Present Action Is Not Persistent Write: Causal Rights of Optimizer History in Replay-Free Continual Learning

Stateful optimizers normally grant a learning signal two permissions at once: it may change parameters on the present update, and it may write persistent state that conditions future updates. We ask whether these permissions are experimentally separable in replay-free continual learning. We study a strict replay-free Split CIFAR-100 learner with one fixed 100-class head, current-task-only training, raw global inference, and no task routing, model growth, or post-hoc calibration. In a five-seed action-by-write factorial, a write-only intervention, denying the source its same-update parameter action while retaining its persistent Adam write, increases current acquisition by 0.00774 relative to the comparator, while increasing forgetting by 0.00604 and old-to-final recapture by 0.00569; the action-only cell increases acquisition by only 0.00058. Successive interventions localise this durable pathway predominantly to first-moment state, accumulated within-task history, and the current-relative orthogonal action of inherited history. We then follow acquisition-bearing history across the task lifecycle: in four independent paired seeds, with six origin tasks nested within each seed, all 24 provenance units show source-distinct classifier weights and Adam moments at the current-to-old boundary followed by source-distinct row-relative old-row displacement under exactly zero natural classifier gradient. This provides direct cross-lifecycle provenance evidence, not behavioural mediation. Finally, a function-preserving reparameterisation with transported Adam state leaves final features, all 100 logits, predictions, and the classifier head exactly unchanged at the branch, yet all four fresh pairs diverge on the first lawful subsequent update and develop different continual-learning trajectories. Within this tested Adam setting, present parameter action and persistent-history ownership are distinct causal rights, and persistent optimizer history contributes to the causal state governing future learning.