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The depths quoted for the rival-coalition mechanism came from an exploratory run made before the coalition-sizing fix, where beta=0.4 was realising 0.47. Measured properly (median over 6 replicates, deepest fork off the canonical chain): K=1 865 blocks (784-964) K=2 17 K=3 9 K=4 7 not the "~2000 and ~2" first written. The mechanism is unchanged and the contrast is still stark. Also notes why the lead cap does not bound this: it caps the LEAD, not the chain length, so a private chain can run long while the public chain keeps pace beside it — the near-tie race that produces the deepest forks. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>