Orientation and abstract

Technical Supplement: Continuous Reader Optimization and Deployment Interfaces

Jeremy Rodgers Independent Researcher www.everythingequation.com

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27 October 2026

Abstract

We give supporting methods and restricted benchmarks for common-sign readout of a fixed four-state qubit source: deterministic measurement allocation, an expanded rational menu, continuous-risk lower backups, fixed-nuisance polynomial certificates and physical timing/calibration interfaces. Every result retains its own measurement and stability contract. These methods support the associated reader frontiers without settling the remaining adjacent copy thresholds or a universal total-resource optimum.

This supplement develops optimization and deployment interfaces within Shadow Theory’s pre-existing source–readout programme [5]. It supplies independently checkable methods for the fixed-label four-state source. Copies are independent conditional on one label throughout a block; the preparation controller is inaccessible. The shared detector law iscossin The asymmetric parent separately applies one fixed Pauli channel with multipliers ( before a reader with fixed phase offset and independent sign-blind erasure. These response laws are premises, not inferred from equal one-copy marginals. The current one-percent copy intervals are [13 14] nominally and [16 17] for the specified asymmetric robust task, separately for both local policy classes. Supporting lower comparisons and unsuccessful candidates do not alter those status statements.

Contents

1 A physically admissible weighted completion-design frontier 2 1.1 Source, allowed interventions and retained outputs . . . . . . . . . . . . . . . . . . . . 2 1.2 An exact ideal fixed-schedule optimum . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Exact rational noisy design with matching certificates . . . . . . . . . . . . . . . . . . 4 1.4 Controlled deviations and fair physical accounting . . . . . . . . . . . . . . . . . . . . 5

2 A larger rational measurement menu: the copy gap closes but feedback still helps 6 2.1 Declared settings, noise and symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Exact adaptive and randomized-nonadaptive certificates . . . . . . . . . . . . . . . . . 7 2.3 Implementation and limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Nominal threshold: a checked obstruction and a continuous lower-backup method 9 3.1 The thirteen-copy operator comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 A rational lower dynamic programme for the full circle . . . . . . . . . . . . . . . . . . 9 3.3 Exact demonstrations and scalability ceiling . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Original robust task: fixed-nuisance certification and an unresolved sixteen-copy endpoint 11 4.1 A three-variable exact interface for a frozen reader . . . . . . . . . . . . . . . . . . . . 11 4.2 Exact Bernstein cover certificates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.3 Why gain-endpoint checks alone are invalid . . . . . . . . . . . . . . . . . . . . . . . . 13 4.4 Searches and exact updated status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5 Uniform angular approximation 14 5.1 A certified angular-net transfer, not a grid optimum . . . . . . . . . . . . . . . . . . . 14 5.2 Verification and exact status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

6 From the continuous feedback gap to a physical resource certificate 15 6.1 A nonzero noise and control-error operating region . . . . . . . . . . . . . . . . . . . . 15 6.2 Actual phase travel, rather than a generic switch charge . . . . . . . . . . . . . . . . . 16 6.3 A full-menu copy advantage with a conditional time advantage . . . . . . . . . . . . . 18 6.4 Finite calibration covering all continuous angles . . . . . . . . . . . . . . . . . . . . . . 18 6.5 Reproducible checks and remaining limits . . . . . . . . . . . . . . . . . . . . . . . . . 20