INTERACTIVE FIGURE 7The urgency horizon — measured curves on a live board
ring liberties2
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.