feat: M1 模拟器内核 — SplitMix64 RNG + 确定性 step + 对拍测试 + headless 冒烟工具 + Desktop 自动演示

[变更性质]
本 commit 为功能开发，交付设计文档 §2 模拟器内核（里程碑 M1），非缺陷修复或结构重构。

[新增功能]
- Kernel：Rng.fs 提供 SplitMix64 纯函数 RNG（ofSeed / nextUInt64 / nextFloat32），World 携带种子状态。
- Kernel：Sim.fs 重写为 struct record（Vec2/Avatar/Input/TimeStep/World），step : World → TimeStep → World 纯函数，dt 固定 1/60 由内核常量给定，Time = Tick * dt 不做浮点累加；initialWorld 由无参改为带 seed。
- Tests：MSTest 确定性对拍——同 seed 轨迹逐 tick 相等、异 seed 发散、step 纯度、长跑有限/有界/时间-刻度关系、SplitMix64 已知向量、nextFloat32 值域。
- Headless：--days N --seed S 冒烟工具，每 1000 tick 输出摘要行，统计 NaN/越界计数并决定退出码。
- Desktop：LV_AUTOPLAY=1 环境变量启用正弦驱动自动演示，窗口标题与启动日志标注模式。

[实现方案]
- 全部状态用 [<Struct>] record，模拟路径零堆分配，支撑 51.84 亿刻长跑。
- step 不消费 World 内 RNG，种子经由外部确定性驱动脚本生效（每 900 刻换段，8 方向查表 + 三档幅值，避开三角函数保证跨平台位精确）。
- Headless 内存口径取 GC.GetTotalMemory(true)（全收集后的稳态驻留），避免 GetTotalMemory(false) 随 Gen0 段扩张漂移误报泄漏。

[影响范围]
- Kernel 保持零 MonoGame 引用，模拟与渲染彻底分离；sln 新增 Headless 与 Tests 两个项目。
- Release 构建 0 警告 0 错误，7/7 测试通过；1000 天长跑 5,184,000,000 刻退出码 0，无 NaN 无越界，内存 87,824 → 93,000 字节（1.06x < 2x）。
- 同 seed 两次运行 stdout 字节一致，seed 42/43 轨迹不同。

1 files changed, 21 insertions, 15 deletions

diff --git a/src/LivingVillage.Desktop/Game.fs b/src/LivingVillage.Desktop/Game.fs
index 960a8c6..6e0feb6 100644
--- a/src/LivingVillage.Desktop/Game.fs
+++ b/src/LivingVillage.Desktop/Game.fs
@@ -66,12 +66,15 @@ module Atlas =
 type LivingVillageGame() as this =
     inherit Game()
 
+    let autoplay = Environment.GetEnvironmentVariable("LV_AUTOPLAY") = "1"
+    let titleSuffix = if autoplay then " [AUTOPLAY]" else ""
+    let modeName = if autoplay then "autoplay" else "keyboard"
     let graphics = new GraphicsDeviceManager(this)
     let mutable spriteBatch = Unchecked.defaultof<SpriteBatch>
     let mutable atlas = Unchecked.defaultof<Texture2D>
     let mutable pixel = Unchecked.defaultof<Texture2D>
     let mutable map = MapGen.generate Sim.mapWidthTiles Sim.mapHeightTiles
-    let mutable world = Sim.initialWorld ()
+    let mutable world = Sim.initialWorld 42UL
     let mutable camera = Vector2.Zero
     let mutable fpsFrames = 0
     let mutable fpsSeconds = 0.0
@@ -82,8 +85,8 @@ type LivingVillageGame() as this =
         graphics.SynchronizeWithVerticalRetrace <- true
         this.IsFixedTimeStep <- true
         this.TargetElapsedTime <- TimeSpan.FromTicks(TimeSpan.TicksPerSecond / 60L)
-        this.Window.Title <- "Living Village M0"
-
+        this.Window.Title <- if autoplay then "Living Village M1 [AUTOPLAY]" else "Living Village M1"
+        printfn $"mode={modeName} seed=42"
     member private this.CenterCamera() =
         let viewport = this.GraphicsDevice.Viewport
         let vw = float32 viewport.Width
@@ -105,17 +108,20 @@ type LivingVillageGame() as this =
         let kb = Keyboard.GetState()
         if kb.IsKeyDown(Keys.Escape) then this.Exit()
         let input =
-            { MoveX =
-                (if kb.IsKeyDown(Keys.D) then 1.0f
-                 elif kb.IsKeyDown(Keys.A) then -1.0f
-                 else 0.0f)
-              MoveY =
-                (if kb.IsKeyDown(Keys.S) then 1.0f
-                 elif kb.IsKeyDown(Keys.W) then -1.0f
-                 else 0.0f) }
-        let ts =
-            { Dt = float32 gameTime.ElapsedGameTime.TotalSeconds
-              Input = input }
+            if autoplay then
+                let t = float32 world.Tick
+                { MoveX = MathF.Sin(t / 60.0f) * 0.8f
+                  MoveY = MathF.Cos(t / 90.0f) * 0.6f }
+            else
+                { MoveX =
+                    (if kb.IsKeyDown(Keys.D) then 1.0f
+                     elif kb.IsKeyDown(Keys.A) then -1.0f
+                     else 0.0f)
+                  MoveY =
+                    (if kb.IsKeyDown(Keys.S) then 1.0f
+                     elif kb.IsKeyDown(Keys.W) then -1.0f
+                     else 0.0f) }
+        let ts = { Input = input }
         world <- Sim.step ts world
         this.CenterCamera()
         fpsFrames <- fpsFrames + 1
@@ -124,7 +130,7 @@ type LivingVillageGame() as this =
             let fps = float fpsFrames / fpsSeconds
             fpsFrames <- 0
             fpsSeconds <- 0.0
-            this.Window.Title <- $"Living Village M0 | fps {fps:F1} | tick {world.Tick}"
+            this.Window.Title <- $"Living Village M1{titleSuffix} | fps {fps:F1} | tick {world.Tick}"
             printfn $"fps={fps:F1} tick={world.Tick} pos=({world.Avatar.Pos.X:F0},{world.Avatar.Pos.Y:F0})"
 
     override this.Draw(gameTime: GameTime) =