How can a physical receiver record an earlier event and preserve that record through repeated copying, resetting, and later operations? This paper constructs a finite protocol that achieves this within a specified effective scalar-current model. A smooth reversible archive reader exposes successive digits of an actual initial position. A sign-preserving loader and coherent copying gate transfer each digit into a separate physical receiver. An exact Ermakov reset restores the scratch wave while retaining its correlations in a reset bank. The analysis follows the complete original configuration law throughout, without assuming a fresh statistical population after reset. For the stated initial-law bound and a schedule lasting 10,000 model time units, the paper proves a joint failure probability below 0.0000002641 for 44 records. This bound covers both correct copying of the earlier archive digits and preservation of the written records through subsequent operations. Any error inherited from an earlier archive warmup must be accounted for separately. Further results establish finite calibration criteria, control of archive motion between operations, and approximate reset uniformly over a specified constant spring-gain interval. Exact counterexamples explain why restoring or exchanging a wave factor does not automatically restore statistical independence.The paper supplies complete proofs and explicit error bounds. Physical preparation of the admitted initial stock, material realization of the controls, and integration into a complete measurement apparatus remain additional requirements.
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Jeremy Rodgers (2026) studied this question.
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