Kakuro / Fillomino / Masyu / Yajilin / Hashiwokakero / Nurikabe / Slitherlink / Star Battle Puzzle Generator with Uniqueness Prover

Solvers (all exhaustive, never heuristic): Kakuro cell-by-cell with row/column sum bounds; Fillomino region placement over fixed polyominoes anchored in scan order (each tiling counted once; the checkerboard reveal guarantees completeness — every region of ≥2 cells contains a revealed clue); Masyu/Yajilin cycle enumeration (anchor edge-order dedupe, pearl/loop rules validated on exit); Hashiwokakero per-line 0/1/2 bridge backtracking with degree caps, precomputed crossings and final connectivity; Nurikabe region placement (each island holds exactly one matching clue, sea connected, no 2×2 pool); Slitherlink vertex-grouped edge backtracking with union-find cycle closure; Star Battle row-by-row star pairs. Difficulty = solver nodes (<2k easy, <30k medium, else hard). Uniqueness: counting stops at two solutions — count=1 without exhausting the budget is a proof of uniqueness; exhaustion is reported honestly as “unproven”. The same family + seed always regenerates the identical board.