sky(phase-3g): fix LCG multiplier — 360 (DaysPerYear), not 7620

Ran a live memory probe against retail acclient.exe (new tool:
tools/RetailTimeProbe/) to read the TimeOfDay struct at
DAT_008ee9c8 and compare against our computed values. The decompile
agent's identification of TimeOfDay+0x10 as "SecondsPerDay (int
copy)" turned out to be WRONG — the live value is **360**, which is
GameTime.DaysPerYear.

The retail FUN_00501990 LCG seed is:
  seed = Year × (*+0x10) + DayOfYear
       = Year × DaysPerYear + DayOfYear
       = flat "total days since epoch" day-index

Our previous Phase 3c port passed 7620 (DayLength in ticks) as the
multiplier, producing seed=883,967 against retail's seed=41,807 —
completely different LCG outputs, completely different DayGroup
picks. That's why the user's retail kept showing stormy/rainy while
acdream showed sunny/clear (or vice versa) even after Phases 3c.1
and 3f aligned Year and DayOfYear.

Also confirmed by the probe:
  - EpochBase / ZeroTimeOfYear = 3600   ✓ Phase 3f already correct
  - BaseYear / ZeroYear = 10            ✓ DerethDateTime.ZeroYear
  - Year=116, DayOfYear=47              ✓ our AbsoluteYear / DayOfYear
  - SecondsPerDay float (+0x0C) = 7620  ✓ DayTicks
  - SecondsPerYear = 2,743,200          ✓ YearTicks

One "finding that's not a fix": retail's +0x48 DayFraction is a
sub-period fraction (fraction through current day/night window)
NOT a full-day fraction. CurDayEnd - CurDayStart = 2857.5 = 0.375
of a day = 6 Dereth hours = night duration. Not relevant for our
keyframe bracket interpolation, which correctly uses a full-day
0..1 scale matching the SkyTime.Begin values. Documented in the
probe research doc so future work doesn't trip on it.

Changes:
- tools/RetailTimeProbe/ — new P/Invoke tool. Forced x86 target to
  match retail's bitness so hardcoded DAT_xxxxxxxx addresses are
  pointer-width-correct. Handles ASLR relocation via
  Process.MainModule.BaseAddress.
- src/AcDream.App/Rendering/GameWindow.cs: RefreshSkyForCurrentDay
  passes 360 (DaysInAMonth × MonthsInAYear) not 7620.
- src/AcDream.Core/World/SkyDescLoader.cs: ActiveDayGroup(ticks)
  and DefaultDayGroup same.
- docs/research/2026-04-23-retail-memory-probe.md — full probe
  results + decompile-agent correction.
- AcDream.slnx — add tools/ folder.

Build + 733 tests green.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

src/AcDream.App/Rendering/GameWindow.cs

@@ -4352,19 +4352,26 @@ public sealed class GameWindow : IDisposable
         if (_loadedSkyDesc is null || _loadedSkyDesc.DayGroups.Count == 0)
             return;
 
-        // Retail FUN_00501990 seeds the LCG with
-        //   (Year_absolute, SecondsPerDay, DayOfYear)
-        // where Year_absolute = TimeOfDay+0x64 = floor(...) + baseYear
-        // (baseYear=10 for Dereth per GameTime.ZeroYear). Our port uses
-        // AbsoluteYear which includes the +10 offset; without it, our
-        // seed would differ from retail's by `10 × SecondsPerDay` and we'd
-        // pick a different DayGroup (verified mismatch in the 2026-04-23
-        // live session — acdream picked "Rainy"[17] while retail showed
-        // "Sunny" at PY 116 ColdMeet 17).
+        // Retail FUN_00501990 seeds the LCG with the triple stored in
+        //   TimeOfDay +0x64 (Year), +0x10 (misc. int), +0x68 (DayOfYear)
+        //
+        // The decompile agent labeled +0x10 "SecondsPerDay (int copy)"
+        // but a live memory probe of retail's acclient.exe (2026-04-23,
+        // tools/RetailTimeProbe) shows the value is actually **360** —
+        // semantically DaysPerYear, not seconds. So the LCG seed is
+        //   seed = Year × DaysPerYear + DayOfYear
+        // which is literally "total days since epoch" (a flat day index),
+        // confirmed against retail's Year=116, DayOfYear=47, seed=41807.
+        //
+        // Previously we passed 7620 (DayTicks), producing seed 883967 —
+        // a completely different LCG output → wrong DayGroup pick →
+        // user-observed weather mismatch (acdream clear while retail
+        // stormy, 2026-04-23). The live probe nailed the fix.
         double ticks = WorldTime.NowTicks;
         int absYear = AcDream.Core.World.DerethDateTime.AbsoluteYear(ticks);
         int dayOfYear = AcDream.Core.World.DerethDateTime.DayOfYear(ticks);
-        int secondsPerDay = (int)AcDream.Core.World.DerethDateTime.DayTicks;    // 7620
+        int secondsPerDay = AcDream.Core.World.DerethDateTime.DaysInAMonth
+                          * AcDream.Core.World.DerethDateTime.MonthsInAYear;  // 360
 
         // Composite day key for change-detection and logging only; the
         // LCG seed is computed inside SelectDayGroupIndex from (absYear,

src/AcDream.Core/World/SkyDescLoader.cs

@@ -237,7 +237,11 @@ public sealed class LoadedSkyDesc
     {
         int absYear = DerethDateTime.AbsoluteYear(serverTicks);
         int dayOfYear = DerethDateTime.DayOfYear(serverTicks);
-        int secondsPerDay = (int)DerethDateTime.DayTicks;    // 7620
+        // Retail's TimeOfDay+0x10 is actually DaysPerYear (= 360 for Dereth,
+        // live probe 2026-04-23), NOT SecondsPerDay as the decompile agent
+        // mis-labeled. See GameWindow.RefreshSkyForCurrentDay for the full
+        // citation.
+        int secondsPerDay = DerethDateTime.DaysInAMonth * DerethDateTime.MonthsInAYear;  // 360
         int idx = SelectDayGroupIndex(absYear, secondsPerDay, dayOfYear);
         return idx < DayGroups.Count ? DayGroups[idx] : null;
     }
@@ -254,7 +258,9 @@ public sealed class LoadedSkyDesc
         get
         {
             int idx = SelectDayGroupIndex(
-                year: 0, secondsPerDay: (int)DerethDateTime.DayTicks, dayOfYear: 0);
+                year: 0,
+                secondsPerDay: DerethDateTime.DaysInAMonth * DerethDateTime.MonthsInAYear, // 360
+                dayOfYear: 0);
             return DayGroups.Count > 0 ? DayGroups[idx] : null;
         }
     }