fix(ground): synchronize act-scene renderStarted with simulation clock domain and guard bounce height

src/game/ground-items.ts

@@ -148,12 +148,11 @@ export function resolveGroundItemMetadata(item: any, specifiedAmount?: number):
 /** Calculate parabolic bounce height h(t) at timestamp now. */
 export function calculateBounceHeight(bounceState: GroundItemBounceState, now: number): number {
   const elapsed = now - bounceState.startTime
-  if (elapsed <= 0) return 0
-  if (elapsed >= bounceState.durationMs) return 0
+  if (elapsed <= 0 || elapsed >= bounceState.durationMs) return 0
 
   const p = elapsed / bounceState.durationMs
   // Parabolic equation: h(p) = 4 * H * p * (1 - p)
-  return 4 * bounceState.peakHeightPx * p * (1 - p)
+  return Math.max(0, 4 * bounceState.peakHeightPx * p * (1 - p))
 }
 
 /**

src/scene/act-scene.ts

@@ -6604,9 +6604,10 @@ if (typeof window !== 'undefined') {
         )
       }
 
+      const groundSimTime = (engine.world.tick + ((engine.world as any).alpha ?? 0)) * 40
       for (const gItem of engine.groundItems.all) {
         pushEntity(gItem.x, gItem.y, () => {
-          drawGroundItem(renderer, gItem, renderStarted, itemsAtlasHandle)
+          drawGroundItem(renderer, gItem, groundSimTime, itemsAtlasHandle)
         })
       }
 

tests/ground-items-scatter-bounce.test.ts

@@ -438,6 +438,24 @@ describe('Milestone M11.3 (Issue #406) — Ground Item & Gold Spawning, Isometri
       expect(entity.bounceState).toBeNull()
       expect(manager.getRenderOffset(entity, 600)).toEqual({ x: 0, y: 0 })
     })
+
+    it('defensively guards calculateBounceHeight against non-positive or expired elapsed times', () => {
+      const bounce = {
+        startTime: 1000,
+        durationMs: 400,
+        peakHeightPx: 24,
+      }
+
+      // Negative elapsed (sub-frame jitter / out of order): returns 0, never negative
+      expect(calculateBounceHeight(bounce, 900)).toBe(0)
+      expect(calculateBounceHeight(bounce, 999.9)).toBe(0)
+      // Exactly at start (t = 1000): returns 0
+      expect(calculateBounceHeight(bounce, 1000)).toBe(0)
+      // At duration boundary (t = 1400): returns 0
+      expect(calculateBounceHeight(bounce, 1400)).toBe(0)
+      // Far in future: returns 0
+      expect(calculateBounceHeight(bounce, 2000)).toBe(0)
+    })
   })
 
   describe('4. 2:1 Isometric Diamond Grid Scatter Algorithm Parity', () => {