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>

src/shared/period.ts

@@ -2,7 +2,8 @@ import { z } from "zod";
 import { DAY } from "./time.ts";
 
 /**
- * Periods longer than a day — a week, a month — in day-key space.
+ * Periods longer than a day — a week, a month, a cycle of N days — in day-key
+ * space.
  *
  * Every key here is a `YYYY-MM-DD` game-day that `dayKey` already cut on a
  * game's own reset clock for the reader's region. Working on keys rather than
@@ -16,10 +17,18 @@ import { DAY } from "./time.ts";
 /** ISO weekday: Monday is 1, Sunday is 7. */
 export const WeekdaySchema = z.number().int().min(1).max(7);
 
+const DayKey = z.string().regex(/^\d{4}-\d{2}-\d{2}$/);
+
 export const PeriodSchema = z.union([
   z.object({ unit: z.literal("week"), startsOn: WeekdaySchema }),
   /** Day of month; 31 means "the last day" in a shorter month. */
   z.object({ unit: z.literal("month"), startsOn: z.number().int().min(1).max(31) }),
+  /**
+   * Every `days` game-days, counted from `from`, a game-day on which a cycle
+   * began — any one, not necessarily the first: cycles run both ways from it,
+   * so an anchor read off this cycle's timer stays right for the ones before.
+   */
+  z.object({ unit: z.literal("cycle"), days: z.number().int().min(2).max(366), from: DayKey }),
 ]);
 export type Period = z.infer<typeof PeriodSchema>;
 
@@ -56,6 +65,10 @@ export function periodOf(
   if (period.unit === "week") {
     start = addDays(today, -((isoWeekday(today) - period.startsOn + 7) % 7));
     next = addDays(start, 7);
+  } else if (period.unit === "cycle") {
+    const since = Math.round((msOf(today) - msOf(period.from)) / DAY);
+    start = addDays(period.from, Math.floor(since / period.days) * period.days);
+    next = addDays(start, period.days);
   } else {
     const t = new Date(msOf(today));
     const y = t.getUTCFullYear();