Aqre
Shade cells so the black cells form one connected group, every numbered region contains exactly that many black cells, and no four consecutive cells in any row or column share a color — the run rule binds black and white alike, so an empty board is already illegal. Click a cell to cycle shaded → white → empty; right-click erases.
The clue budget is the partition
In this series' previous puzzle, Nurimisaki, the answer forced the clue positions — the setter had no dial at all. Aqre is the other extreme: clues sit on regions, and the region partition is drawn freely before any number is printed. Small regions mean many numbers, big regions mean few; borders drawn along the answer's color boundaries make every region all-or-nothing and the counting rule finishes the board alone. The setter owns the information supply — the difficulty lineup is a design choice, not a lottery.
The run rule binds both colors
No four consecutive cells in a row or column may share a color — shaded or unshaded. That makes every 1×4 window owe both colors a cell before a single number is read: black density is pinned into a band, an all-white board is illegal at any size past 3, and the rule propagates in both directions like a pair of interleaved combs.
Four rule sets
quota counts a region both ways: number reached — rest white; free cells exactly the missing blacks — all black. quad closes 1×4 windows about to go monochrome. bridge makes black connectivity local with one articulation-point pass: a cell sealed off from the black group can never be black, the only route between two black cells must be. probe assumes a color on a cell and watches the rules below refute it.