Open the Battle Tower and add the badges' type boosts (Closes #32)

The Route 40 gate, the Battle Tower and its rooms are open with the
offline challenge: the rules, the save before entering, the level menu
with its level and uber checks, seven trainers drawn from
BattleTowerTrainers with Pokémon from BattleTowerMons, BattleTowerText,
save and quit with the receptionist resuming it, cancelling, losing and
the vitamin reward. After each battle the party and Pokédex return to the
quick save's, as LoadPokemonData does.

Battle Tower battles turn off obedience, badge boosts, experience, items,
AI items and prize money, use Falkner's AI attributes, keep Sleep to one
to three turns and never fail the AI's status moves at random. New script
command battletowertext; new specials BattleTowerAction (offline actions),
BattleTowerRoomMenu, CheckForBattleTowerRules, BattleTowerBattle,
LoadOpponentTrainerAndPokemonWithOTSprite, Menu_ChallengeExplanationCancel,
TryQuickSave and Reset.

DoBadgeTypeBoosts was missing from every battle; it now adds an eighth of
the damage for the first badge matching the move's type on the player's
turn, checked against the original routine.

This completes Johto from Azalea to Blackthorn: Kanto, the League and the
S.S. Aqua continue on #33; radio, rematches and Buena's password on #30.

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

docs/NATIVE_PORT.md

@@ -54,6 +54,7 @@ These paths refer to the pinned [PRET source](https://github.com/pret/pokecrysta
 | `game/scripts/lake-of-rage.ts`, Route 42 to Mahogany, the Lake of Rage, the Rocket Hideout and Pryce | `engine/events/magikarp.asm` (`CheckMagikarpLength`, `CalcMagikarpLength`, `PrintMagikarpLength`, `MagikarpHouseSign`), `engine/menus/intro_menu.asm` (`InitializeMagikarpHouse`), `engine/pokemon/search_party.asm` (`FindThatSpecies`), `engine/overworld/scripting.asm` (`DoScene`), `engine/events/money.asm` (`TakeMoney`) | The Magikarp is measured from its own DVs and OT ID with the battle code's `CalcMagikarpLength` (whose `.BCLessThanDE` compares only the high byte). A longer one, compared feet then inches, becomes the record with the Magikarp's OT name as holder; the record starts at 3′6″ by RALPH and is saved as `magikarpRecord`. `FindThatSpecies` reads `wPartySpecies`, where an Egg is EGG, so an Egg is never found. `setmapscene`/`setscene` on a map without a scene variable (Route 43, the Lake of Rage): `GetMapSceneID` leaves `de` alone and `DoScene` still writes the byte through it when it is nonzero. At the Route 43 gate `de` is `EventFlagAction`'s byte offset of `EVENT_CLEARED_ROCKET_HIDEOUT` (4), the MBC3 RAM-enable register, so nothing changes. After the Red Gyarados, `de` is whatever `closetext` left; the port consumes the byte and changes nothing, and that write was not checked in an emulator. `TakeMoney` leaves a short account at zero, so the Route 43 Rockets take all of a smaller balance. The Rocket Hideout's cameras, traps, passwords, executives and Electrodes and Pryce's ice floor run on ported primitives; `PlayCurMonCry` is audio. `tests/mahogany.test.ts` and five playthrough stages cover them. |
 | `game/scripts/blackthorn.ts`, the Radio Tower takeover, Ice Path, Blackthorn and Dragon's Den | `engine/events/dratini.asm` (`GiveDratini`), `engine/events/move_deleter.asm` (`MoveDeletion`), `engine/pokemon/mon_menu.asm` (`ChooseMoveToDelete`), `engine/events/whiteout.asm` (`Script_Whiteout`), `data/maps/setup_scripts.asm` (`MapSetupScript_Continue`) | `GiveDratini` searches the party backwards by species and writes `.Movesets` 0 (WRAP, THUNDER WAVE, TWISTER, EXTREMESPEED) or 1 with each move's base PP; a value of 2 or more changes nothing. `MoveDeletion` follows the routine's order of questions; `ChooseMoveToDelete` is shown as a list of the moves, and `.DeleteMove` shifts the later moves and PP bytes, PP Ups included. A save records objects whose visibility no longer matches their flags: `MapSetupScript_Continue` skips `LoadMapObjects`, so a flagless object a script made disappear (the Radio Tower director) stays gone after Continue and one that appeared with its flag set stays visible; a later visit rebuilds them from the map. A battle lost inside an `scall` jumps to `Script_Whiteout` without unwinding; its `newloadmap` is followed by `endall`, which drops the caller. The switch room's doors, the warehouse's reset, the Ice Path and Blackthorn Gym stone tables, whirlpools and the Dragon Shrine quiz run on ported primitives. `tests/blackthorn.test.ts`, `tests/radio-tower.test.ts` and six playthrough stages cover them. |
 | `game/scripts/tin-tower.ts`, Tin Tower and Whirl Islands | `engine/pokemon/search_owned.asm` (`BeastsCheck`, `MonCheck`, `CheckOwnMonAnywhere`, `CheckOwnMon`) | `CheckOwnMonAnywhere` returns nothing with an empty party, then reads the party structs' species (an Egg counts as its species), `sBox` and the fourteen `sBoxN` copies, matching the player's ID and the OT's first five letters (`NAME_LENGTH_JAPANESE - 2` compares, stopping early at a shared terminator); the Day-Care is not searched. The original's `sBox` is the current box, and its own `sBoxN` slot may still hold an older copy from before the last box change; the port keeps the boxes without stale copies, so a Pokémon only in such a copy is not found. The sages, Suicune, Ho-Oh and Lugia run on ported primitives (`BATTLETYPE_SUICUNE`, `BATTLETYPE_FORCEITEM`). `tests/tin-tower.test.ts` and two playthrough stages cover them. |
+| `game/scripts/battle-tower.ts`, the Battle Tower | `engine/events/battle_tower/battle_tower.asm` (`BattleTowerAction`, `RunBattleTowerTrainer`, `ReadBTTrainerParty`, `CopyBTTrainer_FromBT_OT_TowBT_OTTemp`, `BattleTower_GiveReward`, `BattleTower_RandomlyChooseReward`, `LoadOpponentTrainerAndPokemonWithOTSprite`, `CheckForBattleTowerRules`), `engine/events/battle_tower/load_trainer.asm`, `engine/events/battle_tower/rules.asm`, `engine/events/battle_tower/trainer_text.asm`, `mobile/mobile_46.asm` (`_BattleTowerRoomMenu`, `BattleTower_LevelCheck`, `BattleTower_UbersCheck`), `mobile/mobile_5f.asm` (`Menu_ChallengeExplanationCancel`), `engine/link/link.asm` (`TryQuickSave`), `engine/battle/core.asm`, `engine/battle/effect_commands.asm`, `engine/battle/misc.asm` (`DoBadgeTypeBoosts`) | The Battle Tower's SRAM and the work RAM its scripts share are saved as `battleTower`. The trainer sampler keeps its index as the running byte after a repeated trainer; the Pokémon sampler starts again from `hRandomAdd`; both fold `Random`'s `hRandomAdd` into a byte below a power-of-two mask, which the port draws from its random source. `BattleTowerText` reads the class's gender (1.1 behaviour) and picks the greeting from `hRandomAdd` (0-24 male, 0-14 female), keeping it for the end texts. Each battle start counts the battle and marks the challenge in progress, as `CopyBTTrainer_FromBT_OT_TowBT_OTTemp` does; `LoadPokemonData` then returns the party, Pokédex and Unown Dex to the quick save's. The level menu shows the levels as a list; its CANCEL/B question and the mobile code's YES/NO flow are modelled from their outcomes (YES leaves with $a, NO picks a level again). `TryQuickSave` asks the overwrite question for the player's own save and shows the saving texts; the port keeps the place and Pokémon data `LoadPokemonData` and `Reset` return to. The native game saves itself, so the original's "left without saving" state (a reset during a challenge) cannot arise: a reload replays the room's script. `Reset` returns the player to the quick save's place with the 1F scene set to check the challenge; the original's rollback of money gained by Pay Day is not reproduced. In battle, `wInBattleTowerBattle` turns off obedience, `DoBadgeTypeBoosts`, `BadgeStatBoosts`, experience, the pack (BattleMenu_Pack says items can't be used), AI items and prize money, uses Falkner's AI attributes, keeps Sleep to `%011` and skips the AI's random failure for Sleep, Poison, stat-lowering and Paralyze moves; a loss shows BattleTowerText and does not white out. `DoBadgeTypeBoosts` was added to every battle (it was missing). BATTLETOWERACTION_LEVEL_CHECK and _UBERS_CHECK and the mobile actions are reached only from unreferenced scripts and stay refused. `tests/battle-tower.test.ts`, `tests/battle-tower-engine.test.ts` and `tests/reference-badges.spec.ts` cover them. |
 | `game/scripts/slot-machine.ts`, `game/scripts/card-flip.ts` | `engine/games/slot_machine.asm`, `engine/games/card_flip.asm`, `engine/gfx/cgb_layouts.asm` | Both on a realtime tile screen (two frames per tick, buffered buttons). Slots: reel strips, spin rates and scrolling, bias tables with the lucky machine and seven streak, reel 3's Golem and Chansey replay with their sprites, payouts. Card Flip: deck, 12×11 board, cursor sprites and `ChooseCard_HandleJoypad`, paytable. Tilemaps, all 48 cursor positions, selected reel states and whole Golem/Chansey/Egg sequences are checked against the ROM (`tests/reference-game-corner.spec.ts`, which runs `CardFlip_UpdateCursorOAM`, `Slots_UpdateReelPositionAndOAM`/`.SpinReel` and the sprite-animation engine's own Golem/Chansey/Egg routines): the cursor, the reel symbols and the three creatures each anchor an OAM-relative pixel pair 8 (x) and 16 (y) beyond the screen's, as `cursorSprites` reads; `depixel`'s own two arguments end up swapped by `_InitSpriteAnimStruct` (confirmed against the reference emulator), so Golem/Chansey/Egg's X and Y bases were swapped to match, and Golem's own OAM table X-flips its right half. `PlaySpriteAnimations` is compared frame by frame over a three-Golem run and a Chansey round with two eggs (shadow OAM, `wSlotsDelay` and `hSCY`): frames last 8 ticks (the first draw plus 7 decrements); Golem's frames 3 and 4 flip the whole OAM set (offsets become −8−offset); a sprite removed by `DeinitializeSprite` is still drawn that tick, because `UpdateAnimFrame` runs after the animation function; the Golem's roll toggles `hSCY` by ±2, which the tile screen shows with the space tiles `_SlotMachine` filled the BG map with. The rows scrolled in use palette 0, since the attribute map beyond row 18 is not reproduced. No sound. |
 | Text interpreter                 | `macros/scripts/text.asm`, `constants/charmap.asm`, `home/text.asm`                                                            | Literal/far text, RAM names and string buffers from native state, numbers of dots, and sound or pause cues (consumed). `text_asm` and other RAM reads are refused.                                                                      |