Fix octave day labels: correct commemoration phrasing, closing-day title, and privileged-season precedence

Three related day-label bugs, all found via Aug 19's mislabeled Assumption
octave commemoration:

- A sanctoral winner that displaces the only active octave now shows the
  octave's real "Nth Day within the Octave of X" phrasing (no rank, since
  it's riding along under the winning feast), not a bare feast name.
- An octave's own closing day now titles itself "Octave of X", matching
  the real DO's "in octava" vs. "infra octavam" distinction, instead of
  "8th Day within the Octave of X".
- A sufficiently-ranked octave can now outrank a privileged temporal
  season (e.g. the Immaculate Conception's octave outright winning several
  of its days against Advent, live-verified against Divino Afflatu 1954),
  via a new shared octaveGoverningPrivilegedDay helper used by both the
  day label and the actual office-content resolver. Deliberately excludes
  Christmastide, whose own stacked octaves are structurally already that
  season's temporal content rather than a foreign add-on.

Updates a Matins test fixture that had unknowingly relied on the
Dec 15 bug (Advent ferial + a lone commemorated saint) and splits it into
a clean ferial case plus a dedicated commemorated-saint case.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

src/calendar/day-label.ts

@@ -14,7 +14,7 @@ import { easterSunday } from './easter';
 import { adventStart, firstSundayStrictlyAfter, sundayOnOrBefore } from './temporal';
 import { addDays, daysBetween, toIsoDate } from './date-math';
 import { getTemporalFeastRecord } from './temporal-feasts';
-import { resolveActiveOctave, type ActiveOctave } from './octaves';
+import { activeOctavesFor, octaveGoverningPrivilegedDay, resolveActiveOctave, type ActiveOctave } from './octaves';
 import { resolveTemporalId } from './temporal-id';
 
 function capitalize(text: string): string {
@@ -210,15 +210,36 @@ function temporalLabel(day: LiturgicalDay): string {
   return `${weekdayName} in the ${ordinalStr} week ${config.preposition} ${config.ordinalName}`;
 }
 
-/** "Third Day within the Octave of St. Lawrence" — the real DO title an
- * octave day carries on its own (e.g. "Tertia die infra Octavam S.
- * Laurentii Martyris") when nothing else has displaced it. Day 1 shouldn't
- * normally reach this (that day's own winner is the feast itself, handled
+/** "Third Day within the Octave of St. Lawrence" for an ordinary mid-octave
+ * day (e.g. "Tertia die infra Octavam S. Laurentii Martyris"), or plain
+ * "Octave of St. Lawrence" for the octave's own closing day — real DO
+ * Latin distinguishes "infra octavam" (within the octave, days 2-7) from
+ * "in octava" (on the octave day itself, day 8), live-verified: Aug 17
+ * (St. Lawrence's closing day) titles itself "In Octava S. Laurentii
+ * Martyris", not "Octava die infra Octavam...". Day 1 shouldn't normally
+ * reach either branch (that day's own winner is the feast itself, handled
  * above before this is ever called) — kept simple rather than
  * special-cased for that rare edge case (see applyOctaves's own
  * `isOwnStartDay` comment in calendar/index.ts for when it can happen). */
+function octaveCoreName(octave: ActiveOctave): string {
+  return octave.isClosingDay ? `Octave of ${octave.name}` : `${ordinal(octave.dayNumber)} Day within the Octave of ${octave.name}`;
+}
+
 function octaveLabel(octave: ActiveOctave): string {
-  return `${ordinal(octave.dayNumber)} Day within the Octave of ${octave.name} (${formatRank(octave.wins)})`;
+  return `${octaveCoreName(octave)} (${formatRank(octave.wins)})`;
+}
+
+/** Same phrasing as `octaveLabel`, but without the parenthesized rank —
+ * the real DO commemoration line for a displaced octave day carries no
+ * rank at all (e.g. Aug 19's real Divino Afflatu 1954 commemoration reads
+ * plain "Quinta die infra Octavam S. Assumptionis Beatæ Mariæ Virginis",
+ * no "~ Semiduplex"). `octaveLabel`'s own rank parenthetical only belongs
+ * to an octave day when it's the day's own primary winner (rank is what
+ * it *won as*, not a fact worth restating once a duplex-or-higher saint
+ * has displaced it and it's just riding along as a commemoration
+ * instead). */
+function octaveCommemorationLabel(octave: ActiveOctave): string {
+  return octaveCoreName(octave);
 }
 
 /** Every `kind: 'octave'` commemoration on `day` other than `excludeId` —
@@ -239,6 +260,27 @@ function otherActiveOctaveNames(day: LiturgicalDay, excludeId: string | undefine
     .map((c) => c.name);
 }
 
+/** Same commemoration-filtering as `otherActiveOctaveNames`, but rendered
+ * with `octaveCommemorationLabel`'s fuller "Nth Day within the Octave of X"
+ * phrasing rather than a plain name — the real DO title an octave day
+ * carries even when it *lost* outright to an occurring saint (e.g. Aug 19's
+ * real Divino Afflatu 1954 title is "S. Joannis Eudes Confessoris ~ Duplex"
+ * with the commemoration read as "Quinta die infra Octavam S. Assumptionis
+ * Beatæ Mariæ Virginis", not a bare "The Assumption of the Blessed Virgin
+ * Mary"). Only used from the sanctoral-winner branch below — the
+ * octave-vs-octave secondary mention (`otherActiveOctaveNames` itself,
+ * still used in the octave-headline branch further down) keeps its plain
+ * name on purpose, per that function's own doc comment. */
+function commemoratedOctaveDayLabels(day: LiturgicalDay, excludeId: string | undefined): string[] {
+  const active = activeOctavesFor(day.date);
+  return day.commemorations
+    .filter((c): c is Extract<Commemoration, { kind: 'octave' }> => c.kind === 'octave' && c.id !== excludeId)
+    .map((c) => {
+      const octave = active.find((a) => a.id === c.id);
+      return octave ? octaveCommemorationLabel(octave) : c.name;
+    });
+}
+
 const RANK_LABELS: Record<FeastClass, string> = {
   simplex: 'Simplex',
   vigil: 'Vigil',
@@ -295,7 +337,7 @@ export function getDayLabel(day: LiturgicalDay): string {
     // also day 8 of Pentecost's own octave) never mentions an octave —
     // same "nobody calls it that" convention anchorDayName's own doc
     // comment already established for the anchor-day case.
-    const otherOctaves = day.temporalCategory === 'ordinary-feria' ? otherActiveOctaveNames(day, undefined) : [];
+    const otherOctaves = day.temporalCategory === 'ordinary-feria' ? commemoratedOctaveDayLabels(day, undefined) : [];
     const winnerName = `${day.winner.name} (${formatRank(day.winner.rank)})`;
     return [winnerName, ...otherOctaves].join(' — ');
   }
@@ -326,24 +368,33 @@ export function getDayLabel(day: LiturgicalDay): string {
   // identity in the live engine, not a footnote — e.g. "Tertia die infra
   // Octavam S. Laurentii Martyris", not "Wednesday in the 11th week after
   // Trinity" — but *only* when the temporal day itself has no standing of
-  // its own (`ordinary-feria`), same gate as hours/resolve-common.ts's
+  // its own (`ordinary-feria`), or a foreign octave's own effective rank
+  // is strong enough to clear a privileged day's real threshold anyway
+  // (`octaveGoverningPrivilegedDay` — the Immaculate Conception's own
+  // octave outright winning several of its days against Advent's
+  // privileged-feria-minor ferias, live-verified: Dec 9/10/12/14 at the
+  // octave's ordinary Semiduplex, Dec 15 at its own elevated Duplex majus
+  // closing day). Same gate as hours/resolve-common.ts's
   // resolveOfficeWinner and for the same reason: live-verified
   // counterexample is the Christmas Octave's own stack (Dec 30, e.g.,
   // `privileged-feria-minor`), where the real title stays the temporal
   // Sunday's own ("De Dominica Infra Octavam Nativitatis") with no octave
-  // name in it at all — this label agreeing with resolveOfficeWinner
-  // about which one wins is what makes "the office is Lawrence's" and
-  // "the label says Lawrence" consistent instead of two independent
-  // guesses that can disagree. When more than one octave is active at
-  // once (resolveActiveOctave), the highest-ranked wins the headline
-  // (ties broken by whichever started more recently) — every other
-  // active octave still gets named too (otherActiveOctaveNames), not
-  // dropped: live-verified real case, Aug 17 -- St. Lawrence's own
-  // elevated closing day wins the headline, but the Assumption's own
-  // day 3 (a real, distinct, simultaneously-active octave, not a
-  // duplicate of Lawrence's) still belongs in the label alongside St.
-  // Hyacinth's commemoration.
-  const activeOctave = day.temporalCategory === 'ordinary-feria' ? resolveActiveOctave(day.date) : undefined;
+  // name in it at all, regardless of rank — `octaveGoverningPrivilegedDay`
+  // excludes `christmastide` for exactly this reason (see its own doc
+  // comment) — this label agreeing with resolveOfficeWinner about which
+  // one wins is what makes "the office is Lawrence's" and "the label says
+  // Lawrence" consistent instead of two independent guesses that can
+  // disagree. When more than one octave is active at once
+  // (resolveActiveOctave), the highest-ranked wins the headline (ties
+  // broken by whichever started more recently) — every other active
+  // octave still gets named too (otherActiveOctaveNames), not dropped:
+  // live-verified real case, Aug 17 -- St. Lawrence's own elevated
+  // closing day wins the headline, but the Assumption's own day 3 (a
+  // real, distinct, simultaneously-active octave, not a duplicate of
+  // Lawrence's) still belongs in the label alongside St. Hyacinth's
+  // commemoration.
+  const activeOctave =
+    day.temporalCategory === 'ordinary-feria' ? resolveActiveOctave(day.date) : octaveGoverningPrivilegedDay(day);
   if (activeOctave) {
     const primary = octaveLabel(activeOctave);
     const rest = [...otherActiveOctaveNames(day, activeOctave.id), ...(commemoratedSaint ? [commemoratedSaint.name] : [])];