Morphogenetic Stability and Triad Basin Structure in Binary Conflict Spaces

This paper develops a morphogenetic framework for analyzing structural stabilityin binary configuration spaces. System states are represented as vertices of theBoolean hypercube Qn, where stabilizing conditions correspond to binary coordinates.Fixing a subset of stabilizer variables induces lower-dimensional subcubes that definestability basins within the global configuration space.A general theorem is derived for stabilizer-generated basins, showing that theirCheeger conductance depends only on the number of fixed stabilizers k and theambient dimension n. The resulting closed-form expression,Φ(BS) =k/ngives the exact leakage rate of a basin defined by k stabilizers in Qn.The framework is illustrated through a triad stabilizer configuration in Q8, producinga 32-state basin with conductance 3/8. Spectral perturbation analysis demonstrateshow interaction terms deform the Laplacian spectrum and promote the triad basinas a dominant structural mode. The results connect Boolean hypercube geometry,Walsh–Fourier analysis, and spectral graph theory, yielding a mathematically explicitdescription of stability formation in Boolean morphogenetic systems