Spectral Graph Coagulation and the Emergence of Hybrid Discrete Geometry

We introduce a dynamical model of graph aggregation governed by spectral compatibility between discrete clusters. Connected graphs merge through pairwise fusion events whose acceptance depends on Laplacian-based observables, yet the resulting dynamics generates highly organized large-scale networks without any background geometry imposed a priori. The model produces an effective coagulation kernel K(i,j) ~ (ij)^gamma with gamma ≈ 0.66, together with sparse graph ensembles exhibiting extensive loop topology, large-scale spectral dimension close to three, extended dominant eigenmodes, and persistent negative discrete curvature. Taken together, these results indicate the emergence of a hybrid discrete geometry: locally finite-dimensional, but globally non-Euclidean. Code, processed data, figures, and manuscript sources are archived separately in the associated Zenodo software/materials record.