The Arche-Cell: A Hardware-Bound Reactive Component for Tripartite Cognitive Architectures

This paper presents the Arche-Cell as a local, memoryful, generative primitive designed for integration into larger cognitive architectures. It is explicitly framed as a low-level, high-speed reactive substrate: the hardware-bound actuator of a tripartite AI system (AI-1, AI-2, AI-3). Its function is to provide ultra-low-latency, ultra-low-power control in response to local sensor states and an externally computed valence field. To address the combinatorial constraints of hardware implementation, the standard operating mode restricts the Hamming search radius to r = 1 (single-bit flips), reducing the candidate space from tens of thousands to W + 1 states per tick. The structural complexity metric is defined as a strictly local function (number of 0-1 transitions in a circular 1D chain), enabling an incremental O(1) update. All terms in the objective functional are explicitly normalised to [0,1] to ensure commensurability. Inter-frame valence dynamics are handled via a precomputable fixed-point decay with explicit error bounds. The formal apparatus of the cell (state space, admissibility correspondence, objective functional, selector operator, and tie-breaking policy) is defined as a direct instantiation of the Arche Selector operator of Kowalski (2026), so that the general theorems of that framework, including the Attractor Basin Partition theorem and the self-loop monotonicity corollary, apply to the Arche-Cell without modification. The paper provides a complete engineering specification, including a fair benchmark comparing the Arche-Cell to a neural network baseline on the same FPGA fabric, ensuring static power overhead is controlled for. The project is offered as a falsifiable engineering hypothesis, with open problems explicitly catalogued.