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。

2 files changed, 113 insertions, 0 deletions

diff --git a/src/LivingVillage.Headless/LivingVillage.Headless.fsproj b/src/LivingVillage.Headless/LivingVillage.Headless.fsproj
new file mode 100644
index 0000000..612b584
--- /dev/null
+++ b/src/LivingVillage.Headless/LivingVillage.Headless.fsproj
@@ -0,0 +1,16 @@
+<Project Sdk="Microsoft.NET.Sdk">
+
+  <PropertyGroup>
+    <OutputType>Exe</OutputType>
+    <TargetFramework>net8.0</TargetFramework>
+  </PropertyGroup>
+
+  <ItemGroup>
+    <Compile Include="Program.fs" />
+  </ItemGroup>
+
+  <ItemGroup>
+    <ProjectReference Include="..\LivingVillage.Kernel\LivingVillage.Kernel.fsproj" />
+  </ItemGroup>
+
+</Project>
diff --git a/src/LivingVillage.Headless/Program.fs b/src/LivingVillage.Headless/Program.fs
new file mode 100644
index 0000000..ea8b1b0
--- /dev/null
+++ b/src/LivingVillage.Headless/Program.fs
@@ -0,0 +1,97 @@
+module Program
+
+open System
+open LivingVillage.Kernel
+open LivingVillage.Kernel.Sim
+
+let ticksPerSecond = 60L
+let secondsPerDay = 86400L
+let ticksPerDay = secondsPerDay * ticksPerSecond
+
+let segmentTicks = 900L
+
+let zeroInput = { MoveX = 0.0f; MoveY = 0.0f }
+
+type Driver =
+    { Rng: RngState
+      Until: int64
+      Input: Input }
+
+let nextSegment (rng: RngState) (until: int64) : Driver =
+    let a, r1 = Rng.nextUInt64 rng
+    let m, r2 = Rng.nextUInt64 r1
+    let diag = 0.70710678f
+    let dirX, dirY =
+        match int (a &&& 7UL) with
+        | 0 -> 1.0f, 0.0f
+        | 1 -> diag, diag
+        | 2 -> 0.0f, 1.0f
+        | 3 -> -diag, diag
+        | 4 -> -1.0f, 0.0f
+        | 5 -> -diag, -diag
+        | 6 -> 0.0f, -1.0f
+        | _ -> diag, -diag
+    let mag =
+        match int (m % 3UL) with
+        | 0 -> 0.4f
+        | 1 -> 0.7f
+        | _ -> 1.0f
+    { Rng = r2
+      Until = until + segmentTicks
+      Input = { MoveX = dirX * mag; MoveY = dirY * mag } }
+
+let runSimulation (days: int64) (seed: uint64) : int =
+    let totalTicks = days * ticksPerDay
+    printfn "living-village headless days=%d seed=%d ticks=%d tickrate=%d" days seed totalTicks ticksPerSecond
+    let mutable world = Sim.initialWorld seed
+    let mutable driver = { Rng = Rng.ofSeed seed; Until = segmentTicks; Input = zeroInput }
+    let maxX = float32 (Sim.mapWidthTiles * Sim.tilePixels - Sim.tilePixels)
+    let maxY = float32 (Sim.mapHeightTiles * Sim.tilePixels - Sim.tilePixels)
+    let mutable nonFinite = 0L
+    let mutable outOfBounds = 0L
+    let mutable t = 0L
+    while t < totalTicks do
+        let d, input =
+            if t < driver.Until then driver, driver.Input
+            else
+                let d = nextSegment driver.Rng driver.Until
+                d, d.Input
+        driver <- d
+        world <- Sim.step { Input = input } world
+        t <- t + 1L
+        let p = world.Avatar.Pos
+        if Single.IsNaN p.X || Single.IsNaN p.Y || Single.IsInfinity p.X || Single.IsInfinity p.Y then
+            nonFinite <- nonFinite + 1L
+        if p.X < 0.0f || p.X > maxX || p.Y < 0.0f || p.Y > maxY then outOfBounds <- outOfBounds + 1L
+        if t % 1000L = 0L then
+            let mem = GC.GetTotalMemory(true)
+            let day = float t / float ticksPerDay
+            printfn "tick=%d time=%.4fs day=%.4f pos=(%.1f,%.1f) mem=%d rng=%016x" t world.Time day p.X p.Y mem world.Rng.State
+    printfn "done tick=%d non-finite=%d out-of-bounds=%d" world.Tick nonFinite outOfBounds
+    if nonFinite > 0L || outOfBounds > 0L then 1 else 0
+
+[<EntryPoint>]
+let main argv =
+    let rec parse (i: int) (days: int64 option) (seed: uint64 option) : Result<int64 * uint64, string> =
+        if i >= argv.Length then
+            match days, seed with
+            | Some d, Some s -> Ok(d, s)
+            | _ -> Error "missing --days/--seed"
+        else
+            match argv.[i] with
+            | "--days" when i + 1 < argv.Length ->
+                (match Int64.TryParse argv.[i + 1] with
+                 | true, d when d > 0L -> parse (i + 2) (Some d) seed
+                 | _ -> Error $"invalid --days '{argv.[i + 1]}'")
+            | "--seed" when i + 1 < argv.Length ->
+                (match UInt64.TryParse argv.[i + 1] with
+                 | true, s -> parse (i + 2) days (Some s)
+                 | _ -> Error $"invalid --seed '{argv.[i + 1]}'")
+            | other -> Error $"unknown argument '{other}'"
+
+    match parse 0 None None with
+    | Ok(days, seed) -> runSimulation days seed
+    | Error msg ->
+        eprintfn $"headless: {msg}"
+        eprintfn "usage: dotnet run -c Release --project src/LivingVillage.Headless -- --days N --seed S"
+        2