Geometry Of Classicality: Hamming Distance as the Universal Principle of Decoherence

Two recent results suggest Hamming distance organizes quantum coherence dynamics, but no  unified framework connects them. We establish the Hamming Persistence Principle: quantum correlations at Hamming distance persist with amplitude scaling as e−κd, where κ depends on context but the geometric structure is universal. The principle unies two independent discoveries: (1) In open systems under local noise, density matrix elements decay as ρij(t) = ρij(0)e−γH(i,j)ta theorem following from locality of interactions. (2) In isolated systems, Strasberg et al. observed numerically that o-diagonal elements of the decoherence functional correlate negatively with Hamming distance, but noted they had no elaborate theoretical explanation.

We provide that explanation: both phenomena arise because physical interactions are local, making Ham-ming distancethe minimum number of single-bit operations connecting two congurationsthe dynamically privileged metric. Numerical verication conrms the framework: (i) Coherence magnitude decreases with Hamming distance(r =−0.26, p < 10−70), reproducing Strasberg's Figure 12. (ii) The decay coecient scales as α ≈0.5 ln D(r= 0.965), supporting the locality derivation. (iii) Maverick histories that deviate from Born statistics cluster at smaller Hamming distance (3/4 tests p < 0.05) and are 2×more coherent with each otherexplaining why they recohere together. The synthesis resolves why entanglement fails to predict decoherence rates: entanglement ignores Hamming geometry. It also suggests a geometric origin for branch selection: histories spread across Hamming space (large D∗H) are stable, while clustered histories (small D∗H) recohere away. The classical world may emerge not from environmental monitoring but from the intrinsic geometry of conguration space.