Yajilin
Shade some cells, then run one closed loop through every cell you did not shade. No two shaded cells touch. Each black clue is outside the loop and its arrow counts the shaded cells in that direction, all the way to the edge. Click a cell to cycle shaded → on-the-loop → blank; drag from cell to cell to draw the loop.
Only half of this puzzle can be pinned by clues
The shading and the loop are not two stages you can do in order. A cell is shaded exactly when the loop does not pass through it, so every deduction about one is a deduction about the other. But they are not symmetric, and the asymmetry decides how the whole thing has to be built: a clue cell is off the loop by definition. Adding a clue can therefore remove a cell from the loop, and that is the only thing it can do to it. It can never steer the routing.
So if the cells the loop covers admit two different closed circuits, the board has two solutions and no amount of extra clues will ever fix it. Uniqueness of the routing has to be designed into the loop's shape before a single clue exists. Grown freely, these loops have exactly one circuit 0% of the time at 8×8 and above — median 52 rival circuits at 8×8. The generator descends the loop's shape against that count until it reaches one.
A pretty argument that turned out to be worthless
A grid is bipartite, so a closed loop alternates colours and must cover equally many of each. That fixes the difference between the shaded counts on the two colours from the clue positions alone, before the puzzle starts. It is true, it costs one pass over the board, and measured against the arrow rules it decides zero extra cells on 0 of 40 boards and refutes 1 wrong guess in 1090. The identity only bites at the two ends of a feasible interval, and that interval stays wide until the board is nearly solved anyway. It ships here as the rival that loses — pick parity in the hint menu and watch it match arrows exactly.
What actually carries the load is the loop's own structure: degrees, dead ends, circuits that would close too early, cells stranded out of reach. Drop it and the strongest fixpoint falls from 78% of cells to 39%. A rule set that finishes a board without guessing is also a proof that the board has one solution, because every propagator here is sound.