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A fixed structural edit can preserve a spike sequence under one input and change it under another. We study this dependence using statistics-preserving edge swaps, controlled inputs and finite-horizon parameter certificates. The original 125-chunk numerical model is tested on ten artificial graphs from three connection rules. Despite identical total external drive at every slot, global and focal inputs change the visibility of 4--13 of nineteen fixed swaps per graph. A paired homogeneous and heterogeneous leaky integrate-and-fire validation in brian2-atlas reuses three originals and extends observation from 30 to 300 ms under a constant background drive sufficient for isolated-cell firing. Heterogeneous short-window switching persists, but by 300 ms every tested swap differs from its reference, saturating the binary visibility readout. Fixed-support weight families provide a complementary regional guarantee. Positive certified intervals cover 4,308 of 4,320 LIF direction conditions and include distinct floating-point configurations. A post hoc comparison finds a long-window failure inside the short-window certified interval in 710 of 720 heterogeneous conditions; 394 of 829 direction pairs ordered under both matched-drive inputs change order at 300 ms. Input-specific filtering and threshold-margin scores retain useful ordering but degrade with horizon and do not consistently beat activity controls. Earlier temporal-error, paired-dose and unsuccessful structural-selection results delimit what these findings imply. Together, the evidence links input-conditioned structural effects to finite-horizon fidelity regions in two deterministic kernels, without establishing universal topology rankings, model compression or asymptotic robustness.