solver: replace cell DFS with skyline search

Represent partial placements as column heights and branch on the narrowest local valley. This removes the board-area cell state and makes first-solution search substantially smaller for feasible orders.

Expose direct-search and candidate-order benchmark controls so the skyline core can be measured independently of odd-order construction. Document the completeness argument and the 10/11 test-tier decision.

Tests: Release, Debug, ASan, and UBSan CTest (10 passed each)

Refs: #4

TESTING.md

@@ -13,9 +13,13 @@ The tests independently check board dimensions, square multiplicities, bounds,
 overlap, and complete coverage.  They cover small unsatisfiable solver inputs, a
 known order-8 solution, invalid placement diagnostics, and construction of an
 order-9 solution from the order-8 fixture.  The routed order-9 solver test
-checks that its search counters exactly match order 8.  The rendering test also
-formats the known order-8 solution and checks the resulting grid dimensions and
-coverage.
+checks that its search counters exactly match order 8.  The skyline tests check
+smallest-width valley selection and deterministic tie-breaking, validate an
+order-8 result with descending candidates, and independently validate a direct
+order-9 search with ascending candidates.  That direct test is deliberately
+separate from the public order-9 route, which uses even-predecessor
+construction.  The rendering test also formats the known order-8 solution and
+checks the resulting grid dimensions and coverage.
 
 When Python is available, `reference-support` also tests the dependency-free
 placement JSON validator.  If the optional OR-Tools package is present, it
@@ -45,6 +49,4 @@ ctest --test-dir build-ubsan --output-on-failure
 ```
 
 The sanitizer flags shown are supported by Clang and GCC.  Other compilers may
-require different flags.  A feasible solver run currently exposes the
-pre-existing defect tracked by issue #14; the test additions deliberately do
-not include its separate fix.
+require different flags.