Certified Current–Response Bounds for a Finite Fermionic Source

This preprint establishes certified current–response inequalities for an explicitly defined finite fermionic source. Version 1.1 distinguishes absent transitions, static contact cancellation and zeros of a sampled response. It adds a time-window lower bound and an explicit finite-sampling error estimate while preserving the original source and certificates. The accompanying archive provides reproducible exact and numerical checks. Identifying these mathematical responses with experimental transport requires an additional physical model.