# Abstract and publication identity

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**Abstract.**

We prove quantitative response estimates that retain coherent quantum sources, complete physical currents, spectral poles and actual feedback. An ordered inverse lift converts temporally regular form-dual forcing into a first-form response under common-form work bounds. A finite spectral-window theorem controls varying Hilbert-space inputs, and ordered closed-form resolvent identities transfer noncommuting physical-energy weights. Far-frequency and damped estimates retain the endpoint and source-graph costs. Complementary force, invariant and temporal-domain estimates distinguish valid current resources for singular interactions. In a compact-profile electron–oscillator model, we derive the full Coulomb forcing measure and an actual-source low-window sandwich below $4.05\times10^{-9}$. A separate finite-time calculation bounds the electron and source current differences by $.046$ and $.004$ in their respective coordinate lengths. The spectral supremum is taken over the actual spectrum; a spectral floor supplies only an upper bound. Full-source forcing compression and causal feedback are developed in appendices. These results provide explicit analytic inputs to physical transport and record problems. Event probabilities and a realized measurement apparatus require additional flow, preparation and decoder premises.