This white paper compares the Coptic symbols ⳦ (Pi Ro) and ⳨ (King) or tau-rho as mathematical objects in grapheme space Σ. We formalize their differences using topology, category theory, and combinatorial obstruction theory.

Pi Ro exemplifies functorial inheritance from alphabetic structure, while King represents emblematic emergence.

We show that these symbols occupy disjoint strata of Σ, exhibit distinct obstruction dynamics, and satisfy different axiomatic regimes.