feat(tasks): a task can repeat every N days from a dated start

A third period, { unit: "cycle", days, from }, cut in day-key space like
weeks and months, so each game's per-server reset carries over. Tasks on
it are tallied and switched apart (showCycleTasks, on by default), show
the days left in their chip, and the lower row's heading now names the
periods it holds.

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

test/task.test.ts

@@ -124,3 +124,27 @@ describe("taskCaption", () => {
     ).toBe("every month from the 22nd · 3 days");
   });
 });
+
+describe("a task on a cycle", () => {
+  test("its status is by its cycle, and its caption names the start", () => {
+    const t = task({
+      period: { unit: "cycle", days: 14, from: "2026-10-16" },
+      measure: { kind: "days", required: 5 },
+    });
+    expect(TaskSchema.safeParse(t).success).toBe(true);
+    expect(taskCaption(t)).toBe("every 14 days from 16 Oct 2026 · 5 days");
+    const s = taskStatus({
+      task: t, region: "europe", now: noon("2026-10-20"),
+      logged: ["2026-10-15", "2026-10-16", "2026-10-18"],
+    });
+    expect(s).toMatchObject({ scope: "cycle", periodStart: "2026-10-16", count: 2, required: 5, open: 10 });
+  });
+
+  test("a short cycle never asks for more days than it holds", () => {
+    const t = task({
+      period: { unit: "cycle", days: 3, from: "2026-10-16" },
+      measure: { kind: "days", required: 5 },
+    });
+    expect(taskStatus({ task: t, region: "europe", now: noon("2026-10-16"), logged: [] }).required).toBe(3);
+  });
+});