Tri-Organism Geometry: Deterministic Multi-Organism Coordination via Three-Body Governance in the Lume 4/42 Architecture

I present the Tri-Organism Geometry — a formal framework for the two-dimensional and three-dimensional visual representation of, and deterministic interaction modeling between, three Lume-native physical flow organisms: Meridian (energy domain), Verdara Ultra (outdoor domain), and HydroCore (hydrological domain). Each organism implements the Lume 4/42 architecture independently, maintaining its own four primitive flows and forty-two operational nodes. The Tri-Organism Geometry defines how these three organisms are co-located in a shared geometric frame, how their pairwise interactions are encoded visually and computationally, and how their combined state is synthesized into a central meta-core that provides a single composite view of tri-organism equilibrium. The framework makes four primary architectural contributions. First, it defines a triangular organism layout — an equilateral arrangement with Meridian at the apex, Verdara Ultra at the lower left, and HydroCore at the lower right — that preserves each organism’s full 4/42 internal structure while situating them in a shared coordinate system. Second, it specifies three pairwise interaction channels — Meridian↔Verdara Ultra (energy-outdoor), Verdara Ultra↔HydroCore (outdoor-water), and HydroCore↔Meridian (water-energy) — as directed, bidirectional conduits encoding the physical coupling relationships between domains. Third, it defines a cross-node linking system that identifies specific nodes across different organisms whose states are physically coupled and renders those couplings as optional visual overlays. Fourth, it specifies a central meta-core — a small three-axis composite organism at the centroid of the triangle — that encodes the aggregate health of all three organisms in a single glanceable structure. A three-dimensional extension stacks the three organisms as layered planes — Meridian above (infrastructure layer), Verdara Ultra at center (surface layer), HydroCore below (subsurface layer) — with tetrahedral interaction geometry connecting them across all three spatial dimensions. Alert propagation across organism boundaries — where a critical node in one organism triggers visual signaling on the connecting edge and distortion of the central meta-core — is formally specified, enabling operators and practitioners to immediately identify cascades that originate in one domain and propagate into another. The Tri-Organism Geometry is the first published framework for multi-organism interaction geometry in the Lume ecosystem. It establishes the foundational visual and computational language for systems in which multiple Lume organisms must coexist, interact, and be simultaneously governed in real time. Keywords: multi-organism geometry, Lume synthetic organism, deterministic interaction framework, physical flow organisms, tri-organism system, cross-domain coupling, Meridian, Verdara Ultra, HydroCore, organism visualization, meta-core, interaction channels Repository: cryptocreeper94-sudo/lume42