feat(domain): add MonthId arithmetic

Uses a month ordinal rather than Date, so month stepping is timezone-proof.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

src/domain/months.ts

@@ -0,0 +1,59 @@
+import type { IsoDate, MonthId } from "./types.ts";
+
+function parse(id: MonthId): { year: number; month: number } {
+  const match = /^(\d{4})-(\d{2})$/.exec(id);
+  if (!match) throw new Error(`Invalid MonthId: ${id}`);
+  return { year: Number(match[1]), month: Number(match[2]) };
+}
+
+function format(year: number, month: number): MonthId {
+  return `${String(year).padStart(4, "0")}-${String(month).padStart(2, "0")}`;
+}
+
+/** Months since year 0. Avoids Date and therefore avoids timezones entirely. */
+function toOrdinal(id: MonthId): number {
+  const { year, month } = parse(id);
+  return year * 12 + (month - 1);
+}
+
+function fromOrdinal(ordinal: number): MonthId {
+  return format(Math.floor(ordinal / 12), (ordinal % 12) + 1);
+}
+
+export function monthOf(date: IsoDate): MonthId {
+  const match = /^(\d{4})-(\d{2})/.exec(date);
+  if (!match) throw new Error(`Invalid IsoDate: ${date}`);
+  return `${match[1]}-${match[2]}`;
+}
+
+export function yearOf(id: MonthId): number {
+  return parse(id).year;
+}
+
+export function addMonths(id: MonthId, count: number): MonthId {
+  return fromOrdinal(toOrdinal(id) + count);
+}
+
+export function nextMonth(id: MonthId): MonthId {
+  return addMonths(id, 1);
+}
+
+export function prevMonth(id: MonthId): MonthId {
+  return addMonths(id, -1);
+}
+
+export function compareMonths(a: MonthId, b: MonthId): number {
+  return toOrdinal(a) - toOrdinal(b);
+}
+
+export function monthRange(from: MonthId, to: MonthId): MonthId[] {
+  const start = toOrdinal(from);
+  const end = toOrdinal(to);
+  const out: MonthId[] = [];
+  for (let i = start; i <= end; i++) out.push(fromOrdinal(i));
+  return out;
+}
+
+export function monthsOfYear(year: number): MonthId[] {
+  return monthRange(format(year, 1), format(year, 12));
+}