Abstract and publication identity

We construct a finite effective scalar-current protocol in which different physical receivers record earlier actual archive digits and retain them through every later operation. A smooth compact stock-preserving baker exposes the digits, a scalar loader preserves their signs, a coherent two-coordinate gate writes each sign, and an exact positive Ermakov reset restores the scratch wave while retaining its correlations in a reset bank. The full original configuration law is dominated once by the complete reference law; no fresh actual population is assumed after a reset. Localized graph and Hilbert-valued slice-current estimates prove one joint 44-record failure bound below $2.641\times10^{-7}$ for the stated 10,000-unit schedule. A prior warmup's history error is a separate input. We also prove one-module flow-derivative and original-law preparation bounds, a complete finite-calibration digit criterion, and an approximate four-channel scalar reset uniform over a constant spring-gain interval. Exact examples show why wave SWAP does not imply actual freshness and why spring-gain tolerance does not cover idle-trap curvature. A distinct retained-symbolic-history calibration is proved in an appendix. These results provide explicit mathematical record and control mechanisms under declared premises; physical stock, actual-law and material-control warrant remain additional requirements.