The Solution
The Reduced Domains
At a fixpoint, propagation has repeated every constraint until nothing else changes. For the A<B<C toy, that fixpoint is already a full solution because every domain is a singleton. The diagram reads the solution directly from domains, showing how a solver can sometimes finish before any search branch is needed.
Every domain is singleton
At the fixpoint, the domains are A{1} B{2} C{3}. Interpretation: a fixpoint with all singleton domains is already a complete assignment. Why: there is no remaining choice for any task, so search has nothing left to decide.
Read the solution
The unique solution is A=1, B=2, C=3. Each singleton domain contributes its one remaining value. Why: the solution is read from the domains themselves, not from a separate authored answer.
No search needed
Propagation alone solved this instance. Why: repeated sound pruning reduced every domain to one value without making a trial assignment. That is the best case for a propagator: the constraints do the search work before branching begins.
Diagram note
Solved cells are singleton values; the grid is recomputed from the precedence chain. The exact claim is narrow: for this finite-domain toy, deterministic propagation reaches the unique assignment. No separate search trace is hidden off-screen; the domain grid itself is the certificate here. Every remaining candidate is therefore part of the assignment. Pixel positions are rounded for layout; every number shown is exact.