calendar: compute real Easter dates and temporal-cycle seasons

resolveDay() no longer hardcodes season: 'trinitytide'. Easter is
computed via the Anonymous Gregorian algorithm (verified against 16
known reference dates spanning 1583-2100); Advent/Christmastide/
Epiphanytide follow the Christmas-anchored rules (including Advent's
"Sunday nearest Nov 30"); Septuagesima through Trinitytide come from
easter-offsets.yml, reshaped from single named anchor points into real
ranges plus single-day overrides for Corpus Christi and Sacred Heart.

occurring feasts (calendar/feasts.ts) are still a stub — the sanctoral
calendar and Double-vs-not ranking are a separate, larger project.

src/calendar/date-math.ts

@@ -0,0 +1,27 @@
+// Small ISO-date ("YYYY-MM-DD") arithmetic helpers shared by easter.ts and
+// temporal.ts. Parsed/formatted as UTC midnight throughout, same convention
+// as weekday.ts, so results don't shift with the caller's local timezone.
+
+export interface CalendarDate {
+  year: number;
+  month: number; // 1-12
+  day: number;
+}
+
+export function toIsoDate(date: CalendarDate): string {
+  const mm = String(date.month).padStart(2, '0');
+  const dd = String(date.day).padStart(2, '0');
+  return `${date.year}-${mm}-${dd}`;
+}
+
+export function addDays(isoDate: string, days: number): string {
+  const d = new Date(`${isoDate}T00:00:00Z`);
+  d.setUTCDate(d.getUTCDate() + days);
+  return d.toISOString().slice(0, 10);
+}
+
+export function daysBetween(fromIsoDate: string, toIsoDate: string): number {
+  const from = new Date(`${fromIsoDate}T00:00:00Z`).getTime();
+  const to = new Date(`${toIsoDate}T00:00:00Z`).getTime();
+  return Math.round((to - from) / 86_400_000);
+}

src/calendar/easter.ts

@@ -1,8 +1,29 @@
 // Computus (the date of Easter, and everything the temporal cycle hangs off
 // of it — Septuagesima, Ash Wednesday, Ascension, Pentecost, Trinity Sunday).
-// Not implemented yet: unused until milestone 4 (Lauds/Vespers), which is the
-// first hour content that actually varies by season. Deliberately left empty
-// rather than half-built ahead of need — see the "content stores" section of
-// the plan for why calendar-rule logic is being kept swappable rather than
-// front-loaded.
-export {};
+//
+// This is the Anonymous Gregorian algorithm (a.k.a. Meeus/Jones/Butcher),
+// valid for the whole Gregorian era (1583 onward). Hand-rolled rather than
+// pulling in a dependency: it's ~15 lines of pure integer arithmetic with a
+// long history of independent verification (see calendar/easter.test.ts),
+// not something that benefits from a library's abstraction or maintenance
+// surface for an app with zero runtime dependencies otherwise.
+import type { CalendarDate } from './date-math';
+
+export function easterSunday(year: number): CalendarDate {
+  const a = year % 19;
+  const b = Math.floor(year / 100);
+  const c = year % 100;
+  const d = Math.floor(b / 4);
+  const e = b % 4;
+  const f = Math.floor((b + 8) / 25);
+  const g = Math.floor((b - f + 1) / 3);
+  const h = (19 * a + b - d - g + 15) % 30;
+  const i = Math.floor(c / 4);
+  const k = c % 4;
+  const l = (32 + 2 * e + 2 * i - h - k) % 7;
+  const m = Math.floor((a + 11 * h + 22 * l) / 451);
+  const n = h + l - 7 * m + 114;
+  const month = Math.floor(n / 31);
+  const day = (n % 31) + 1;
+  return { year, month, day };
+}

src/calendar/index.ts

@@ -1,21 +1,20 @@
 import type { LiturgicalDay } from './types';
 import { weekdayOf } from './weekday';
+import { resolveSeason } from './temporal';
 
 /**
  * Resolves everything about a given day *except* hour content — weekday,
- * season, and any occurring feasts. Season and occurring feasts are stubs
- * until calendar/easter.ts and calendar/feasts.ts land at milestone 4;
- * hours that only need weekday (Prime, Compline, Terce, Sext, None) can
- * already rely on this fully.
+ * season, and any occurring feasts. Season is real (see
+ * calendar/temporal.ts); occurring feasts are still a stub until
+ * calendar/feasts.ts lands (the sanctoral calendar — which saint, if any,
+ * is kept on a given day, and Double-vs-not ranking — is a separate,
+ * larger project from temporal-cycle season resolution).
  */
 export function resolveDay(isoDate: string): LiturgicalDay {
   return {
     date: isoDate,
     weekday: weekdayOf(isoDate),
-    // Placeholder string, not a real resolution — real season/temporal-id
-    // lookup (data/calendar/easter-offsets.yml + fixed-date-calendar.yml)
-    // lands at milestone 4.
-    season: 'trinitytide',
+    season: resolveSeason(isoDate),
     occurring: [],
   };
 }

src/calendar/temporal.ts

@@ -1,8 +1,96 @@
-// Temporal-cycle occurrence resolution: given a date, which temporal-id
-// applies (season, proper Sunday/feria), by combining two offset systems —
-// data/calendar/easter-offsets.yml (Septuagesima through Trinitytide) and
-// data/calendar/fixed-date-calendar.yml (Christmas, Epiphany). Also where
-// the Advent-start and Epiphanytide-length wrinkles noted in
-// fixed-date-calendar.yml get arbitrated. Depends on calendar/easter.ts for
-// the Easter date itself. Unused until milestone 4.
-export {};
+// Temporal-cycle occurrence resolution: given a date, which season applies.
+// Combines two independent anchor systems that hand off to each other once
+// a year, right around Epiphanytide -> Septuagesima:
+//   - Christmas-relative (data/calendar/fixed-date-calendar.yml): Advent,
+//     Christmastide, Epiphanytide. Advent's start is "the Sunday nearest
+//     Nov 30", not a plain fixed date, so that rule lives in code here.
+//   - Easter-relative (data/calendar/easter-offsets.yml, via
+//     calendar/easter.ts): Septuagesima through the end of Trinitytide.
+//
+// Does NOT resolve occurring feasts (calendar/feasts.ts, still a stub) —
+// a season is the temporal-cycle backdrop a day sits on; which saint (if
+// any) is being kept that day, and whether it outranks the season, is a
+// separate, larger project.
+import type { Season } from './types';
+import { easterSunday } from './easter';
+import { addDays, daysBetween, toIsoDate } from './date-math';
+import fixedDateData from '../data/calendar/fixed-date-calendar.yml';
+import easterOffsetsData from '../data/calendar/easter-offsets.yml';
+
+const fixedDates = fixedDateData as { dates: Record<string, string> };
+const easterOffsets = easterOffsetsData as {
+  ranges: { season: string; fromOffset: number }[];
+  days?: Record<string, string>;
+};
+
+function fixedDateFor(id: string): { month: number; day: number } {
+  const entry = Object.entries(fixedDates.dates).find(([, value]) => value === id);
+  if (!entry) {
+    throw new Error(`fixed-date-calendar.yml has no entry for '${id}'`);
+  }
+  const [monthStr, dayStr] = entry[0].split('-');
+  return { month: Number(monthStr), day: Number(dayStr) };
+}
+
+const CHRISTMAS = fixedDateFor('christmas-day');
+const EPIPHANY = fixedDateFor('epiphany');
+
+/** The Sunday nearest Nov 30 (St. Andrew's Day) — Advent's real start rule. */
+function adventStart(year: number): string {
+  const nov30 = `${year}-11-30`;
+  const dow = new Date(`${nov30}T00:00:00Z`).getUTCDay(); // 0 = Sunday
+  const delta = dow <= 3 ? -dow : 7 - dow;
+  return addDays(nov30, delta);
+}
+
+function seasonFromEasterOffset(offset: number): Season {
+  const dayOverride = easterOffsets.days?.[String(offset)];
+  if (dayOverride) {
+    return dayOverride;
+  }
+  const sorted = [...easterOffsets.ranges].sort((a, b) => a.fromOffset - b.fromOffset);
+  const first = sorted[0];
+  if (!first) {
+    throw new Error('easter-offsets.yml has no ranges');
+  }
+  let season: Season = first.season;
+  for (const range of sorted) {
+    if (offset >= range.fromOffset) {
+      season = range.season;
+    }
+  }
+  return season;
+}
+
+export function resolveSeason(isoDate: string): Season {
+  const [, monthStr, dayStr] = isoDate.split('-');
+  const month = Number(monthStr);
+  const day = Number(dayStr);
+  const year = Number(isoDate.slice(0, 4));
+
+  // Advent: the Sunday nearest Nov 30 through Dec 24.
+  const advent = adventStart(year);
+  const isChristmasDayOrLater = month === CHRISTMAS.month && day >= CHRISTMAS.day;
+  if (isoDate >= advent && !isChristmasDayOrLater) {
+    return 'advent';
+  }
+
+  // Christmastide: Christmas Day through Jan 5, wrapping across the civil
+  // year boundary (so checked as two separate month/day windows, not one
+  // date range).
+  if (isChristmasDayOrLater || (month === 1 && day < EPIPHANY.day)) {
+    return 'christmastide';
+  }
+
+  // Epiphanytide: Epiphany until Septuagesima cuts in. Septuagesima's
+  // earliest possible date (Jan 18, when Easter falls on its earliest
+  // possible date, Mar 22) is always after Epiphany, so no year-rollover
+  // Easter lookup is ever needed to make this comparison.
+  const easterIso = toIsoDate(easterSunday(year));
+  const septuagesimaStart = addDays(easterIso, -63);
+  if (isoDate < septuagesimaStart) {
+    return 'epiphanytide';
+  }
+
+  return seasonFromEasterOffset(daysBetween(easterIso, isoDate));
+}

src/calendar/types.ts

@@ -14,6 +14,26 @@ export type Weekday =
 // actually resolves the "opinionated but configurable" tension: the opinion
 // (trinitytide) lives in editable data, not in a TS enum you'd recompile to
 // change.
+//
+// A real limitation this doesn't fully solve: a single `season` string can
+// only hold one mutually-exclusive value per day, but several independent
+// liturgical windows overlap without sharing boundaries. For example, on a
+// real day between Candlemas (Feb 2) and Ash Wednesday, Compline's Marian
+// antiphon should already be Ave Regina Caelorum, but Lent's Alleluia
+// suppression and hymn swap shouldn't have started yet — two things that
+// are both true at once, which one `season` value can't represent.
+//
+// Real season resolution now exists (calendar/temporal.ts, calendar/easter.ts),
+// and the Marian-antiphon case above is handled — but not by adding a
+// `season` value for it. hours/marian-antiphon.ts checks the real date
+// directly instead of going through `season` at all for that one window.
+// That's a fine, scoped fix for one known overlap; it isn't a general
+// solution. If another mechanism turns up with the same shape (a window
+// that doesn't nest inside one `season` bucket), reach for the same
+// pattern — a direct date check bypassing `season` — rather than trying to
+// force `season` to hold two truths at once. Only worth generalizing into
+// several independent named windows/flags on `LiturgicalDay` itself if a
+// third case shows up and the duplication starts to hurt.
 export type Season = string;
 
 // Open-ended on purpose — the actual ranking scheme (double/semidouble/simple,
@@ -35,11 +55,7 @@ export interface LiturgicalDay {
   /** ISO date, e.g. "2026-08-09" */
   date: string;
   weekday: Weekday;
-  /**
-   * Real season resolution depends on Easter's date (see calendar/easter.ts,
-   * not implemented until milestone 4). Until then this is a placeholder and
-   * must not be trusted by any hour's logic.
-   */
+  /** Real temporal-cycle season, computed via calendar/temporal.ts. */
   season: Season;
   /** Always [] until milestone 4 wires up calendar/feasts.ts. */
   occurring: OccurringFeast[];

src/data/calendar/easter-offsets.yml

@@ -1,18 +1,30 @@
 # Offsets in days from Easter Sunday (0). Negative = before Easter, positive
 # = after. Covers the whole Easter-anchored span: Septuagesima through the
-# last Sunday of Trinitytide. A temporal-id's *name* (and hence whether it
-# reads "trinitytide" or "time after pentecost") lives here as data, not as
-# a compiled TS enum — see calendar/types.ts's Season type.
+# last Sunday of Trinitytide. A season's *name* (and hence whether it reads
+# "trinitytide" or "time after pentecost") lives here as data, not as a
+# compiled TS enum — see calendar/types.ts's Season type.
 #
-# PLACEHOLDER: only a handful of anchor points, to prove the shape. The full
-# set of Sundays/ferias between anchors is content-authoring work for
-# milestone 4.
-offsets:
-  -63: septuagesima-sunday
-  -56: sexagesima-sunday
-  -49: quinquagesima-sunday
-  -46: ash-wednesday
-  0: easter-sunday
-  39: ascension-thursday
-  49: pentecost-sunday
-  56: trinity-sunday
+# `ranges` gives the season that starts at each offset and runs until the
+# next range's offset (or, for the last entry, until Advent cuts it off —
+# see calendar/temporal.ts). `days` overrides a single specific offset with
+# its own one-day season, for movable feasts that aren't a whole season
+# but that other by-season tables (prime-chapter-responsory-by-season.yml,
+# hymn-doxology-by-season.yml) already reference by name.
+ranges:
+  - season: septuagesima
+    fromOffset: -63
+  - season: lent
+    fromOffset: -46
+  - season: passiontide
+    fromOffset: -14
+  - season: eastertide
+    fromOffset: 0
+  - season: ascensiontide
+    fromOffset: 39
+  - season: pentecost
+    fromOffset: 49
+  - season: trinitytide
+    fromOffset: 56
+days:
+  60: corpus-christi # Thursday after Trinity Sunday
+  68: sacred-heart # Friday after the octave of Corpus Christi

tests/calendar/easter.test.ts

@@ -0,0 +1,32 @@
+import { describe, expect, it } from 'vitest';
+import { easterSunday } from '../../src/calendar/easter';
+import { toIsoDate } from '../../src/calendar/date-math';
+
+// Reference dates are public record (Western/Gregorian Easter Sunday),
+// spanning different centuries and both early and late extremes.
+const KNOWN_EASTER_DATES: Record<number, string> = {
+  1583: '1583-04-10', // first year the Gregorian algorithm is valid
+  1900: '1900-04-15',
+  1954: '1954-04-18',
+  2000: '2000-04-23',
+  2019: '2019-04-21',
+  2020: '2020-04-12',
+  2021: '2021-04-04',
+  2022: '2022-04-17',
+  2023: '2023-04-09',
+  2024: '2024-03-31', // one of the earliest possible dates
+  2025: '2025-04-20',
+  2026: '2026-04-05',
+  2027: '2027-03-28',
+  2028: '2028-04-16',
+  2038: '2038-04-25', // one of the latest possible dates
+  2100: '2100-03-28',
+};
+
+describe('easterSunday', () => {
+  for (const [year, expected] of Object.entries(KNOWN_EASTER_DATES)) {
+    it(`resolves ${year} to ${expected}`, () => {
+      expect(toIsoDate(easterSunday(Number(year)))).toBe(expected);
+    });
+  }
+});

tests/calendar/temporal.test.ts

@@ -0,0 +1,54 @@
+import { describe, expect, it } from 'vitest';
+import { resolveSeason } from '../../src/calendar/temporal';
+
+// Easter 2026 = Apr 5. Reference boundaries computed by hand from that.
+describe('resolveSeason', () => {
+  it('resolves Advent (the Sunday nearest Nov 30) through Dec 24', () => {
+    // Nov 30, 2025 is a Sunday -> Advent I starts that day.
+    expect(resolveSeason('2025-11-29')).toBe('trinitytide');
+    expect(resolveSeason('2025-11-30')).toBe('advent');
+    expect(resolveSeason('2025-12-24')).toBe('advent');
+  });
+
+  it('resolves Christmastide across the year boundary (Dec 25 - Jan 5)', () => {
+    expect(resolveSeason('2025-12-25')).toBe('christmastide');
+    expect(resolveSeason('2025-12-31')).toBe('christmastide');
+    expect(resolveSeason('2026-01-01')).toBe('christmastide');
+    expect(resolveSeason('2026-01-05')).toBe('christmastide');
+  });
+
+  it('resolves Epiphanytide from Jan 6 until Septuagesima', () => {
+    expect(resolveSeason('2026-01-06')).toBe('epiphanytide');
+    // Easter 2026 is Apr 5, so Septuagesima (-63 days) is Feb 1.
+    expect(resolveSeason('2026-01-31')).toBe('epiphanytide');
+  });
+
+  it('resolves the Easter-offset seasons for 2026 (Easter = Apr 5)', () => {
+    expect(resolveSeason('2026-02-01')).toBe('septuagesima'); // Easter - 63
+    expect(resolveSeason('2026-02-18')).toBe('lent'); // Ash Wednesday, Easter - 46
+    expect(resolveSeason('2026-03-22')).toBe('passiontide'); // Easter - 14
+    expect(resolveSeason('2026-04-05')).toBe('eastertide'); // Easter Sunday
+    expect(resolveSeason('2026-05-14')).toBe('ascensiontide'); // Easter + 39
+    expect(resolveSeason('2026-05-24')).toBe('pentecost'); // Easter + 49
+    expect(resolveSeason('2026-05-31')).toBe('trinitytide'); // Easter + 56
+  });
+
+  it('resolves the Corpus Christi and Sacred Heart single-day overrides', () => {
+    expect(resolveSeason('2026-06-04')).toBe('corpus-christi'); // Easter + 60
+    expect(resolveSeason('2026-06-12')).toBe('sacred-heart'); // Easter + 68
+    // The days immediately around them are still plain Trinitytide.
+    expect(resolveSeason('2026-06-05')).toBe('trinitytide');
+  });
+
+  it('resolves plain Trinitytide between Trinity Sunday and Advent', () => {
+    expect(resolveSeason('2026-09-15')).toBe('trinitytide');
+  });
+
+  it('never needs a cross-year Easter lookup for January dates', () => {
+    // A year with a very early Easter (2027-03-28) still keeps Septuagesima
+    // (Jan 24) safely after Epiphany (Jan 6).
+    expect(resolveSeason('2027-01-06')).toBe('epiphanytide');
+    expect(resolveSeason('2027-01-23')).toBe('epiphanytide');
+    expect(resolveSeason('2027-01-24')).toBe('septuagesima');
+  });
+});