Buffered Voronoi Safety Projection

1) Integration point: use this as an action shield after a decentralized graph policy. Each agent i receives its local observation and neighbor predictions, produces a nominal velocity or displacement z_i with a GNN or MLP, rolls it forward for H steps, and applies the projection independently at each time step. The announced trajectory is the previous iteration's trajectory; the projected trajectory is broadcast to neighbors. 2) Pseudocode: initialize all announced trajectories p_i^a from the policy; for k=0,...,K-1, compute q_ij and n_ij for every local threat edge, construct the half-space right-hand side n_ij^T p_j^a+r_ij, solve the small Euclidean projection QP for each agent, and replace p_i^a by the result. In Jacobi mode all agents use iteration-k announcements; in Gauss-Seidel mode process agents in a fixed order and immediately broadcast each new result. Execute only the first action, then replan. 3) Computed from the mechanism: half-space normals, local projection QPs, and the safety buffer. Estimate empirically: the Jacobian G by finite differences of the decentralized update map, its spectral radius, and prediction uncertainty sigma_ij from an ensemble or recent residuals. 4) First cheap experiment: train five agents with a two-layer graph policy on 2-D particle navigation, comparing no shield, centralized pairwise projection, buffered Jacobi, and buffered Gauss-Seidel. Sweep K and r. The quantitative prediction is a sharp practical transition: for fixed coupling, violation probability should fall to approximately zero once r exceeds the maximum unmodeled relative displacement, while iteration residuals should decay geometrically when the estimated rho(G)<1 and fail to decay when rho(G)>1. Measure whether the observed convergence boundary agrees with rho(G)=1 within 20%.