History-Dependent Scalar Branch Selection in a Coupled Cosmological Field: Matched-History Dynamics and Finite-Time Retention

This research note investigates whether different density-forcing histories can select and retain distinct scalar-field configurations after the final environment becomes identical. Using the hypothetical two-field B3 model, comprising a nonlinear memory field coupled to a density-sensitive mediator, we perform a preregistered matched-history intervention with clear density pulses, subthreshold controls, and no-pulse controls. For the comfortable bistable profile, all 10 crossed phase blocks and all 12 independent replication blocks satisfy the preregistered scalar-retention criterion. All 64 clear-pulse contrasts preserve distinct written and unwritten scalar configurations through observation windows ending at 12,000 wall times, and all 35 numerical convergence sentinels pass, including checks using an independent fourth-order Runge–Kutta integrator. The original joint two-field equilibrium classifier remains unsettled for the written trajectories. Four exploratory near-fold blocks also remain unresolved. The results therefore establish reproducible finite-time scalar branch selection under controlled matched forcing, not asymptotic convergence of the complete coupled field or observational evidence for cosmological memory. The accompanying reproducibility archive provides the manuscript source, numerical audit materials, frozen results, preregistration records, figure-generation scripts, and SHA-256 provenance information. Full checkpoint replay requires the separately retained bulk execution archives. This work extends the author's earlier studies of hypothetical cosmological memory fields by directly testing the dynamical selection and finite-time retention of distinct scalar configurations.