Deterministic phase memory II: Cascaded bistable systems with explicit coupling bounds and quantitative addressability

We construct cascades of N identical bistable phase-memory cells, producinga 2N-dimensional dynamical system that realizes an exponential memory archi-tecture. Building on the minimal bistable cell and explicit switching thresholdsestablished in Part I [1], we prove: (i) the existence of 2N asymptotically stableequilibria at weak coupling via persistence of hyperbolic equilibria; (ii) an explicitsucient bound on the coupling strength guaranteeing stability, with quantitativecontrol of the perturbation remainder; (iii) strong addressability: a write pulse ap-plied to the i-th cell switches it without causing any other cell to leave an explicitneighborhood of its equilibrium, even during the transient; (iv) a spectral analysisof the bidirectional cascade via block-tridiagonal Jacobian structure, showing thatdiusive coupling is unconditionally stabilizing. A concrete numerical example withβ = 2.5 and N = 8 illustrates the theory. This work is a preprint and has not yet been peer reviewed. This record is Part II of the three-part foundational program “Deterministic Phase Memory”, providing the discrete-cascade bridge between the minimal bistable cell of Part I and the continuum-field formulation of Part III. Part I — Deterministic phase memory I: A minimal bistable gate model with explicit switching thresholds https://doi.org/10.5281/zenodo.18663867 Part III — Deterministic phase memory III: Spatial fields, domain walls, and continuum information storage https://doi.org/10.5281/zenodo.18664124