Physics Letter: A Structural No-Go on Bias without Record-Cost Asymmetry in Causal Memory Architectures

We present a deliberately minimal, non-dynamical toy framework whose purpose is to isolate a structural condition for persistent class bias under compositional constraints. Statesare connected by directed morphisms carrying non-negative additive costs, and admissiblepaths are filtered by a record-persistence requirement formulated as a lax functor to relations. Analysis is performed at fixed composition depth, which explicitly does not representphysical or cosmological time. Selection over paths is modeled by a broad family of sharpmonotone weights depending on total cost, with Gibbs-type measures treated as a representative but non-privileged example. Within this setting, we establish a constraint-level result:persistent dominance between two label classes is impossible unless there exists an asymmetry in the minimal cost required to create and maintain their records. If the cost structureis symmetric under label exchange, no sharp monotone selection can generate a stable classimbalance. Conversely, when a cost gap is present, selection concentrates on the cheaperrecord class under mild and explicitly stated combinatorial assumptions. These statementsare purely structural and do not invoke microscopic dynamics, conservation laws, temporalevolution, or specific physical interactions. The framework does not model baryogenesis,does not implement Sakharov conditions, does not reproduce Standard Model CP violation, and does not derive or predict any physical asymmetry parameter. The label-exchangeasymmetry considered here is a structural analogue only. Moreover, the framework itselfcannot determine whether record-cost asymmetries are realized in nature; it merely showsthat, without such asymmetries, no selection mechanism of this type can produce persistentbias. No mapping is provided between composition depth and physical history, and the construction cannot account for early-universe dynamics or out-of-equilibrium processes. Thecontribution of this work is therefore negative and clarificatory rather than mechanistic. Itdelineates a boundary on what selection-based architectures with record persistence can andcannot explain, and reframes the relevant open question away from selection toward physics:which concrete theoretical constraints, if any, enforce or forbid asymmetries in the cost offorming and maintaining records? The framework is offered as a conversation-level scaffoldfor discussing this issue across foundations, statistical selection, and high-energy contexts,rather than as a candidate physical mechanism.