Geometry, Membranes, and Life as a Resource Boundary: A Correct-by-Construction Operational Pipeline from Static Suppression to Maintenance Costs

We present a logically explicit operational program connecting three themes: geometry as suppressibility of cross-region influence, membranes as engineered interfaces implementing that suppressibility, and life as sustained maintenance of internal organization under finite resources. The program composes: (i) a law-grade thermodynamic inequality relating incremental maintenance power to the instantaneous loss rate of an organization functional, imported in its corrected operational hierarchy; (ii) a static geometric suppression layer in which cross-interface leakage admits an envelope f(eps) ~ poly(m eps) e^{-m eps} (with K_nu(m eps) as a canonical representative in massive homogeneous models); and (iii) a dynamical hinge (the Rate Inheritance Principle, RIP) connecting static suppression to separation-dependent effective dynamical rates. This version distinguishes upper and lower rate envelopes kappa_up(eps) and kappa_down(eps) to avoid sign/quantifier errors -- a distinction now vindicated by the companion series -- separates a law-grade Delta-track (energy pinching) from a conditional biology-grade E-track (general conditional expectations), and adds two interface anchors: a recoverability layer via conditional mutual information (CMI) and the Fawzi-Renner guarantee, and a minimal Davies interface lemma showing how correlator envelopes imply Davies-rate upper envelopes (supporting RIP-U microscopically in standard weak-coupling settings). A concrete electrical testbed using membrane-embedded spin probes is proposed to measure dephasing-rate envelopes and detect near-zero-frequency floors that create a resource horizon. A dependency and falsification matrix makes the logical structure audit-friendly.