Cell time constants broke equal spectra in five of 19 matched Allen circuit model pairs

We tested whether equal spectra survive a change from common to cell-specific time constants in signed linear circuit models. We used published Allen slice connectivity graphs from 247 inferred mice and 17 inferred human donors. Ten graph sets gave 19 state pairs with matched wiring summaries and exact common-time spectra. Exact principal-minor tests showed that 14 pairs kept equal spectra for all positive cell time constants and all common gains. Five pairs in one mouse set did not. All 19 pairs kept equal spectra for arbitrary excitatory and inhibitory class time constants. In a selected six-cell example, doubling one cell time at gain 0.85 gave asymptotic decay rates of 0.0990392 and 0.1500000 per fast-cell time unit. Both models were stable. Independent integer and symbolic determinant checks passed. The result tests an assumed unit-weight model, not measured cell times or brain dynamics. Sparse selected circuits, inferred donors, absent activity linkage, and one human comparison limit biological inference. Original code, aggregate evidence, source hashes, and retrieval instructions support reproduction; external source records are not bundled.

Allen Institute · circuit structure · time constants · spectrum · principal minors · linear dynamics · exact certificate