Sharp State Complexity of Cyclic One-Pass Readout with One Adaptive Protected Source Record

The paper arises from our investigation of exact information retention in one-pass stack readout and protected-source storage. It considers a frozen stack of named records whose payloads must be emitted in a query-selected cyclic owner order, while the machine may pop each source record only once and protect one genuine, immutable owner–payload record for repeated inspection. Unlike a fixed buffer, the protected owner may be chosen adaptively using information read earlier. Counting every controller phase, the paper proves the asymptotically sharp state complexity Theta_m(m^n/n) and a factor-linear-in-n saving compared with fixed-owner staging. The upper-bound construction encodes previously observed symbols in the identity of a later genuine owner and uses a literal output prefix to avoid an extra logarithmic state overhead; the lower bound accounts for all information physically retained in control and the protected record. Its main novelty is an exact asymptotic separation between adaptive source-identity storage and fixed-identity buffering under the same one-record capacity, without assuming a scratch stack or uncounted encoding channel. Exact finite-instance state complexity remains open.