Hic Sunt Dracones: A Formal Framework for Epistemic Frontier Mapping, Unknown Unknown Detection, and Knowledge Boundary Quantification in Individual Cognitive Universes

All prior systems for mapping individual cognitive knowledge have focused exclusively on representing what is known. None has provided a formal mathematical framework for mapping the boundary between known and unknown knowledge, detecting unknown unknowns through comparison with collective knowledge architectures, or quantifying the rate at which the frontier of individual knowledge expands over time. This paper proposes such a framework.

We introduce a three-zone epistemic architecture partitioning the individual cognitive universe into Zone 1 (Terra Cognita: known knowns), Zone 2 (Terra Incognita: known unknowns), and Zone 3 (Hic Sunt Dracones: unknown unknowns). We formalize zone boundaries using k-nearest neighbor distance computation in both Euclidean and Manhattan metrics, topological boundary theory in metric spaces, Shannon entropy gradients, and Kolmogorov complexity. We propose a collective universe comparison mechanism that makes Zone 3 visible to the individual from the outside through federated and privacy-preserving methods. We describe a frontier expansion rate metric that tracks the rate at which unknown unknowns become known unknowns over time.

The framework operationalizes the philosophical tradition of negative epistemology, from Wittgenstein's proposition that whereof one cannot speak thereof one must be silent, through Popper's falsifiability criterion as a frontier marker, to Taleb's Black Swan theory of unknown unknowns as structural events that reshape knowledge architectures. The cartographic phrase Hic Sunt Dracones, here there be dragons, is adopted as a formal technical designation for Zone 3, recovering the epistemically honest acknowledgment encoded in early modern cartography that the boundary of the known world is not nothing but uncharted.

The framework is implemented as part of the Cognitive Universe System (CUS), an AI-powered architecture for mapping individual and collective knowledge universes whose governance and sovereignty dimensions are addressed in a companion working paper. This is a working paper presenting a conceptual synthesis and an architectural blueprint rather than a field-tested empirical result; its contribution lies in the synthesis itself, the systematized use of density and distance metrics to construct an outward-facing map of individual ignorance, rather than in the underlying mathematical primitives, which are individually well established.