Shared sites changed variance gain limits by at most 0.0031 in eight nonnegative C. elegans count models with input normalization and independent 50% site success per step

We tested whether shared chemical synapse sites change a recurrent noise limit when all connection means and marginal laws stay equal. We used eight C. elegans maps and a fixed panel of 162 neurons. All weights were nonnegative. Counts were divided by target input totals, then scaled to give a mean spectral radius of one. Each site succeeded independently with probability 0.5 at each step. Shared incidences used one success variable; the comparison used separate variables. The critical gain for finite second moments changed by zero to 0.003092. Four maps had no change within 1e-10. Small components without internal shared-site noise set their full-graph limits. At gain 0.9, five maps had stable mean activity but no finite stationary covariance under unit independent additive input. The package gives an exact sparse covariance operator based on source and target-pair counts. It also gives a threshold-order proof, an exact three-cell example, source checks, sensitivity results, figures, and offline repeat code. All primary spectra passed direct and separate solver checks. Fresh source files rebuilt the reused factual tables exactly. These are conditional model results. The data do not measure release synchrony, release probability, gain, or activity noise. Boundary sampling, omitted inhibition, and assumed temporal independence limit biological interpretation.

connectome · polyadic synapse · shared transmission · activity variance · mean-square stability · C. elegans · covariance operator · reproducible method