Abstract
We propose that the evolution of complex knowledge systems (scientific, legal, biological, or cognitive) is not a linear march toward perfection, but a staged, differential process of topological selection. We distinguish between two distinct morphism classes: Rough Edges (high-entropy, exploratory, locally optimal but globally fragile) and Resonant Yoneda Edges (low-entropy, persistent, globally coherent).
The Conjecture of Differential Resonant Pruning (CDRP) states that a system achieves maximal resilience and coherence only when it dynamically shifts its pruning strategy based on a Yoneda-like Stability Indicator (Y_γ). Early stages require the preservation of Rough Edges to generate diversity and explore the solution space; later stages require the differential application of the γ-minimum principle to select only those edges that form persistent homology cycles (topological capacitors). The transition between these regimes is governed by the Prune-Timing Law, which dictates when roughness becomes noise and when resonance becomes rigidity.
