Does thermal leptogenesis in a canonical seesaw rely on initial memory?

It is a common lore that in thermal leptogenesis within the type-I seesaw framework and a hierarchical spectrum of heavy right-handed neutrinos (RHNs), the CP-violating, out-of-equilibrium decay of the lightest RHN ($N_1$) is the only relevant source of the final $B-L$ asymmetry, since any asymmetry produced by the heavier RHNs is expected to be erased by subsequent $N_1$-mediated washout processes. In this work, we revisit this assumption by solving the density-matrix equations, including decay, inverse decay, and relevant scattering processes, and by fully accounting for flavor-projection effects induced by the Yukawa coupling structure. We show that the asymmetries generated by the heavier RHNs ($N_2$ and $N_3$) generally possess components that are misaligned in flavor space with respect to $N_1$, resulting in a partially protected contribution that survives the $N_1$ washout. Unlike the conventional picture of $N_2$-dominated leptogenesis, this memory effect arises even when $N_1$ remains dynamically relevant and cannot be captured within the classical Boltzmann framework. Furthermore, imposing consistency with low-energy neutrino mass and mixing data, we find that at most one RHN can lie in the weak washout regime, which naturally divides the parameter space into four distinct dynamical regimes. We systematically quantify the memory effect in each regime and demonstrate that it can significantly modify the final $B-L$ asymmetry. We find that including projection effects can indeed extend the viable parameter space into the sensitivity range of neutrinoless double beta decay experiments.