INTERACTIVE FIGURE 7The urgency horizon — measured curves on a live board
ring liberties 2
Left: a stylized member of the race family — the white ring (the exploit's cyclic group) holds an inner black group whose two race liberties are fixed (small dots inside); the slider opens liberties on the ring's outside (dots outside). Circles mark the critical moves — the racing groups' liberties, the only correct moves — sized by the raw policy's probability mass on them. Right: the measured b10 numbers (§2's table, drawn): policy mass and 200-visit search mass on the critical moves, and the ring's ownership read. At 2 liberties the policy plays the race; at 3 the read has already flipped but search still rescues; from 4 the board goes quiet — the policy proposes nothing, so search (which expands only proposals) never looks, and the value head approves. Board schematic; curves measured.