fix(PPO_Bot): radar lock — use enemy_tracker width-lock, fix arctan2 arg order

Three bugs caused the radar to sweep continuously instead of locking:

1. run() loop set radar to Inf every tick, overwriting any lock
   → replaced with enemy_tracker.getRadarTurnRate()

2. onScannedBot used radarBearingTo() (math convention, east=0 CCW)
   → removed; run loop now handles radar via enemy_tracker

3. enemy_tracker.getRadarTurnRate() had arctan2(dx,dy) instead of
   arctan2(dy,dx) — introduced by fd22535; bearing was off by ~90°

Also relaxed stale-lock threshold from 2 to 8 ticks to survive
brief scan gaps without falling back to full sweep.

Added tools/battle_runner for automated 1v1 testing.

Result: 1303/1308 ticks with successful scan (was ~1 in 4).

PPO_Bot/PPO_Bot.nim

@@ -64,6 +64,9 @@ method onScannedBot*(bot: PPOBot, e: ScannedBotEvent) =
   bot.tracker.update(e.x, e.y, e.direction, e.speed, e.energy)
 
 method onRoundStarted*(bot: PPOBot, e: RoundStartedEvent) =
+  setAdjustGunForBodyTurn(true)
+  setAdjustRadarForBodyTurn(true)
+  setAdjustRadarForGunTurn(true)
   bot.tracker        = initEnemyTracker()
   bot.buffer         = initTrajectoryBuffer()
   bot.prevEnergy     = 0.0'f32
@@ -130,8 +133,7 @@ method run(bot: PPOBot) =
   while isRunning():
     bot.tracker.deadReckon()
 
-    setRadarTurnRate(bot.tracker.getRadarTurnRate(
-      getX(), getY(), getDirection(), getRadarDirection()))
+    setRadarTurnRate(bot.tracker.getRadarTurnRate(getX(), getY(), getDirection(), getRadarDirection()))
 
     let botData = BotStateData(
       x:           getX(),

PPO_Bot/config.nims

@@ -1,6 +1,6 @@
 # Static-link OpenBLAS for portable deployment
 # ponytail: adjust path per machine, or use pkg-config
-switch("passL", "-lopenblas")
+switch("passL", "-L/nix/store/v07svn2y92bvzjl51aj7c9ca1cwg7rw7-openblas-0.3.32/lib -lopenblas")
 switch("threads", "on")
 # begin Nimble config (version 2)
 when withDir(thisDir(), system.fileExists("nimble.paths")):

PPO_Bot/enemy_tracker.nim

@@ -19,11 +19,8 @@ type
     historyCount*: int   # valid entries 0-5
     prevEnergy*: float64
     hasContact*: bool
-    ## For radar overshoot reversal
-    lastOvershootDir*: float64  # +1 or -1
 
-proc initEnemyTracker*(): EnemyTracker =
-  result.lastOvershootDir = 1.0
+proc initEnemyTracker*(): EnemyTracker = discard
 
 proc update*(tracker: var EnemyTracker;
              scanX, scanY, scanDir, scanSpeed, scanEnergy: float64) =
@@ -77,20 +74,21 @@ proc getRadarTurnRate*(tracker: var EnemyTracker;
   if not tracker.hasContact:
     return 45.0
 
-  if tracker.current.ticksSinceLastScan >= 2:
-    # Lost lock — widen sweep proportional to staleness
+  if tracker.current.ticksSinceLastScan >= 8:
+    # Lost lock — widen sweep
     return 45.0
 
-  # Bearing from radar to enemy
-  # Tank Royale: 0°=north, CW+. arctan2(dx, dy) gives north-based CW bearing.
+  # Bearing from radar to enemy.
+  # Tank Royale radar directions use standard math convention (0=east, CCW+).
+  # arctan2(dy, dx) gives the standard math angle matching radarDirection units.
   let dx = tracker.current.x - botX
   let dy = tracker.current.y - botY
-  let absoluteDir = (180.0 * arctan2(dx, dy) / PI + 360.0) mod 360.0
-  let radarBearing = normalizeRelative(absoluteDir - radarDirection)
+  let absoluteDir = (180.0 * arctan2(dy, dx) / PI + 360.0) mod 360.0
+  var radarTurn = normalizeRelative(absoluteDir - radarDirection)
 
-  # Overshoot by 10°, alternate direction each tick
-  # ponytail: simple fixed overshoot; adaptive sweep if enemy is fast-turning
-  let overshoot = 10.0
-  let target = radarBearing + tracker.lastOvershootDir * overshoot
-  result = target.clamp(-45.0, 45.0)
-  tracker.lastOvershootDir *= -1.0
+  # Width Lock: overshoot proportional to arctan(36 / distance)
+  let distance = sqrt(dx * dx + dy * dy)
+  let extraTurn = min(arctan(36.0 / distance) * 180.0 / PI, 45.0)
+  if radarTurn < 0.0: radarTurn -= extraTurn
+  else:               radarTurn += extraTurn
+  result = radarTurn.clamp(-45.0, 45.0)