Geodesometry of Coherence: A Discrete Dynamical Extension of Hamming Decay in Quantum State Spaces

This work introduces the geodesometry of coherence, a minimal discrete dynamical extension of the Hamming Decay Theorem in quantum state spaces. The Hamming Decay law establishes that off-diagonal elements of a density matrix decay exponentially with Hamming distance under local noise channels. However, this metric does not account for the physical structure through which coherence is lost. In this work, the Hamming hypercube is endowed with anisotropic physical weights on its edges, representing local noise, coupling asymmetry, or entropic cost. A minimal 3-qubit model with non-uniform weights (3, 2, 1) demonstrates that pairs of states with equal Hamming distance can exhibit different accumulated transition costs, leading to a falsifiable prediction: equal Hamming distance does not necessarily imply equal decoherence rate under anisotropic conditions. Explicit GO/KILL conditions are defined, and a minimal experimental protocol is proposed. The formulation is deliberately restricted to the quantum discrete sector and does not claim extension to gravity, cosmology, or gauge theories. It is presented as a falsifiable intermediate step between: Hamming geometry (metric structure), geodesometry (discrete dynamics), and a potential continuous effective action Seff[C]Seff[C]Seff[C] within the Radial Coherential Dynamics (RCD) program. This work is intended as a minimal, testable framework rather than a complete theory.