diff --git a/fixos/diagnostics/venv_cleanup.py b/fixos/diagnostics/venv_cleanup.py
index 4c43326..0b1cb9d 100644
--- a/fixos/diagnostics/venv_cleanup.py
+++ b/fixos/diagnostics/venv_cleanup.py
@@ -119,7 +119,13 @@ def observe(field, callback, pid=process_pid):
 
 
 def _within(path: Path, parent: Path) -> bool:
-    return path == parent or parent in path.parents
+    # Every process path is compared with many projects and mounts. Walking
+    # all its ancestors repeatedly makes inventory needlessly expensive.
+    if os.path.normcase(path.anchor) != os.path.normcase(parent.anchor):
+        return False
+    return tuple(map(os.path.normcase, path.parts[: len(parent.parts)])) == tuple(
+        map(os.path.normcase, parent.parts)
+    )
 
 
 def _measure_project_source(project: Path, exclude: tuple[str, ...]) -> dict:
diff --git a/project/ticket-116/README.md b/project/ticket-116/README.md
new file mode 100644
index 0000000..71e1f96
--- /dev/null
+++ b/project/ticket-116/README.md
@@ -0,0 +1,38 @@
+# Ticket 116: Avoid repeated ancestor walks in project containment checks
+
+- **ID**: ticket-116
+- **Owner**: agent:codex
+- **Status**: IN_PROGRESS
+- **Workflow state**: PUBLICATION
+- **Created**: 2026-10-31
+
+## Goal and scope
+
+Project inventory repeatedly compares every visible process path and mount
+against project/artifact paths. The old containment helper constructs and
+compares every ancestor each time. Live MCP inventory exceeded 90 seconds;
+a diagnostic equivalent-prefix comparison completed the project phase in
+9.3 seconds and state inventory in 20.2 seconds. Preserve lexical and native
+case behavior while eliminating the repeated ancestor walk.
+
+SESSION_EXECUTION_AUTHORIZATION: the user requested execution of the remaining
+FixOS/host repairs on 2026-10-31. This bounded fix includes independent protected
+publication and deployment to both existing host installations.
+
+## Acceptance criteria
+
+- [x] AC-01: Equality, descendants, sibling boundaries, relative anchors,
+  lexical parent segments and native-case semantics match existing behavior.
+- [x] AC-02: Unrelated deep paths do not enumerate their ancestors; affected
+  tests and managed governance pass with unchanged cleanup protections.
+- [ ] AC-03: Required full checks, independent exact-head publication and
+  installed-module/MCP inventory verification succeed.
+
+## Validation
+
+The new ancestor-walk regression failed before the change. After the change,
+56 affected tests pass, including all 14 containment tests. The affected
+Testless coverage scan also passes all 56 tests. Ruff passes for both changed
+implementation paths. Required full checks and independent publication bind
+the final commit; live deployment will verify both installed module hashes
+and the actual MCP project-inventory duration.
diff --git a/project/ticket-116/intent.json b/project/ticket-116/intent.json
new file mode 100644
index 0000000..f8a669d
--- /dev/null
+++ b/project/ticket-116/intent.json
@@ -0,0 +1,76 @@
+{
+  "schema": "new-project.intent/v3",
+  "ticket": "ticket-116",
+  "summary": "Avoid repeated ancestor walks in project containment checks",
+  "workstream": "application",
+  "classification": {
+    "kind": "BUG",
+    "priority": "P1",
+    "origin": "requested"
+  },
+  "allowedPaths": [
+    "project/ticket-116/**",
+    "fixos/diagnostics/venv_cleanup.py",
+    "tests/unit/test_path_scope.py"
+  ],
+  "forbiddenPaths": [
+    "project/ticket-*/user-*.md"
+  ],
+  "stacks": [
+    "python"
+  ],
+  "dependsOn": [],
+  "conflictsWith": [],
+  "integrationTicket": null,
+  "delivery": {
+    "acceptedBaseSha": "1badd07decd568bc1012c823354c03ee62a0981b",
+    "targetBranch": "main",
+    "outcome": "Independently publish and deploy equivalent lexical containment checks that allow project inventory to complete on the live host without repeated ancestor traversal.",
+    "nonGoals": [
+      "No cleanup eligibility, process protection, retention or storage-floor changes",
+      "No filesystem resolution or removal of unknown work",
+      "No MCP schema or new runtime dependency"
+    ],
+    "complexity": "XS",
+    "estimatedMinutes": 10,
+    "budgets": {
+      "maxImplementationFiles": 2,
+      "maxAffectedComponents": 1,
+      "maxPublicInterfaceChanges": 0,
+      "maxRuntimeDependencies": 0
+    },
+    "architecture": {
+      "status": "accepted",
+      "decision": "Compare native-case normalized anchors and path component prefixes, preserving lexical containment while avoiding Path.parents enumeration per process/project pair.",
+      "components": [
+        {
+          "name": "project-path-scope",
+          "paths": [
+            "fixos/diagnostics/venv_cleanup.py",
+            "tests/unit/test_path_scope.py"
+          ]
+        }
+      ],
+      "responsibilityChanges": false,
+      "interfaceChanges": [],
+      "dataChanges": [],
+      "ui": {
+        "impact": "none",
+        "states": [],
+        "evidence": []
+      },
+      "rollback": "Revert through independent protected publication and reinstall the previous reviewed artifact."
+    },
+    "runtimeDependencies": [],
+    "validation": [
+      {
+        "criterion": "AC-01",
+        "commands": [
+          "python -m pytest tests/unit/test_path_scope.py tests/unit/test_venv_cleanup.py -q",
+          "./project/governance-check.sh"
+        ],
+        "evidence": "project/ticket-116/README.md"
+      }
+    ]
+  }
+}
diff --git a/tests/unit/test_path_scope.py b/tests/unit/test_path_scope.py
new file mode 100644
index 0000000..ec7256b
--- /dev/null
+++ b/tests/unit/test_path_scope.py
@@ -0,0 +1,48 @@
+"""Lexical containment must stay conservative without walking every ancestor."""
+
+import os
+from pathlib import Path
+
+import pytest
+
+from fixos.diagnostics.venv_cleanup import _within
+
+
+@pytest.mark.parametrize(
+    ("path", "parent", "expected"),
+    [
+        ("/", "/", True),
+        ("/repo", "/repo", True),
+        ("/repo/.venv/bin/python", "/repo", True),
+        ("/repo-old/file", "/repo", False),
+        ("/repo", "/repo/child", False),
+        ("/elsewhere/file", "/repo", False),
+        ("repo/child", "repo", True),
+        ("repo/child", ".", True),
+        ("/repo/child", ".", False),
+        ("repo/child", "/repo", False),
+        ("/repo/../elsewhere", "/repo", True),
+    ],
+)
+def test_existing_lexical_scope_boundaries(path, parent, expected):
+    assert _within(Path(path), Path(parent)) is expected
+
+
+def test_native_case_rules_are_preserved():
+    assert _within(Path("REPO/child"), Path("repo")) is (os.name == "nt")
+
+
+def test_distinct_absolute_anchors_remain_distinct():
+    assert Path("//host/share/file").anchor != Path("/host/share").anchor
+    assert not _within(Path("//host/share/file"), Path("/host/share"))
+
+
+def test_unrelated_deep_path_does_not_enumerate_ancestors():
+    class NoAncestorWalk(type(Path())):
+        @property
+        def parents(self):
+            raise AssertionError("Containment must not enumerate all ancestors")
+
+    path = NoAncestorWalk("/unrelated/" + "/".join(["nested"] * 2048))
+
+    assert not _within(path, Path("/home/tom/github/project"))