solver: prune insufficient valley capacity

A selected valley cannot admit a square wider than itself until it reaches the lower neighbouring rim. Reject states whose remaining narrow-square area cannot fill that strip, including width-one and width-two gaps.

Keep an unpruned benchmark mode and dedicated counters so the rule remains independently measurable. Record the soundness argument and the measured default-on improvement.

Tests: Debug CTest (12 passed)

Tests: ASan+UBSan CTest (12 passed)

Refs: #10

benchmarks/run.py

@@ -80,7 +80,7 @@ def environment(binary):
 
 
 def run_once(
-    binary, order, mode, search_policy, search_route, symmetry, timeout
+    binary, order, mode, search_policy, search_route, symmetry, pruning, timeout
 ):
     started = time.monotonic()
     try:
@@ -92,6 +92,7 @@ def run_once(
                 search_policy,
                 search_route,
                 symmetry,
+                pruning,
             ],
             check=False,
             capture_output=True,
@@ -237,6 +238,11 @@ def main():
         action="store_true",
         help="disable unique-unit-square D4 symmetry breaking",
     )
+    parser.add_argument(
+        "--no-pruning",
+        action="store_true",
+        help="disable valley-capacity pruning",
+    )
     parser.add_argument(
         "--measure-overhead",
         action="store_true",
@@ -269,6 +275,7 @@ def main():
                     args.search_policy,
                     "direct" if args.direct_search else "public",
                     "none" if args.no_symmetry else "d4",
+                    "none" if args.no_pruning else "valley-capacity",
                     args.timeout,
                 )
         for trial in range(args.repetitions):
@@ -281,6 +288,7 @@ def main():
                         args.search_policy,
                         "direct" if args.direct_search else "public",
                         "none" if args.no_symmetry else "d4",
+                        "none" if args.no_pruning else "valley-capacity",
                         args.timeout,
                     )
                 )
@@ -310,6 +318,7 @@ def main():
             "candidate_order": args.search_policy,
             "search_route": "direct" if args.direct_search else "public",
             "symmetry_breaking": "none" if args.no_symmetry else "d4",
+            "pruning": "none" if args.no_pruning else "valley-capacity",
             "stdout": "captured; rendered grid suppressed by probe",
         },
         "cases": cases,