FEAT-1b: Inzuchtkoeffizient endpoints via Wright path method

- PedigreeCalculator: pure, EF-free Wright path-method engine (recursive F_A,
  per-common-ancestor contributions, generationsAvailable, cycle guards)
- InbreedingService: loads pedigree from ApplicationContext shadow FKs
  (Gerbils.LitterId, Litters.FatherId/MotherId) into in-memory maps
- InbreedingController: GET /gerbils/{id}/inbreeding-coefficient,
  POST /genetics/test-inbreeding (hypothetical pairing for Probeverpaarung)
- Injects ApplicationContext directly; no Program.cs change (Dwight owns it)

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

GerbilManagerWebAPI/Genetics/InbreedingService.cs

@@ -0,0 +1,74 @@
+using GerbilManagerWebAPI.Models;
+using Microsoft.EntityFrameworkCore;
+
+namespace GerbilManagerWebAPI.Genetics
+{
+    /// <summary>
+    /// Loads the pedigree out of the database into in-memory lookups (the home dataset
+    /// is small) and delegates the actual maths to <see cref="PedigreeCalculator"/>.
+    ///
+    /// Parent links live in EF shadow foreign keys: a gerbil's birth litter is
+    /// <c>Gerbils.LitterId</c>; that litter's parents are <c>Litters.FatherId</c> and
+    /// <c>Litters.MotherId</c>.
+    /// </summary>
+    public sealed class InbreedingService
+    {
+        private readonly ApplicationContext _db;
+
+        public InbreedingService(ApplicationContext db) => _db = db;
+
+        /// <summary>F for an existing gerbil, or null if no such gerbil exists.</summary>
+        public InbreedingResult? ForGerbil(Guid id)
+        {
+            var calculator = BuildCalculator();
+            return calculator.Contains(id) ? calculator.ForIndividual(id) : null;
+        }
+
+        /// <summary>F for the hypothetical offspring of the given sire and dam.</summary>
+        public InbreedingResult ForPairing(Guid? fatherId, Guid? motherId)
+        {
+            return BuildCalculator().ForOffspringOf(fatherId, motherId);
+        }
+
+        private PedigreeCalculator BuildCalculator()
+        {
+            var litters = _db.Set<Litter>()
+                .Select(l => new
+                {
+                    l.Id,
+                    FatherId = EF.Property<Guid?>(l, "FatherId"),
+                    MotherId = EF.Property<Guid?>(l, "MotherId"),
+                })
+                .ToDictionary(l => l.Id, l => (l.FatherId, l.MotherId));
+
+            var gerbils = _db.Set<Gerbil>()
+                .Select(g => new
+                {
+                    g.Id,
+                    g.Name,
+                    LitterId = EF.Property<Guid?>(g, "LitterId"),
+                })
+                .ToList();
+
+            var parents = new Dictionary<Guid, (Guid? Father, Guid? Mother)>(gerbils.Count);
+            var names = new Dictionary<Guid, string>(gerbils.Count);
+
+            foreach (var g in gerbils)
+            {
+                names[g.Id] = g.Name;
+
+                Guid? father = null;
+                Guid? mother = null;
+                if (g.LitterId is Guid litterId && litters.TryGetValue(litterId, out var litterParents))
+                {
+                    father = litterParents.FatherId;
+                    mother = litterParents.MotherId;
+                }
+
+                parents[g.Id] = (father, mother);
+            }
+
+            return new PedigreeCalculator(parents, names);
+        }
+    }
+}