refactor: switch index from SQLite to JSON with relative paths

manage_index.py:
- Complete rewrite from SQLite to JSON file format
- All file paths stored as relative (relative to video directory)
- Moving the entire video directory does not break references
- Paths outside video dir stored as absolute (editable in text editor)
- Same 8 subcommands, same CLI interface

SKILL.md:
- Step 5: SQLite schema replaced with JSON structure example
- Verification checklist: .vedit.db → .vedit.json

README.md + README.zh.md:
- Features: 'SQLite database' → 'JSON file with relative paths'
- Project structure: 'SQLite index management' → 'JSON index management'
- 'Index Database' section → 'Index File' with relative path explanation

.gitignore:
- *.vedit.db → *.vedit.json

SKILL.md

@@ -102,47 +102,55 @@ uv run --directory SKILL_DIR/scripts/transcription funasr-nano VIDEO_PATH --list
 
 ### Step 5 — Manage index file
 
-An SQLite database tracks all processing artifacts to avoid duplicate work. It lives **next to the video file**.
+A JSON file tracks all processing artifacts to avoid duplicate work. It lives **next to the video file** and is human-readable and editable.
 
 ```
-<video_dir>/<video_stem>.vedit.db
+<video_dir>/<video_stem>.vedit.json
 ```
 
-Schema (managed by `scripts/index/manage_index.py`):
+**All file paths are stored as relative paths** (relative to the video directory). Moving the entire directory does not break any references. If files are split across directories, paths outside the video directory are stored as absolute paths — the user can edit the JSON directly with a text editor to fix them.
 
-```sql
-CREATE TABLE IF NOT EXISTS transcription (
-    id INTEGER PRIMARY KEY AUTOINCREMENT,
-    json_path TEXT NOT NULL,
-    track_index INTEGER NOT NULL,
-    created_at REAL NOT NULL,    -- Unix timestamp
-    duration_s REAL
-);
+Structure (managed by `scripts/index/manage_index.py`):
 
-CREATE TABLE IF NOT EXISTS clips (
-    id INTEGER PRIMARY KEY AUTOINCREMENT,
-    start_time REAL NOT NULL,    -- seconds from video start
-    end_time REAL NOT NULL,
-    path TEXT NOT NULL,
-    created_at REAL NOT NULL,    -- Unix timestamp
-    reason TEXT                  -- why this clip was extracted
-);
-
-CREATE TABLE IF NOT EXISTS frames (
-    id INTEGER PRIMARY KEY AUTOINCREMENT,
-    clip_id INTEGER NOT NULL REFERENCES clips(id),
-    timestamp REAL NOT NULL,     -- seconds from video start
-    path TEXT NOT NULL,
-    scene_score REAL,            -- ffmpeg scene score if available
-    method TEXT NOT NULL,        -- 'scene' | 'sample' | 'both'
-    created_at REAL NOT NULL     -- Unix timestamp
-);
+```json
+{
+  "transcriptions": [
+    {
+      "id": 1,
+      "json_path": "video_track1_fun-asr-nano.json",
+      "track_index": 1,
+      "created_at": 1783997794.78,
+      "duration_s": 120.5
+    }
+  ],
+  "clips": [
+    {
+      "id": 1,
+      "start_time": 30.0,
+      "end_time": 60.0,
+      "path": "video_clips/clip_30-60.mkv",
+      "created_at": 1783997794.85,
+      "reason": "user asked about this segment"
+    }
+  ],
+  "frames": [
+    {
+      "id": 1,
+      "clip_id": 1,
+      "timestamp": 32.0,
+      "path": "video_frames/frame_0001.jpg",
+      "scene_score": 0.45,
+      "method": "scene",
+      "created_at": 1783997795.0
+    }
+  ]
+}
 ```
 
 Use `scripts/index/manage_index.py` for all CRUD operations:
 
 ```bash
-# Initialize database (idempotent)
+# Initialize index file (idempotent)
 uv run --directory SKILL_DIR python scripts/index/manage_index.py init --video VIDEO_PATH
 
 # Add transcription record
@@ -165,6 +173,9 @@ uv run --directory SKILL_DIR python scripts/index/manage_index.py list
 
 # Check if a time range has already been extracted
 uv run --directory SKILL_DIR python scripts/index/manage_index.py check-range --start S --end E
+
+# Remove records for files that no longer exist on disk
+uv run --directory SKILL_DIR python scripts/index/manage_index.py clean
 ```
 
 **Completion criteria:** index file exists and all produced artifacts are recorded in it.
@@ -349,7 +360,7 @@ Check only the items relevant to the steps actually executed. Not all items appl
 - [ ] Video path and audio track index(es) confirmed. *(Step 2 — required when video processing is needed)*
 - [ ] User's editing goal understood. *(Step 3 — skip if not relevant to the user's request)*
 - [ ] Transcription completed for all requested tracks, or reused from cache. *(Step 4)*
-- [ ] Index file initialized at `<video_dir>/<video_stem>.vedit.db`. *(Step 5 — always required when any processing is done)*
+- [ ] Index file initialized at `<video_dir>/<video_stem>.vedit.json`. *(Step 5 — always required when any processing is done)*
 - [ ] All extracted clips and frames recorded in the index. *(Step 6 — only if frames were extracted)*
 - [ ] Vision analysis performed where needed. *(Step 7 — only if frames were extracted)*
 - [ ] Edit plan produced as Markdown table with overall recommendation. *(Step 8 — skip if not relevant to the user's request)*