Known uniform partial gap block gives lower DC self response bounds with hidden cells in passive reciprocal models with fixed gains

We asked whether partial gap block can limit a full-block response when some cells are hidden. We prove a lower self response bound for passive reciprocal linear models at DC and nonnegative real Laplace rates. The block fraction must be known and uniform. Cell properties and positive input and output gains must stay fixed. Two complete square port maps are required. Schur complement concavity makes their inverse secant forecast a lower response bound. Stronger measured block tightens the bound. We derive the exact hidden-load term for global gap removal. A two-cell family has the same intact and half-block maps but permits every full-block self response above 6/7 in chosen units. Thus those maps alone give no finite upper limit. We checked 1,620 settings on 302 Cook worm neural slots and 1,091 electrical pairs, plus 96 local-block settings. Matrix order held to roundoff. At DC and gap scale 0.8, median panel-mean shortfall for 20 ports fell from 8.37% at quarter block to 5.40% at three-quarter block. A noisy-data tool gives conditional lower certificates from supplied error limits. Exact examples show failure for directed chemical coupling, changing gains, cross entries and sine response magnitude. These are proof and chosen-model results, not measured animal block effects. A clean repeat matched nine core result files. The package preserves code, facts, source hashes, proof, full results, figures and repeat steps.

gap junction · partial block · hidden neurons · response bound · connectome · passive circuit · Schur complement · Caenorhabditis elegans