feat(superkart): add beach theme and AI rubber-banding

- Add beach theme artwork and register paths in artwork JSON
- Implement AI rubber-banding that scales AI top speed based on gap to player
- Configure engine classes with varying rubber-band strength (Cruiser most forgiving, Turbo least)
- Balance racer stats: boost Kona top speed, reduce heavy racer accel/handling
- Update verification script to validate new rubber-banding configuration

data/superkart-artwork.json

@@ -41,7 +41,7 @@
     "zanthor":   { "key": "superkart-kart-zanthor",   "path": "assets/images/superkart/racer-zanthor.png", "frameWidth": 64, "frameHeight": 64, "angles": 8 }
   },
   "themeSheets": {
-    "beach":     { "key": "superkart-theme-beach",     "path": null, "frameWidth": 64, "frameHeight": 64 },
+    "beach":     { "key": "superkart-theme-beach",     "path": "assets/images/superkart/theme-beach.png", "frameWidth": 64, "frameHeight": 64 },
     "volcano":   { "key": "superkart-theme-volcano",   "path": null, "frameWidth": 64, "frameHeight": 64 },
     "scrapyard": { "key": "superkart-theme-scrapyard", "path": null, "frameWidth": 64, "frameHeight": 64 },
     "swamp":     { "key": "superkart-theme-swamp",     "path": null, "frameWidth": 64, "frameHeight": 64 },
@@ -49,7 +49,7 @@
     "nightcity": { "key": "superkart-theme-nightcity", "path": null, "frameWidth": 64, "frameHeight": 64 }
   },
   "backdrops": {
-    "beach":     { "key": "superkart-backdrop-beach",     "path": null },
+    "beach":     { "key": "superkart-backdrop-beach",     "path": "assets/images/superkart/backdrop-beach.png" },
     "volcano":   { "key": "superkart-backdrop-volcano",   "path": null },
     "scrapyard": { "key": "superkart-backdrop-scrapyard", "path": null },
     "swamp":     { "key": "superkart-backdrop-swamp",     "path": null },

data/superkart-racers.json

@@ -35,7 +35,7 @@
       "id": "kona",
       "archetype": "Featherweight",
       "stats": {
-        "topSpeed": 0.35,
+        "topSpeed": 0.45,
         "accel": 0.7,
         "handling": 0.95,
         "weight": 0.15,
@@ -96,8 +96,8 @@
       "archetype": "Speed Demon",
       "stats": {
         "topSpeed": 1.0,
-        "accel": 0.45,
-        "handling": 0.4,
+        "accel": 0.10,
+        "handling": 0.2,
         "weight": 0.55,
         "offroad": 0.3,
         "drift": 0.45

data/superkart-rules.json

@@ -6,9 +6,9 @@
     "After editing, run `node tools/verifySuperKart.js` to re-check invariants."
   ],
   "engineClasses": [
-    { "id": "cruiser", "label": "CRUISER CLASS", "desc": "Relaxed speeds, forgiving rivals.", "speedMult": 0.8, "aiSkillMult": 0.75 },
-    { "id": "racer",   "label": "RACER CLASS",   "desc": "The intended Super Kart experience.", "speedMult": 1.0, "aiSkillMult": 1.0 },
-    { "id": "turbo",   "label": "TURBO CLASS",   "desc": "Everything faster, rivals ruthless.", "speedMult": 1.15, "aiSkillMult": 1.25 }
+    { "id": "cruiser", "label": "CRUISER CLASS", "desc": "Relaxed speeds, forgiving rivals.", "speedMult": 0.8, "aiSkillMult": 0.75, "rubberBandMult": 1.75 },
+    { "id": "racer",   "label": "RACER CLASS",   "desc": "The intended Super Kart experience.", "speedMult": 1.0, "aiSkillMult": 1.0, "rubberBandMult": 1.0 },
+    { "id": "turbo",   "label": "TURBO CLASS",   "desc": "Everything faster, rivals ruthless.", "speedMult": 1.15, "aiSkillMult": 1.25, "rubberBandMult": 0.25 }
   ],
   "physics": {
     "kartRadius": 14,

src/games/superkart/SuperKartLogic.js

@@ -175,9 +175,26 @@ function emit(state, type, data) {
 
 function classSpeedMult(state) { return state.engineClass?.speedMult ?? 1; }
 
+// Gap-to-player rubber-banding: AI karts trailing the player get a top-speed
+// boost, karts ahead get held back, scaled to 0 at the player's own
+// progress and saturating at +/-rubberBandRange world units of gap. Engine
+// class scales the whole effect (rubberBandMult) — Cruiser leans on this
+// hard for forgiving rivals, Turbo barely uses it to stay ruthless.
+function rubberBandMultOf(state, kart) {
+  if (kart.isPlayer) return 1;
+  const player = state.karts[state.playerIndex];
+  if (!player?.isPlayer) return 1;
+  const { physics } = state;
+  const gain = physics.rubberBandGain * (state.engineClass?.rubberBandMult ?? 1);
+  if (gain <= 0) return 1;
+  const gap = player.progress - kart.progress; // + = kart trails the player
+  const t = Math.max(-1, Math.min(1, gap / physics.rubberBandRange));
+  return 1 + gain * t;
+}
+
 function effTopSpeed(state, kart) {
   const { physics } = state;
-  let mult = classSpeedMult(state);
+  let mult = classSpeedMult(state) * rubberBandMultOf(state, kart);
   mult *= 1 + kart.coins * physics.coinTopSpeedBonus;
   if (kart.starMs > 0) mult *= itemParams(state, 'overdrive').mult ?? 1.2;
   if (kart.empMs > 0) mult *= itemParams(state, 'emp').mult ?? 0.6;

tools/verifySuperKart.js

@@ -57,6 +57,8 @@ for (const key of statKeys) {
 
 check('3 engine classes', rules.engineClasses.length === 3);
 check('classes ordered by speed', rules.engineClasses.every((c, i, a) => i === 0 || c.speedMult > a[i - 1].speedMult));
+check('classes ordered by inverse rubber-band strength (cruiser most forgiving)',
+  rules.engineClasses.every((c, i, a) => i === 0 || c.rubberBandMult < a[i - 1].rubberBandMult));
 check('points table has 9 entries', rules.pointsTable.length === 9);
 check('points table descending', rules.pointsTable.every((p, i, a) => i === 0 || p <= a[i - 1]));
 for (const item of rules.items) {
@@ -68,7 +70,7 @@ for (let col = 0; col < 9; col += 1) {
   check(`weight column ${col + 1} sums > 0`, total > 0);
 }
 const physKeys = ['baseTopSpeed', 'baseAccel', 'turnRateBase', 'hopMs', 'offroadMultMin',
-  'boostPadMult', 'spinMs', 'gridSpacing', 'rouletteMs', 'rubberBandGain'];
+  'boostPadMult', 'spinMs', 'gridSpacing', 'rouletteMs', 'rubberBandGain', 'rubberBandRange'];
 for (const k of physKeys) check(`physics.${k} present`, typeof rules.physics[k] === 'number');
 
 check('3 cups', cups.cups.length === 3);