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。

3 files changed, 56 insertions, 9 deletions

diff --git a/src/LivingVillage.Kernel/LivingVillage.Kernel.fsproj b/src/LivingVillage.Kernel/LivingVillage.Kernel.fsproj
index a8ed312..8a4fad1 100644
--- a/src/LivingVillage.Kernel/LivingVillage.Kernel.fsproj
+++ b/src/LivingVillage.Kernel/LivingVillage.Kernel.fsproj
@@ -5,6 +5,7 @@
   </PropertyGroup>
 
   <ItemGroup>
+    <Compile Include="Rng.fs" />
     <Compile Include="Sim.fs" />
   </ItemGroup>
 
diff --git a/src/LivingVillage.Kernel/Rng.fs b/src/LivingVillage.Kernel/Rng.fs
new file mode 100644
index 0000000..9564b56
--- /dev/null
+++ b/src/LivingVillage.Kernel/Rng.fs
@@ -0,0 +1,24 @@
+namespace LivingVillage.Kernel
+
+[<Struct>]
+type RngState =
+    { State: uint64 }
+
+module Rng =
+
+    let goldenGamma = 0x9E3779B97F4A7C15UL
+
+    let ofSeed (seed: uint64) : RngState = { State = seed }
+
+    let nextUInt64 (rng: RngState) : uint64 * RngState =
+        let s = rng.State + goldenGamma
+        let mutable z = s
+        z <- (z ^^^ (z >>> 30)) * 0xBF58476D1CE4E5B9UL
+        z <- (z ^^^ (z >>> 27)) * 0x94D049BB133111EBUL
+        let out = z ^^^ (z >>> 31)
+        out, { State = s }
+
+    let nextFloat32 (rng: RngState) : float32 * RngState =
+        let z, rng' = nextUInt64 rng
+        let bits = uint32 (z >>> 40)
+        float32 bits / 16777216.0f, rng'
diff --git a/src/LivingVillage.Kernel/Sim.fs b/src/LivingVillage.Kernel/Sim.fs
index d1b2e57..0e3683b 100644
--- a/src/LivingVillage.Kernel/Sim.fs
+++ b/src/LivingVillage.Kernel/Sim.fs
@@ -2,10 +2,12 @@ namespace LivingVillage.Kernel
 
 module Sim =
 
+    [<Struct>]
     type Vec2 =
         { X: float32
           Y: float32 }
 
+    [<Struct>]
     type Avatar =
         { Pos: Vec2 }
 
@@ -14,33 +16,53 @@ module Sim =
           MoveY: float32 }
 
     type TimeStep =
-        { Dt: float32
-          Input: Input }
+        { Input: Input }
 
+    [<Struct>]
+    type NoHost =
+        { Reserved: uint64 }
+
+    [<Struct>]
     type World =
         { Tick: int64
-          Avatar: Avatar }
+          Time: float
+          Rng: RngState
+          Avatar: Avatar
+          NoHost: NoHost }
+
+    let ticksPerSecond = 60L
+    let secondsPerDay = 86400L
+    let ticksPerDay = secondsPerDay * ticksPerSecond
+    let dtSeconds = 1.0 / float ticksPerSecond
+    let dtSecondsF = 1.0f / float32 ticksPerSecond
 
     let mapWidthTiles = 64
     let mapHeightTiles = 48
     let tilePixels = 32
     let avatarSpeed = 160.0f
 
-    let initialWorld () : World =
+    let initialWorld (seed: uint64) : World =
         let centerX = float32 (mapWidthTiles * tilePixels / 2 - tilePixels / 2)
         let centerY = float32 (mapHeightTiles * tilePixels / 2 - tilePixels / 2)
         { Tick = 0L
-          Avatar = { Pos = { X = centerX; Y = centerY } } }
+          Time = 0.0
+          Rng = Rng.ofSeed seed
+          Avatar = { Pos = { X = centerX; Y = centerY } }
+          NoHost = { Reserved = 0UL } }
 
     let clamp v lo hi = if v < lo then lo elif v > hi then hi else v
 
     let step (ts: TimeStep) (world: World) : World =
+        let tick = world.Tick + 1L
         let maxX = float32 (mapWidthTiles * tilePixels - tilePixels)
         let maxY = float32 (mapHeightTiles * tilePixels - tilePixels)
-        let dx = ts.Input.MoveX * avatarSpeed * ts.Dt
-        let dy = ts.Input.MoveY * avatarSpeed * ts.Dt
-        { Tick = world.Tick + 1L
+        let dx = ts.Input.MoveX * avatarSpeed * dtSecondsF
+        let dy = ts.Input.MoveY * avatarSpeed * dtSecondsF
+        { Tick = tick
+          Time = float tick * dtSeconds
+          Rng = world.Rng
           Avatar =
             { Pos =
                 { X = clamp (world.Avatar.Pos.X + dx) 0.0f maxX
-                  Y = clamp (world.Avatar.Pos.Y + dy) 0.0f maxY } } }
+                  Y = clamp (world.Avatar.Pos.Y + dy) 0.0f maxY } }
+          NoHost = world.NoHost }