We construct a distinction engine from the minimal axiom A̸ = B applied to two primitives and show that exhaustive iteration produces exactly 137 permanent objects at directed acyclic graph (DAG) size 7, matching the OEIS sequence A255841. Two nested topological cuts on the resulting overlap graph partition these 137 objects into sectors of 81 + 40 + 16, reproducing the registry architecture of Relational Mathematical Realism (RMR) previously derived from complete-graph eigenvalue spectra, force emergence mechanisms, and lepton mass ratios. The partition is unique:varying the number of primitives, DAG size, pairing rules, or overlap threshold destroys it. A heterogeneous dynamical simulator with algebraically typed update rules—ternary condensation (34 = 81), binary polarity (24 = 16), and relational activation (52 × 4 = 40)—produces sector-differentiated behavior with exact energy conservation. Ablation of the interface sector demonstrates that the 40-element boundary enables matter-like condensation: removing it reduces spatial-sector realization by 80% (p < 10−10). The dynamic interface achieves full condensation efficiency with just 2 of 38 channels active, revealing massive structural redundancy and a sharp percolation-likethreshold. Seven of twelve integers in the established RMR set A appear as direct structural counts in the engine; the remaining five appear as derived ratios, including the generation factor 17 = 136/8. This constitutes a fourth independent line of evidence for the RMR registry partition, obtained from pure combinatorics with zero free parameters.