Two known noise conditions recovered a fixed drift in six fly and mouse model tests with separate covariance eigenvalues

We tested whether two stationary covariance matrices identify directed circuit weights when known input noise changes and drift stays fixed. A matrix proof gives unique unrestricted drift if the generalized covariance eigenvalues are all distinct. Three distributed noise designs on each of two published structural graphs, with 75 fly regions and 304 Allen-based mouse parcels, met this numerical test. Exact simulated covariances gave relative drift errors below 1.7e-12. A uniform noise scale adds no information. A single-node change gave many eigenvalue gaps below numerical resolution. At a whitened covariance error bound of 0.001, a direct inverse gave median drift errors of 13.5% in fly and 23.3% in mouse. These are model tests, not fits to measured neural activity. Known noise, fixed drift, complete observation, and linear stationary dynamics are required. Code, proof, scalar results, a figure, and external-input retrieval instructions support reproduction.

connectome · covariance · identifiability · noise intervention · Allen Institute · linear dynamics