Self-boiling lattice of complex links: finite domains, elastic coexistence and a massless gauge mode in a 2D toy model of cosmogenesis

We study a toy model of a pre-geometric medium: a triangular network of complex links with a loop energy, a rotated interaction force and a conserved total intensity, coupled to a scalar order parameter with two unequal minima. When the intensity budget lies below the vacuum value of the links, the ordered network boils without external noise, and finite domains of the second phase ("worlds") nucleate from islands of aligned link phases and near-vacuum link intensity (destroying both in an island suppresses nucleation there); a hole cut into the substrate seeds a domain on its rim, but only above a size and a depth threshold. Without further ingredients the domains merge until a single domain holds about two thirds of the system, as the lever rule predicts. An elastic response of the substrate makes coexistence of many domains stable, with a domain size fixed by one number, P = γℓ², and independent of system size. Inside domains a postulated matrix field with SO(5) gauge symmetry condenses; its massless O(2) mode is held in domains for a finite time, is blind to the anisotropy of the network and has a purely quadratic dispersion correction, which LHAASO data turn into a bound on the lattice spacing, a ≲ 1.1 × 10⁻²⁷ m. Z₂ vortices of the field form by the Kibble mechanism and are candidate particles. We also report negative results with their diagnosis: the model has no long-range gravity (a scalar strain stops at the Nordtvedt effect), in 3D coherent islands do not grow to critical size, and the gauge group is not derived from the network architecture. Code and data to reproduce all figures: https://github.com/batrukh/Nul-matrix-v1 (archived: https://doi.org/10.5281/zenodo.23838150)