A Liminal Topological Bridge for Lossless Continuous-to-Discrete Translation.

Every digital system in existence destroys information at its analogue boundary. The conversion is one-way, lossy, and irreversible, a fundamental constraint baked into the hardware. This paper describes an architecture that removes that constraint. By using a specific mathematical surface as a native translation layer, the system moves continuously between analogue and digital domains without clocks, without quantisation, and without information loss. The translation is proven lossless and reversible in both directions. For AI systems in particular, this opens a direct path to hybrid architectures where probabilistic and symbolic reasoning share the same continuous substrate — eliminating the conversion bottlenecks that currently force a hard boundary between the two. The approach is mathematically verified, fully specified, and independently reproducible.