Cavity Memory and Calibrated Readout of Fixed-Ambient Normal-Graph Waves: Exact Fabry–Pérot Storage, Suspended Endpoints, and Closed-Loop Phase Reconstruction

This paper develops the optical storage, mechanical response, and calibrated readout of fixed-ambient normal-graph waves within the VGM research program. Building on the finite-arm phase kernel derived in Paper XIX, it constructs a linear apparatus model for two identical, resonant Fabry–Pérot arms with suspended endpoints and negative feedback. Repeated optical traversals produce an exact discrete-delay cavity memory. The analysis establishes its causal impulse response, stable pole structure, bandwidth, delay moments, and absence of finite real-frequency zeros. For identical cavities, optical storage therefore preserves the zero set of the specified differential phase input. A causal inverse filter and an explicit memory-tail bound quantify reconstruction gain and the history required for a stationary local calculation. Endpoint motion is introduced through a damped mechanical susceptibility before optical storage. Identical endpoint plants yield a factorized cavity–mechanical–geometric response, while distinct plants retain their separate contributions. The free-mass and single-bounce limits recover Paper XIX. The feedback calculation reconstructs the external differential phase by combining residual and control paths. An exact calibration identity, a model-mismatch operator, and explicit error-propagation bounds relate sensing, actuation, and controller uncertainties to the reconstructed channel. The operating conditions include accumulated-phase smallness, stationarity over the relevant memory, internal loop stability, and bounded sensing inversion. The resulting framework connects the normal-graph phase to a calibrated apparatus channel. It retains the full round-trip delay at first order in perturbation amplitude within the stated local approximation. Experimental implementation supplies the excitation spectrum and independently measured instrument parameters. This deposit contains the English manuscript, revised version 1.1 dated 6 November 2026, and its XeLaTeX source. Series: VGM Empirical Correspondence, Calibration, and Falsification Series III — Overall Paper XX. DOI: https://doi.org/10.5281/zenodo.24022670