A prior distinction-engine construction recovered a 137-object registry at DAG size 7 and partitioned it into sectors of 81+40+16, aligning with the spatial, interface, and gravitational sectors proposed in Relational Mathematical Realism. The present manuscript consolidates two subsequent analyses. First, we study mature registry carriers: larger relational objects that contain the full 137-type registry as an embedded motif. Exact DAG-size joins and 137-bit registry signatures recover DAG-8, DAG-9, and DAG-10 layers while compressing motif state space by factors of 6.85x, 20.43x, and 46.01x. Minimal full-registry carriers have DAG size 309. Eight non-isomorphic carrier histories preserve the same condensable typed mediation geometry: 72 spatial nodes, 38 interface nodes, 16 gravitational nodes, and 288 mediated S-G edges per condensable interface node. Typed dynamics lifted onto these mature carriers show no statistically detectable topology effect on interface-enabled condensation. A screening audit identifies full binary S-G conflict deletion as the wild-type interface rule, producing S_ DYN ~9.61, S_OFF~2.04, and a 4.73x dynamic/OFF enhancement. Loss-of-function tests identify the true invariant as complete I-mediated coverage of the active S-G conflict graph: the 38 condensable I nodes split into two complementary 19-node half-covers, each covering 288 of 576 active S-G edges.Second, we extend the analysis to an open-token distinction engine, in which finite type identity is separated from lineage-distinct token identity. The type-guarded open-token process preserves the canonical 137 DAG-7 type layer exactly while allowing unbounded token multiplicity. Particle-detector tests on open-token dynamics recover robust K3/baryon-like candidates: five stable candidates with k3_score=1.0, high closure, and fixed carrier support. I-cage/lepton-like structures appear as suggestive precursors, including a high-scoring cage-localized candidate, but not yet as fully closed localized leptons. These results support a layered interpretation: the DAG-7 registry is a finite reusable type grammar; DAG-309 carriers are mature local embeddings of that grammar; and open-token dynamics permit stable particle-like excitations over repeated registry instances. We identify a mathematically natural route from distinction-generated registry types to mature carriers and K3-centered particle-like object.