History-Dependent Functional Continuity Under Delayed and Counterfactual Source-State Probes

This preprint extends PreservationBench-AST with delayed, counterfactual, and perturbation-based source-state probes. The paper asks whether the strongest prior copied-attention condition was merely a clean-episode shortcut or whether it preserved source-like history-dependent responses under harder stress families. The copied-attention condition is evaluated against frozen random target state across thirteen 22-seed validated-source recurrent stress families and one 22-seed perturbation family. The recurrent families include selected source-policy histories, deterministic unselected histories, shifted-policy histories, random-policy histories, scripted-cycle histories, longer report delays, longer histories, and an alternate random master seed. Across all thirteen recurrent families, copied attention remained separated from frozen random on warm-action agreement, source-hidden-state distance, and report-delta distance. Warm-action improvement ranged from 0.653 to 0.756, hidden-state MSE improvement ranged from 0.0961 to 0.1027, and report-delta improvement remained positive but smaller, ranging from 0.0022 to 0.0030. In the perturbation layer, copied attention reached 0.850 perturbed-action agreement versus 0.214 for frozen random and had near-zero attention-delta distance to source. The result supports a bounded toy-benchmark conclusion: copied attention/source-state machinery preserves source-like history-dependent and perturbation-dependent response profiles better than frozen random target state. It does not measure consciousness, personal identity, survival, biological preservation, or whole-agent equivalence.