Your kin is the outlined group you belong to. Your kith is every cell you touch. No arithmetic, no row or column rules — and never a guess.
The outlined group you belong to. A kin of five holds 1 to 5, a kin of three holds 1 to 3. No number twice in the same kin.
Every cell you touch — sides and corners both. No number may sit beside its own kind. On the board it is a dot, so it survives greyscale and crosses a kin outline.
The same grid for everybody, seeded by the date. It stiffens through the week, and the number of printed givens falls with it.