Port the PC and boxes

Read TileCollisionStdScripts from the ROM so the Pokémon Center PC runs
PokemonCenterPC: Bill's PC (deposit, withdraw, release, change and name
boxes), the player's item storage (withdraw, deposit, toss, mail box) and
Oak's Pokédex rating. The house PC now opens the full player's PC menu.

A catch with a full party goes to the current box through SendMonIntoBox;
a full box keeps the ball, and filling it queues Bill's call as a memory
script after the battle. Saves gain boxes, box names and PC items,
migrated by absence.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

docs/PLAN.md

@@ -116,15 +116,28 @@ The numbered sections below keep their full scope. Each one opens with a checkli
 - `GetPokeBallWobble` runs with `WobbleProbabilities` for each shake and picks the break-free message. Every throw uses the ball and, if the Pokémon breaks free, the turn. In trainer battles the ball is blocked, but the ball and turn are still used.
 - A caught Pokémon is reloaded as `LoadEnemyMon` does, which redraws the wild item roll (the item itself is kept). It keeps its current HP, status, item and DVs, and gets back the moves and full PP it appeared with. It joins the party with `SetCaughtData`, is registered as caught (with the new-data message once the Pokédex is owned) and can be nicknamed; a blank name keeps the species name. The Pokédex page itself is not presented yet.
 - Route 29's `Route29Tutorial1/2` and `CatchingTutorialDudeScript` run from the ROM. `catchtutorial` runs the battle as "DUDE": no Pokémon is sent out, the Dude's own Poké Ball always catches, and the Rattata is only seen, not kept. Messages advance on their own, as with `CatchTutorial`'s auto input.
-- A catch with six Pokémon in the party would go to the PC (`SendMonIntoBox`), which is not ported, so the battle is refused and discarded. Other balls (Kurt's balls, Park and Safari) and non-ball items in battle are not usable yet.
+- A catch with six Pokémon in the party goes to the current box (see the PC section below). Other balls (Kurt's balls, Park and Safari) and non-ball items in battle are not usable yet.
 - A local stress run of 2,160 wild battles (three starters, ten early species, six levels) caught 2,047 Pokémon without refusals.
 - Next: the PC and boxes, player switching and other items in battle, then party and bag menus.
 
+## Implemented: the PC and boxes
+
+- `TileCollisionStdScripts` is read from the ROM, so facing a `COLL_PC` tile (in any direction, as in the original) runs `PCScript`. Bookshelves, TVs and similar tiles no longer need the player to face up.
+- `PokemonCenterPC` checks for a Pokémon, then lists the PCs from `PokemonCenterPC.WhichPC`: Bill's PC and the player's PC, plus Oak's PC once the Pokédex is owned. The Hall of Fame PC is refused, since no Hall of Fame entry can exist yet.
+- Bill's PC: deposit (`BillsPC_CheckMail_PreventBlackout` keeps the last Pokémon and the last one that has not fainted; `RestorePPOfDepositedPokemon`), withdraw (`CalcLevel`, then `CalcMonStats` with stat experience, full HP and no status), release with confirmation ("Bye," with the species name), and change box: switch with the ROM's confirmation, name (a blank name keeps the old one) and print (only the empty-box message). Menus and messages come from the ROM; lists are presented natively with each Pokémon's level or each box's count.
+- The player's PC withdraws, deposits (from every pocket; untossable items move one at a time) and tosses items (up to 50 stacks, `RemoveItemFromPocket` slot rules), and shows the empty mail box. The house PC adds DECORATION, which closes the PC after a change.
+- Oak's PC rates the Pokédex from `OakRatings`.
+- Capture with a full party runs `SendMonIntoBox`: the Pokémon goes first in the current box, with restored PP and `SetBoxMonCaughtData`, can be nicknamed and shows `BallSentToPCText`. If the box is already full the ball is not used (`Ball_BoxIsFullMessage`). A catch that fills the box sets `BATTLERESULT_BOX_FULL`; `reloadmapafterbattle` then queues Bill's call (`Script_SpecialBillCall`) as a memory script that runs at the next `PlayerEvents` and is not saved, as in the original.
+- `VAR_BOXSPACE` reads the current box.
+- Save format 3 gained `storage` (boxes, the current box and box names; a null name is the ROM default) and `pcItems`, migrated by absence to empty storage.
+- Not ported: MOVE PKMN W/O MAIL and the stats screen (both show a notice and return to the menu), printing, a `givepoke` with a full party (refused; no open map reaches it) and the tutorial with a full party and box (the original repeats the unusable ball). Changing boxes does not show the save messages; the native session saves continuously.
+- Next: the introduction's naming and clock screens, player switching and other items in battle, then party and bag menus.
+
 ## Native battles: current state
 
-The battle core, ROM tables, encounter hooks, battle UI and whiteout hooks are present. Unit tests cover wins, escape, loss, experience, move learning and capture; reference tests compare damage and type effectiveness. Browser tests drive a test-only wild encounter through the real UI: victory with level-up and move learning, escape, whiteout, catching with a nickname, keyboard and on-screen D-pad menu navigation, mid-battle backup restore, and rollback of unsupported effects. Real Route 29 encounters now use the ROM's encounter tables. Player switching, items other than balls in battle and the PC remain unfinished.
+The battle core, ROM tables, encounter hooks, battle UI and whiteout hooks are present. Unit tests cover wins, escape, loss, experience, move learning and capture; reference tests compare damage and type effectiveness. Browser tests drive a test-only wild encounter through the real UI: victory with level-up and move learning, escape, whiteout, catching with a nickname, keyboard and on-screen D-pad menu navigation, mid-battle backup restore, and rollback of unsupported effects. Real Route 29 encounters now use the ROM's encounter tables. Player switching and items other than balls in battle remain unfinished.
 
-This is still not a complete new game. Full party/bag/Pokégear menus, PC storage, story progression beyond Route 30 and Mr. Pokémon's house, and audio remain unfinished. The Key Items menu supports the Bicycle; the bedroom PC supports decorations. Surfing and terrain animation now have native implementations; later maps remain gated. Save slots, a Johto/Kanto atlas, Pokédex records, online Link, friends and real-world steps come later.
+This is still not a complete new game. Full party/bag/Pokégear menus, story progression beyond Route 30 and Mr. Pokémon's house, and audio remain unfinished. The Key Items menu supports the Bicycle; the PCs store Pokémon, items and decorations. Surfing and terrain animation now have native implementations; later maps remain gated. Save slots, a Johto/Kanto atlas, Pokédex records, online Link, friends and real-world steps come later.
 
 ## 1. Complete the overworld foundation
 
@@ -191,7 +204,7 @@ their scripts and story progression are supported.
 - [x] Capture and the catching tutorial
 - [x] Battles: stats, damage, types, accuracy, criticals, status, turn order, fainting, experience, move learning, trainer AI, trainer send-outs and prize money
 - [ ] Player switching, and items other than balls, in battle
-- [ ] The PC and boxes (catching with a full party)
+- [x] The PC and boxes (catching with a full party)
 - [ ] The introduction's naming and clock screens
 - [ ] Controlled-seed comparisons with the original beyond damage and type effectiveness
 - [ ] Acceptance: one continuous playthrough of the opening quest with save/reload. The scenes are tested individually from fixtures so far.
@@ -200,7 +213,7 @@ Introduce native player, party, Pokémon, inventory, money and quest models. Rea
 
 Expand script calls, choices, scene state, inventory commands and native special handlers. Translate routines reached through assembly calls into explicit native services; never fall back to emulator execution in the shipping game.
 
-Meeting Mom, Elm's introduction, the starter, the aide's Potion, Route 29, Cherrygrove, Route 30's trainers, Mr. Pokémon's house, the Cherrygrove rival battle, the return to Elm, capture and the catching tutorial run now. Next: the PC, then the introduction's naming and clock screens.
+Meeting Mom, Elm's introduction, the starter, the aide's Potion, Route 29, Cherrygrove, Route 30's trainers, Mr. Pokémon's house, the Cherrygrove rival battle, the return to Elm, capture, the catching tutorial and the PC run now. Next: the introduction's naming and clock screens.
 
 Complete and validate the native battle engine: deterministic randomness, stats, move selection, accuracy/critical checks, damage, status, turn order, switching, fainting, experience, capture and rewards. Compare controlled seeds and states with the original, including integer rounding and overflow behavior.