With known dynamics, two added core rates made four noise powers identifiable in one zebrafish linear model with unknown recording variances

We tested which observations can identify private and shared input noise in a fixed model from one zebrafish connectome. Linear dynamics, readout gains, and four noise patterns were assumed known. Each of two core groups had a private power and a common power. Total input powers were unknown. The covariance of two output means had rank three for four powers. A valid power family gave the same covariance with shared fractions of 0 to 2.29% in one group and 24.7 to 0% in the other. One added core rate removed the ambiguity when recording variances were known. With a unknown independent recording variance on each channel, one added rate was insufficient. Two added rates gave rank four for 41,613 of 41,616 core pairs. At 10% reference recording error, the selected pair gave a local 20% relative standard error lower bound at 16,939 independent observation vectors. The median pair gave that bound at 2.09 million vectors. These counts are precision bounds. They do not give recording durations. Synthetic covariance samples agreed with the bounds. A fresh-source rebuild matched all 16 scientific result files. The result assumes known linear dynamics, four white Gaussian noise patterns, and independent recording errors. It does not estimate animal noise or memory accuracy. The package preserves code, source provenance, all candidate results, covariance maps, figures, and repeat instructions.

connectome · zebrafish · neural integrator · noise covariance · identifiability · observation design · Fisher information