Environmental recurrence changes the transmission advantage of private memory in a finite-budget population model

Using stored information may help a strategy spread without improving every population-performance endpoint. We distinguish these outcomes in an abstract 32-individual, 32-bit population model with private one-record memory, inherited strategy labels and an equal objective-evaluation budget. A historical probe and a fresh random probe occupy the same candidate slot. Their separate-introduction ranking reverses between alternating recurrent and independent targets, and an independent cohort reproduces both directions. Intermittent recurrence preserves a historical transmission advantage under two survival rules; direct competition and resident-policy preparation extend the comparison. A crossed experiment then holds prepared populations fixed while changing their future target law. After partial-recurrence preparation, future partial recurrence increases the matched historical-use founder effect by 22.76 percentage points relative to renewed targets (approximate pointwise 95% block-bootstrap interval, 17.12 to 28.95). A prospectively specified, independently generated cohort reproduces that direction, with 16.20 points (11.23 to 21.02), and also supports the corresponding contrast after renewed-target preparation. Cohorts are not pooled. A prospectively fixed challenge using new paired inputs retains a positive future-recurrence contribution under one four-bit-trap objective: 23.74 points (17.26 to 30.23), exceeding a separate one-expected-descendant benchmark. The direct trap-minus-Hamming difference remains unresolved; individual introductions still usually disappear. Preparation interactions remain partly unresolved. In the new partial-recurrence cohort, switching from historical to fresh use lowers the matched founder effect by 2.74 points while improving terminal population accuracy by 0.32 points; every introduced fresh-use founder nevertheless disappears in that sample. Fixed-cost introductions in earlier non-retrieving backgrounds often decline. Exact local calculations show why candidate-pair geometry does not determine global selection. A one-update fresh-exploration pulse leaves terminal population accuracy unresolved despite increasing founder representation relative to continuous fresh expression. A fixed bounded-error transfer challenge retains a positive founder recurrence effect while leaving its noisy-versus-exact change unresolved; noise lowers average population accuracy. A separate 256-state mathematical model with continuing symmetric policy switching shows a small, numerically certified recurrence increase in stationary H frequency (0.458 percentage points), with opposite active-versus-neutral accuracy effects under renewed and recurrent targets. The finite-population findings characterize conditional transmission of an available memory-use policy. They do not establish memory's spontaneous origin, equilibrium invasion, a general costly advantage, or measured biological effects. Research preprint version 1.5.0; not externally peer reviewed. Includes studies 045-060 with 15,284 statistical estimates, and a separate study 061 with 14 certified mathematical quantities; 18 figures. The new two-individual/one-bit supplied-memory model has ongoing symmetric policy switching and a small +0.458222476-point recurrence effect on stationary H frequency. Active-minus-neutral accuracy is adverse under ZERO (-0.259357994 points) and positive under HALF (+0.702715312 points). Numerical enclosures are not statistical confidence intervals, empirical replication, or stationarity evidence for the 32-individual model. The unresolved 059 population-accuracy primary and 060 noise interaction, frequent founder loss and adverse outcomes remain. The compact release excludes raw candidate trajectories and random tapes. Manuscript/data: CC BY 4.0; original code: MIT. AI assistance is disclosed. Versioned GitHub release: https://github.com/jackchenx3/private-memory-recurrence/releases/tag/v1.5.0 Previous version remains available: https://doi.org/10.5281/zenodo.22949032