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Shadow Theory

Robust Phase-to-Record Conversion with Retained Loss Outputs

Operating examples, compatibility and reproducibility

Jeremy RodgersSection 7 of 8Original PDF ↗Publication DOI ↗

Operating examples, compatibility and reproducibility

For overlap s = .6, G = l= 1 s−1 and deadline 2 s, the sharp coherent optimum has active time 1.3613444250 s, weaker coupling .3764245988 s−1, and each correct conclusive probability .2025106210. The static reciprocal absorbing bank instead has wrong-click probability .0394994846 by time 2/γ; the moving bounded-hazard reader repairs this back-action in its different model. For source box p ∈[.7, .9], v ≥.95, |δ| ≤10◦, the calibrated-loss model has error floor .05764696773. At conditional-error ceiling .08 its exact conclusive guarantee is .1809098506. Unknown internal loss cannot be handled by inserting a worst-case transfer factor into a fixed nominal unequal pulse: the nominal pulse can exceed its error ceiling even when loss decreases. For common rectangular uncertainty g ∈[.9, 1.1], l∈[.8, 1.2] in inverse seconds and t ∈[.9, 1.1] seconds, the optimized unequal-tap guarantee is .09490563225, while the calibrated-filter/common-cell subclass gives .1120453274. Its 18.0597% improvement costs one extra filter-failure port and a calibrated prefix. It is not universal hardware superiority. With additional full-response mismatch Θ = .05 radians and log-filter error .01, the sharp protected design gives .1018845501 at conditional error .08; the formerly matched filter fails at .09010468261. This compares protection under a larger uncertainty set, not a rate increase over perfect matching. The analytical proofs establish the quantifiers. Replayed NumPy/SciPy calculations independently reconstruct Hamiltonians,

Gram matrices, retained-reference normalization and numerical optima; their decimals are binary64 diagnostics, not rigorous enclosures or physical data. The clean supplement preserves actual inputs and the exact code used. Calibration of terminal effects does not identify a full residual instrument; finite-reference, detector-comparison and monitoring interfaces are developed separately in the technical companion. The bounded coherent-coupling, bounded hazard, common-cell and imperfect-matching theorems use different declared physical parents. They may not be concatenated without proving common preparation, controller, clock, reference, loss and access conditions. All future uses require fresh stock or a separately established reuse law. No reset alone supplies independence, no flag constitutes a perspective, and the original measurement obligations remain open.

Research assistance and status. AI assistance was used for computational review and testing.

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