Robust Phase-to-Record Conversion with Retained Loss Outputs

This paper develops phase-sensitive source–readout constructions within Shadow Theory’s research programme. It asks how a relative-phase distinction, invisible in separate mode intensities, can be converted into stable detector records under bounded coupling, finite source lifetime and preparation uncertainty. A complete quantum instrument connects a two-mode source to a coherent reader and terminal detector flags. Every trial uses one original source preparation, with conclusive, null and loss outputs explicitly retained. The construction includes arbitrary inert reference systems and distinguishes coherent quantum outputs from classically registered records. The main results establish: • A sharp attainable limit on error-free conclusive detection under bounded coherent coupling and independent irreversible source loss. • A separate optimum for a bounded jump-hazard model, together with a finite collision realization, showing why the two apparatus models require different resource accounting. • An analytic minimax tradeoff between conditional error and guaranteed conclusive probability under joint amplitude, phase and visibility uncertainty, including uncertain upstream attenuation. • An exact separation between a calibrated entrance filter and uncertain common conversion dynamics, followed by sharp robustness bounds for imperfect matching based on controlled-path overlaps. The analysis keeps source preparation, reader dynamics, retained outputs and permitted measurement access explicit. Retaining a loss output or reference does not automatically make it accessible to the decoder, and agreement of detector counts does not establish equivalence of complete quantum outputs. The accompanying technical companion develops absorbing detector models, complete retained-output comparisons, finite charge-reference measurements, preparation-resource requirements, and calibration and adaptive monitoring methods. Supporting code and verification materials accompany the manuscripts. These are mathematical apparatus constructions within Shadow Theory’s source–readout programme, using standard quantum probabilities and stated preparation and control assumptions. The results do not derive the Born rule or establish a biological or consciousness mechanism.