Betweenness

Return betweenness centrality over the well-supported co-stress graph.

Phase 2.4 / B3 — which entities are systemic BRIDGES connecting otherwise- separate stress clusters: shortest-path betweenness on the directed co-stress graph, computed by the pure module app.contagion.betweenness and persisted by the slow-cycle calibration pass.

SELF-GATING: betweenness is computed ONLY when the well-supported subgraph (sample_floor_met AND n_joint_tail>=50) clears 120 edges / 35 nodes. When it does NOT (true today, ~54 edges / 20 nodes), this returns a 200 with an explicit status='insufficient_graph_density' carrying the observed and required counts — the honest "not yet", NOT an empty 200 that would read as zero centrality. When it IS computed, returns nodes by betweenness desc + the provenance envelope + the §6 disclaimer. Pre-calibration (no run / no B3 record) returns status='not_calibrated' with a null envelope.