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

BENCHMARKING.md

@@ -21,6 +21,8 @@ and `--candidate-order`.  The choices are `ascending`, `descending`, and
 The production default also removes equivalent D4 board orientations by
 constraining the unique unit square.  Pass `--no-symmetry` to obtain an
 otherwise identical unconstrained baseline.
+The production default also applies the valley-capacity rule described below.
+Pass `--no-pruning` to obtain an otherwise identical unpruned search.
 Order 9 uses the constructive odd-order path, searching order 8 and then tiling
 the enlarged border, so it is suitable for normal local benchmarking:
 
@@ -45,8 +47,9 @@ solve time.  Constructed odd-order cases report predecessor search and
 construction separately.  The document also records compiler,
 flags, build type, commit, OS/CPU metadata, worker count, search policy, seed,
 timeouts, errors, invalid outputs, and the stdout policy.  Search counts must
-be stable across repeated runs.  Prune and task counters are zero for the
-current unpruned, single-threaded solver and reserve stable schema fields for
+be stable across repeated runs.  Prune counters report enabled search rules;
+they are zero in the corresponding disabled modes.  Task counters remain zero
+for the current single-threaded solver and reserve stable schema fields for
 later work.
 
 The runner writes its JSON report before returning a failure status if any mode
@@ -72,6 +75,38 @@ Do not use wall-clock thresholds as correctness checks.  Keep the generated
 JSON outside version control unless it is being deliberately added as a named
 comparison baseline.
 
+## Valley-capacity pruning
+
+For a selected valley, let its rim be the lower height of its two neighbours,
+treating a board edge as full height.  Until the valley reaches that rim, no
+square wider than the valley can enter it.  Therefore the combined area of all
+remaining squares no wider than the valley must be at least the valley width
+times its depth below the rim.  Rejecting a state when that necessary
+inequality fails is sound.  At widths one and two it provides the usual
+narrow-gap capacity checks without separate special cases.
+
+The rule is compiled out of the recursive search in `--no-pruning` mode.
+Instrumented output records `valley_capacity_checks` and
+`valley_capacity_prunes` as well as the aggregate pruning counters, allowing
+enabled and disabled runs to report nodes, checks, hits, and elapsed time.
+
+Measurements used the issue #10 working tree based on commit `f37e087`, Apple
+Clang 21.0.0, `-O3 -DNDEBUG`, macOS arm64, one worker, one warm-up, and five
+measured repetitions.  The production ascending policy and D4 constraint were
+enabled.  Every result passed the benchmark's independent validator and all
+counters were stable:
+
+| Order | Valley capacity | Median solve (range) | Nodes | Checks | Prunes |
+| --- | --- | ---: | ---: | ---: | ---: |
+| 7 exhaustive | enabled | 0.996 s (0.990-0.998 s) | 13,833,048 | 13,833,048 | 7,411,551 |
+| 7 exhaustive | disabled | 1.110 s (1.109-1.111 s) | 14,997,603 | 0 | 0 |
+| 8 first solution | enabled | 0.205 s (0.204-0.208 s) | 2,724,096 | 2,724,095 | 1,606,836 |
+| 8 first solution | disabled | 0.228 s (0.228-0.233 s) | 2,931,203 | 0 | 0 |
+
+The rule reduced nodes by 7.8% for order 7 and 7.1% for order 8.  Its low
+per-node cost also reduced median counted solve time by 10.3% and 9.9%,
+respectively, so it remains enabled by default.
+
 ## D4 board symmetry
 
 Every solution contains exactly one 1-by-1 square.  Rotations and reflections