Read the analysis cache before refusing a pass, and own the cache root

Opening a recording while the session that recorded it was still live never reached
``stored_result()``, so the panel reported no result over a recording whose result was on
disk. The guard now follows the cache read, results move to the app's derived-data root
(swept at startup, the old in-recording root ignored), and the panel states which of the
four no-result states it is in, with the pass's own reason.
Verified: apps/studio 462/0/18, shared 431/0/1, autocal 358, ui_check 628/0, both gates
clean, real-GL snapshots per state.

shared/src/orisys_app_shared/paths.py

@@ -121,6 +121,43 @@ def recordings_dir() -> Path:
     return path
 
 
+#: Directory name of the product's per-user data, under the OS's own root for it.
+DERIVED_DIR_NAME = "OrisysStudio"
+#: Subdirectory holding the offline analysis results.
+ANALYSIS_CACHE_DIRNAME = "analysis-cache"
+
+
+def derived_data_dir() -> Path:
+    """The OS-correct per-user root for **derived** (rebuildable) data.
+
+    Windows: ``%LOCALAPPDATA%\\OrisysStudio`` (falling back to
+    ``%USERPROFILE%\\AppData\\Local`` when the variable is unset — a service or a
+    stripped environment, where the fallback is still the right directory). Everywhere
+    else: ``$XDG_CACHE_HOME/OrisysStudio``, or ``~/.cache/OrisysStudio``.
+
+    Deliberately *not* :func:`outputs_dir`: in a packaged build that is the EXE's own
+    directory, and it holds the recordings. Anything the app can rebuild belongs in the
+    user's own derived-data area, where a reinstall cannot destroy it and where writing
+    it needs no permission on the installation.
+    """
+    name = DERIVED_DIR_NAME
+    if os.name == "nt":
+        local = os.environ.get("LOCALAPPDATA", "").strip()
+        base = (
+            Path(local)
+            if local
+            else Path(os.environ.get("USERPROFILE", str(Path.home()))) / "AppData" / "Local"
+        )
+        return base / name
+    cache = os.environ.get("XDG_CACHE_HOME", "").strip()
+    return (Path(cache) if cache else Path.home() / ".cache") / name
+
+
+def analysis_cache_dir() -> Path:
+    """Where the offline analysis results live: the app's own root, never a recording."""
+    return derived_data_dir() / ANALYSIS_CACHE_DIRNAME
+
+
 def preference_path() -> Path:
     return app_root() / "preference.json"