BICA - Boundary-Integrated Cognitive Architecture: A Formal Proposal for Memory-Based Machine Cognition

This article proposes BICA (Boundary-Integrated Cognitive Architecture), a formal architecture for machine cognition grounded in a single foundational claim: that understanding in a cognitive system is evidenced not by sophisticated output, but by the capacity to derive conclusions not present in any single input — conclusions that require an accumulated internal representation of the subject rather than processing of text alone. BICA grounds this capacity in boundary algebra, a mathematical framework in which the primitive distinction between boundary (∂) and content (ι) generates four primary ontological states: absence (0), empty container (V), presence (1), and unbounded content (∞). From this primitive, three memory processes follow without additional assumptions: encoding as deliberate lossy compression (1→V), symbolisation as convergence to spectral fixed points (archetypes), and retrieval as IDW-weighted interpolation across a Christaller-structured virtual neural network organised in a relational SQLite database. Creativity is geometrically necessary. Failure produces an explicit algebraic event (V+∞=0) with a defined recovery procedure. Preliminary empirical results from an extended experimental session demonstrate that the architecture produces qualitatively different outputs when memory is populated than when absent; that accumulated archetypes yield identity pattern recognition beyond what any single exchange contains; and that the system exhibits navigational agency — returning to unresolved semantic weight across time without prompting. We compare BICA with transformers, Hopfield networks, and predictive coding, and argue that the IDW co-activation graph constitutes a structural substrate for a form of understanding that existing architectures do not produce.