A Dyadic Register Model of Observer-System Records in Quantum Measurement

A measurement event produces a finite record available to a physical observer. This paper develops a dyadic register model for such observer-system records. The local state space is derived from three operational requirements: binary distinguishability, a separation between observer-side resolving capacity and system-side record content, and a nondegenerate complementary update structure. For an n-bit subregister, the complement map partitions the space into 2^(n-1) dyads. A cyclic update structure with adjacent and non-adjacent dyad relations requires at least four complementary dyads, hence 2^(n-1) >= 4 and n >= 3. The minimal record-bearing observer subregister is therefore F_2^3, and coupling it to a system subregister of the same minimal type gives G = F_2^3 + F_2^3, a 64-state dyadic register. Observation is represented by a mask-dependent quotient of the system register. Resolving power is the Hamming weight of the observer mask, and the available record is the corresponding projection of the system register. Walsh characters give the natural Fourier basis on the finite group, and dyadic translations give an exactly diagonalizable class of state updates. A quantum embedding is obtained by identifying register states with the computational basis of six qubits and representing observer-limited records by coarse-grained projectors. The resulting framework supplies a precise algebraic vocabulary for record formation, observer-dependent coarse-graining, update spectra, and testable finite-state hypotheses in quantum measurement.