fix: force CDP extraction when formula uses variable-bound domains

- computeRequiredFacts now returns domAncestry flag by scanning formula
  bindings for parentVar references (descendants/children domains)
- extractWorld fast-path gate now requires domAncestry === false — formulas
  with parentVar domains will always use CDP extraction, which provides
  the DOM parentNodeId data needed for ancestor index construction
- Prevents silent indeterminate results when descendants(, sel) is
  used on the fast path (which lacks DOM ancestry data)
- Cache key updated to include domAncestry flag ('a') so cached fast vs
  CDP results for the same selectors don't collide

packages/imhotep-playwright/src/extraction.ts

@@ -186,6 +186,7 @@ export function computeRequiredFacts(formulas: FormulaNode[]): {
   topology: boolean
   styles: boolean
   fragments: boolean
+  domAncestry: boolean
 } {
   const facts = new Set<string>()
   for (const formula of formulas) {
@@ -200,11 +201,33 @@ export function computeRequiredFacts(formulas: FormulaNode[]): {
 
   const needsCssLengthMetrics = formulas.some((formula) => formulaNeedsCssLengthMetrics(formula))
 
+  const needsDomAncestry = formulas.some((formula) => {
+    let found = false
+    const scan = (node: FormulaNode) => {
+      if (found) return
+      if (node.kind === 'forall' || node.kind === 'exists') {
+        for (const b of node.bindings) {
+          if (b.domain.parentVar) { found = true; return }
+        }
+        scan(node.body)
+      } else if (node.kind === 'and' || node.kind === 'or') {
+        scan(node.left); scan(node.right)
+      } else if (node.kind === 'not') {
+        scan(node.operand)
+      } else if (node.kind === 'implies') {
+        scan(node.antecedent); scan(node.consequent)
+      }
+    }
+    scan(formula)
+    return found
+  })
+
   return {
     geometry: true, // Always required for subject resolution
     topology: facts.has('topology.stackingContextOf') || facts.has('subject.clipChain'),
     styles: facts.has('styles') || facts.has('computedStyle') || needsCssLengthMetrics,
     fragments: facts.has('subject.fragmentCount') || facts.has('subject.firstFragmentId'),
+    domAncestry: needsDomAncestry,
   }
 }
 
@@ -355,7 +378,7 @@ export function attachMeasuredChWidths(
 export async function extractWorldFastGeometry(
   playwrightPage: Page,
   selectors: string[],
-  requiredFacts?: { geometry: boolean; topology: boolean; styles: boolean; fragments: boolean },
+  requiredFacts?: { geometry: boolean; topology: boolean; styles: boolean; fragments: boolean; domAncestry: boolean },
 ): Promise<{ world: GeometryWorld; selectorToIds: Map<string, number[]>; errors: ImhotepDiagnostic[] }> {
   interface FastExtractedElement {
     tagName: string
@@ -712,7 +735,7 @@ export async function extractWorldFastGeometry(
 export async function extractWorldCdp(
   playwrightPage: Page,
   selectors: string[],
-  requiredFacts?: { geometry: boolean; topology: boolean; styles: boolean; fragments: boolean },
+  requiredFacts?: { geometry: boolean; topology: boolean; styles: boolean; fragments: boolean; domAncestry: boolean },
 ): Promise<{ world: GeometryWorld; selectorToIds: Map<string, number[]>; errors: ImhotepDiagnostic[] }> {
   const errors: ImhotepDiagnostic[] = []
   const selectorToNodeIds = new Map<string, number[]>()
@@ -840,7 +863,7 @@ export async function extractWorld(
   playwrightPage: Page,
   selectors: string[],
   cacheDir?: string | null,
-  requiredFacts?: { geometry: boolean; topology: boolean; styles: boolean; fragments: boolean },
+  requiredFacts?: { geometry: boolean; topology: boolean; styles: boolean; fragments: boolean; domAncestry: boolean },
   allowFastGeometry = false,
 ): Promise<{ world: GeometryWorld; selectorToIds: Map<string, number[]>; errors: ImhotepDiagnostic[] }> {
   async function resolveViewport(): Promise<{ width: number; height: number }> {
@@ -876,7 +899,7 @@ export async function extractWorld(
   const resolvedCacheDir = cacheDir === null ? null : (cacheDir ?? getDefaultCacheDir())
   const cacheNamespace = getPageCacheNamespace(playwrightPage)
   const cacheSelectors = requiredFacts
-    ? [...filteredSelectors, `__imhotep_facts:${requiredFacts.geometry ? 'g' : ''}${requiredFacts.topology ? 't' : ''}${requiredFacts.styles ? 's' : ''}${requiredFacts.fragments ? 'f' : ''}:${allowFastGeometry ? 'fast' : 'cdp'}`, `__imhotep_page_ns:${cacheNamespace}`]
+    ? [...filteredSelectors, `__imhotep_facts:${requiredFacts.geometry ? 'g' : ''}${requiredFacts.topology ? 't' : ''}${requiredFacts.styles ? 's' : ''}${requiredFacts.fragments ? 'f' : ''}${requiredFacts.domAncestry ? 'a' : ''}:${allowFastGeometry ? 'fast' : 'cdp'}`, `__imhotep_page_ns:${cacheNamespace}`]
     : [...filteredSelectors, `__imhotep_page_ns:${cacheNamespace}`]
 
   if (resolvedCacheDir !== null) {
@@ -894,6 +917,7 @@ export async function extractWorld(
   const useFastGeometry = allowFastGeometry
     && requiredFacts?.geometry === true
     && requiredFacts.topology === false
+    && requiredFacts.domAncestry === false
 
   const result = useFastGeometry
     ? await extractWorldFastGeometry(playwrightPage, filteredSelectors, requiredFacts)