feat(T06): hostPath working-memory sync and repo-relative sink paths

Mount the-custodian memory/working from the railiance01 clone (hostPath)
so sweep writeback commits daily-triage notes; worker runs as uid 1000;
progress events store repo-relative working_memory_path; ops inventory
defaults use custodian:// URIs.

src/activity_core/runtime_paths.py

@@ -34,4 +34,24 @@ def resolve_runtime_path(raw_path: str) -> Path:
     if value.startswith(_ACTIVITY_CORE_SCHEME):
         return (activity_core_root() / value.removeprefix(_ACTIVITY_CORE_SCHEME)).resolve()
 
-    return Path(value).expanduser()
+    return Path(value).expanduser()
+
+
+def custodian_working_memory_dir() -> Path:
+    return resolve_runtime_path("custodian://memory/working")
+
+
+def custodian_repo_relative(path: Path) -> str:
+    """Return a repo-relative POSIX path when under CUSTODIAN_REPO_ROOT."""
+    root = custodian_repo_root().resolve()
+    try:
+        return path.resolve().relative_to(root).as_posix()
+    except ValueError:
+        return path.as_posix()
+
+
+def default_ops_inventory_path() -> Path:
+    raw = os.environ.get("OPS_INVENTORY_PATH", "").strip()
+    if raw:
+        return resolve_runtime_path(raw)
+    return resolve_runtime_path("custodian://ops/service-inventory.yml")