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The quota ceiling was closed-form only. This adds per-node stake so a run can show nodes actually breaking it. - assign_stake: uniform, or heavy-tailed zipf (s ~ 1/rank^a), which is what makes the ceiling bite -- the head sits orders of magnitude above it, the tail far below; - inferred_alpha: converts true relative stake to the sigma/D_hat the lottery actually weighs, so a low estimate inflates every node alpha; - simulate_epoch_emissions: measures the budget over a full epoch. Overrun happens at epoch scale and needs no graph, so this is cheap: proposals are Binomial over the epoch slots, a proposal cancels the next cover, and a node stays at exactly its quota until its wins no longer fit -- at which point it emits more often than everyone else, which is the signal cover traffic exists to suppress. Measured against the closed form at N=20,000, zipf stake, over an epoch: the predicted ceiling falls inside the transition band every time, and at D_hat/D = 1 the smallest overrunning node sits at 0.1468% against a predicted 0.1475%. The D_hat/D normalisation is confirmed empirically -- deflating the estimate to 0.64 pulls the measured ceiling down with it, as the (D_hat/D)*alpha_max form requires. With heavy-tailed stake 99.7% of nodes comply and only the head breaks; the largest holder at 9.5% stake is some 65x over its allowance. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>