Operational Manifold sketches

May 2026 · working notes

Loose notes on the manifold geometry that produced the Toroid. Includes the dimensional collapse arguments — why the topology must be doubly periodic to faithfully represent feedback that returns to its origin without sink.

Sketches range from formal (parameterizations of the toroidal coordinate system) to gestural (which Sabbotarchic modes live in which neighborhood of the manifold).