- Introduce group-based table assembly: grid-adjacent pieces snap together on the table, drag as one rigid unit, and lock onto the board as a block
- Extract join/lock rules into pure `resolveDrop` in JigsawLogic.js with a headless verification suite (tools/verifyJigsaw.js) covering fit guarantee, joining, locking, and win counting
- Replace the flat top-bar buttons with a "Menu ▾" dropdown panel to free the top-right corner for the shared site music HUD
- Integrate MusicPlayer soundtrack via getGameSoundtrack() and pin it to the fixed HUD camera
