refactor: remove global mutable state — registry guard, compat warning, stats

predicates.ts: Replace defaultPredicatesRegistered boolean guard with
  sentinel predicate check inside the registry. registerDefaultPredicates()
  is now always safe to call — no module-scope flag that can drift out
  of sync with the actual registry state. clearPredicateRegistry() no
  longer needs to manually reset a flag.

extraction.ts:
  - Replace compatibilityWarningEmitted process-singleton boolean with
    WeakSet<ImhotepUi> (warnedUis). Each ImhotepUi instance now gets its
    own compatibility warning, fixing the bug where two pages would share
    a single warning gate.
  - Export resetExtractionPathStats() for test isolation of fast-path
    and CDP fallback counters.

598 SDK + 3 conformance + 57 E2E = 658 tests pass.

packages/imhotep-solver/src/predicates.ts

@@ -151,7 +151,6 @@ export function listRegisteredPredicates(): string[] {
 
 export function clearPredicateRegistry(): void {
   globalPredicateRegistry.clear();
-  defaultPredicatesRegistered = false;
 }
 
 export function getPredicateDescriptor(name: string): PredicateDescriptor | undefined {
@@ -1196,11 +1195,16 @@ export const hasGapPredicate: PredicateEvaluator = {
 // Register Defaults
 // ---------------------------------------------------------------------------
 
-let defaultPredicatesRegistered = false;
+/** Sentinel registered to detect if defaults were already installed. */
+const DEFAULT_SENTINEL = '__imhotep_defaults_registered__'
 
 export function registerDefaultPredicates(): void {
-  if (defaultPredicatesRegistered) return;
-  defaultPredicatesRegistered = true;
+  if (globalPredicateRegistry.get(DEFAULT_SENTINEL)) return
+  // Register sentinel first so partial failures don't cause infinite loops.
+  globalPredicateRegistry.register({
+    descriptor: { name: DEFAULT_SENTINEL, arity: 0, domains: [], requiredFacts: [] },
+    evaluateTuple: () => ({ truth: 'indeterminate' }),
+  })
   registerPredicate(widthPredicate);
   registerPredicate(heightPredicate);
   registerPredicate(abovePredicate);