Two things the engine proves
Before a puzzle is allowed into the game, the Lattice engine checks two facts about it. First, that it has a solution at all — a complete set of placements that makes every equation true. Second, and more importantly, that the solution is unique: there is no second, different way to fill the board correctly.
If a candidate puzzle can be solved two ways, it fails the test and is discarded. What ships is only the boards that pass both checks. That's the guarantee behind every Lattice you play.
Why uniqueness matters
Uniqueness is what makes "no guessing" possible. If a board had two valid solutions, then at some point you'd reach a cell where two different numbers both work — and the only way forward would be to pick one and hope. That's a guess, and guessing is exactly what separates a logic puzzle from a lottery.
When the solution is unique, every cell has one correct value that is, in principle, deducible from the others. You might not see the deduction yet, but it exists. Being stuck is never a dead end; it's a clue you haven't found.
How the proof is done
The engine doesn't eyeball a board — it searches. A constraint solver attempts to complete the puzzle and, crucially, keeps searching after it finds one answer to see whether a second, different answer exists. Only boards with exactly one completion survive. The same machinery also grades the puzzle, which is where difficulty comes from.
This is why Lattice can promise things other number games can't. The no-guess rule isn't a design aspiration that occasionally slips; it's enforced board by board, automatically, before release.
What it means for you as a solver
Practically, the guarantee changes your strategy. When you hit a wall, you should never reach for trial and error. Instead, re-scan for the most constrained equation — the one with the fewest unknowns — and resume the deduction from there. The answer is always reachable without backtracking.
It also means a correctness complaint is a serious thing. If a Lattice board ever genuinely looked unsolvable, that would be a bug in the proof, not a feature of the puzzle — which is why the team treats "this puzzle looks wrong" reports as the highest priority. In practice, the wall you've hit is almost always a missed clue, not a broken board.
The payoff: a fair fight every time
A guaranteed-unique puzzle is a fair fight. You and the board both know there's exactly one truth to find, and finding it is entirely within your power. That fairness is the quiet thing that makes cross-math satisfying: you never wonder whether you solved it or just got lucky. You solved it.