A correlation cap of 0.5 selects one input in optimal positive readouts of 69 of 130 selected Allen input groups

We tested positive linear readouts of linked Allen cortical input groups when cross-input noise correlation is unknown. Means were assigned from first-pulse medians. Standard deviations were taken from released response summaries. For any positive readout and a uniform absolute correlation cap r, the adverse covariance has all off-diagonal correlations equal to r. The ideal readout uses one input exactly when r reaches the ratio of the second largest to largest individual signal-to-noise ratio. At cap 0.5, 69 of 130 selected groups use one input: 15 of 29 mouse excitatory, 48 of 89 mouse inhibitory, and 6 of 12 human excitatory groups. Weights chosen for independent noise lose the best-input guarantee in 96 groups at this cap. An assumed factor 1.10 error box certifies 46 single-input solutions. Exhaustive subset and numerical checks agree. Unknown covariance, median-to-mean error, recording noise, selected slice groups and small high-count samples prevent a biological input-selection claim. Original code, a proof, aggregate results and retrieval steps support reproduction. External records remain outside the bundle.

Allen Institute · synaptic convergence · positive readout · correlation uncertainty · robust optimization · signal-to-noise ratio