Thermodynamic Architecture for a Continuous and Persistent Cognitive Substrate

Propose a thermodynamic architecture for continuous, persistent cognitive processing implemented in a hexagonal boron nitride (hBN) phonon-polaritonic substrate. The architecture is grounded in APTADINAMIA Axiom VI, which requires a system to maintain an internal estimate of its own excess load relative to a viability threshold without allowing self-reference to become unstable. Unlike the previous graphene/hBN formulation, the present model does not rely on electronic hydrodynamics, magic-angle phases, or correlated-electron transitions. It uses hBN as an active anisotropic medium supporting hyperbolic phonon polaritons (HPhPs), whose directional confinement, damping, and thermal-structural envelope provide a physically interpretable carrier for non-Markovian memory and active forgetting. The paper defines a dual-variable state model: an unbounded physical occupation-load variable eta, and a bounded operational representation Phi = tanh(eta/eta0). Saturation and falsification are formulated in eta, while operational stability is formulated in Phi. A non-Markovian field equation with spatially patterned damping alpha(r,t) is introduced, and active forgetting is modeled through the kernel transformation K_eff(s,r,t)=K(s) exp[-alpha(r,t)s]. We prove that long-memory kernels produce saturation under sustained forcing in the absence of effective truncation, derive a quantitative upper bound for the saturation time, and distinguish the microscopic HPhP lifetime from the slower thermal-structural memory envelope. The central addition is a linearized stability analysis of the self-referential closure loop. A monomodal reduction yields explicit trace and determinant conditions, a viable closure boundary c > (a - b alpha*)/(b x*), and a minimum thermodynamic cost of viable closure. The resulting architecture converts Axiom VI from a purely formal self-reference requirement into a testable stability-and-dissipation condition for hBN-based phonon-polaritonic devices.

Keywords: hexagonal boron nitride, hyperbolic phonon polaritons, non-Markovian dynamics, active forgetting, operational self-reference, APTADINAMIA, thermal memory, stability analysis, phonon-polaritonic substrate.