Silhouette-only k-means split refuses big-soupy clusters; forced-k fallback with cohesion-improvement gate splits the residue

Use Cheeger spectral certificates and modularity lift to gate community visualization

Community-aware graph stream exceeded node budget because mandatory landmarks bypassed limit

Implement graph visualization community projection phase

Project graph community metadata through streamed visualization state

Replace Neo4j GDS with in-process graphology for PageRank and community detection