Zielkette, Stufe 1: jede Aufgabe kann sagen, wofuer sie da ist (#714)

- TaskItem.ParentId, in der Datei als parent, in der DB als ParentId. Die
  Elternaufgabe ist der Zweck ("wofuer"), blocked_by die Voraussetzung
  ("wann").
- GoalChain: Eltern bis zu acht Stufen, Zyklen brechen den Gang ab und
  werden beim Setzen abgelehnt. Oben steht das Ziel der Einheit - der
  obersten Aufgabe, die zu einer Einheit gehoert (ein Ziel, das ein Mensch
  auf der obersten Ebene setzt, gehoert keiner), sonst der naechsten Einheit
  darueber mit Ziel.
- Der Lauf einer Aufgabe bekommt den Absatz "Why this task exists" und die
  Bitte, zu melden, wenn die Aufgabe ihrem Zweck nicht mehr dient.
- Taskboard-Tool: parent bei task_create/task_update, geprueft auf Existenz,
  Sichtbarkeit (#684) und Zyklen; task_list zeigt "Serves".
- WebUI: Feld im Aufgabendialog, Anzeige auf der Karte; die Verwaltung
  prueft wie das Tool.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

src/ClawdDotNet.Core/Tasks/GoalChain.cs

@@ -0,0 +1,104 @@
+using System.Text;
+using ClawdDotNet.Core.Organisation;
+
+namespace ClawdDotNet.Core.Tasks;
+
+/// <summary>
+/// #714: Why a task exists — its parent, that one's parent, up to the goal of the unit.
+/// Taken from Paperclip (Organisation-Konzept, 9a): an agent that only sees its own order
+/// cannot weigh it. "Write a product text" is a different job when it serves "launch the
+/// spring collection by Friday" than when it serves "clean up old listings".
+///
+/// <para><b>Purpose, not precondition.</b> <see cref="TaskItem.BlockedBy"/> says when a task
+/// may run; the parent says what it is for. Both can point to the same task, and mean
+/// different things.</para>
+///
+/// <para>Walked at run time, never stored as text: a parent that is renamed or finished
+/// shows up as it is now. The walk stops at a cycle and after <see cref="MaxDepth"/> steps,
+/// so a broken chain cannot hang a run or flood its prompt.</para>
+/// </summary>
+public static class GoalChain
+{
+    public const int MaxDepth = 8;
+
+    /// <summary>The parents of a task, nearest first. Stops at a missing parent or a cycle.</summary>
+    public static async Task<IReadOnlyList<TaskItem>> ParentsAsync(
+        TaskItem task, Func<string, CancellationToken, Task<TaskItem?>> lookup, CancellationToken ct)
+    {
+        var parents = new List<TaskItem>();
+        var seen = new HashSet<string>(StringComparer.OrdinalIgnoreCase) { task.Id };
+        var next = task.ParentId;
+
+        while (!string.IsNullOrWhiteSpace(next) && parents.Count < MaxDepth && seen.Add(next))
+        {
+            if (await lookup(next, ct) is not { } parent)
+                break;
+            parents.Add(parent);
+            next = parent.ParentId;
+        }
+        return parents;
+    }
+
+    /// <summary>
+    /// Whether making <paramref name="parentId"/> the parent of <paramref name="taskId"/>
+    /// would close a circle — the parent is the task itself or lies below it.
+    /// </summary>
+    public static async Task<bool> WouldCycleAsync(
+        string taskId, string parentId, Func<string, CancellationToken, Task<TaskItem?>> lookup, CancellationToken ct)
+    {
+        if (string.Equals(taskId, parentId, StringComparison.OrdinalIgnoreCase))
+            return true;
+
+        var seen = new HashSet<string>(StringComparer.OrdinalIgnoreCase);
+        var next = parentId;
+        while (!string.IsNullOrWhiteSpace(next) && seen.Add(next))
+        {
+            if (string.Equals(next, taskId, StringComparison.OrdinalIgnoreCase))
+                return true;
+            next = (await lookup(next, ct))?.ParentId;
+        }
+        return false;
+    }
+
+    /// <summary>
+    /// The goal above the chain: that of the unit of the topmost task that belongs to one —
+    /// a goal a human set on the top level belongs to no unit, so the next one down counts —
+    /// or of the nearest unit above it that has a goal. <c>null</c> without units or without
+    /// a goal.
+    /// </summary>
+    public static (string UnitName, string Goal)? UnitGoal(IReadOnlyList<TaskItem> fromTop, OrgChart? org)
+    {
+        if (org is not { HasUnits: true })
+            return null;
+        var unitId = fromTop.Select(t => TaskBoard.UnitOf(t, org)).FirstOrDefault(u => u is not null);
+        if (org.Unit(unitId) is not { } unit)
+            return null;
+
+        foreach (var candidate in new[] { unit }.Concat(org.Ancestors(unit.Id)))
+        {
+            if (!string.IsNullOrWhiteSpace(candidate.Goal))
+                return (candidate.Name, candidate.Goal.Trim());
+        }
+        return null;
+    }
+
+    /// <summary>
+    /// The paragraph that goes into the run: "you do this because … because … because".
+    /// <c>null</c> when there is nothing above the task — then the run looks as before.
+    /// </summary>
+    public static string? Describe(TaskItem task, IReadOnlyList<TaskItem> parents, OrgChart? org)
+    {
+        var goal = UnitGoal([.. parents.Reverse(), task], org);
+        if (parents.Count == 0 && goal is null)
+            return null;
+
+        var sb = new StringBuilder();
+        sb.AppendLine("Why this task exists — it serves, from nearest to farthest:");
+        foreach (var parent in parents)
+            sb.AppendLine($"- {parent.Id} \"{parent.Title}\" ({TaskText.Of(parent.Status)})");
+        if (goal is { } g)
+            sb.AppendLine($"- the goal of the unit \"{g.UnitName}\": {g.Goal}");
+        sb.Append("Weigh your work against this. If the task no longer serves it — the parent is done or canceled, or the task contradicts the goal — say so in your result instead of working blindly.");
+        return sb.ToString();
+    }
+}