel had only one feasible table and supplied no extra-allocation test. The result places the negative sign in the recorded partners, geometry, and cell totals. Those features can contain real biological selectivity. The study does not test conductance, causal task effects, or variation across animals. Code, all feasible tables, certificates, source hashes, figures, and repeat instructions are preserved.

connectome · posterior parietal cortex · choice selectivity · synapse density · partner identity · conditional count tables · linear bounds · structure and function