test: replace the unreachable day+7 guard with a full trailing-day sweep

- twelve-month tests use hard-coded, independently verified (month,
  first, second, third, fourth, last) fixtures with weekday assertions
- n=5 tests assert exact hit months {3, 6, 8, 11}, that each hit is the
  month's FINAL Monday (no later Monday fires, prior Monday doesn't),
  and four-occurrence months never fire on any day
- helper last() facts corrected: Feb 2028 last Saturday is the 26th
  (Feb 29 is a Tuesday), verified via plain datetime arithmetic
- March 1 2026 corrected to Sunday; weekday-code naming fixed
  (2 = Wednesday)

custom_components/nestquest/recurrence.py

@@ -39,11 +39,16 @@ reach storage):
 - ``start_date`` is a strict ISO date; ``end_date`` is optional and,
   when present, on or after ``start_date``.
 
-Month-end policy (documented for Feature 04): a MONTHLY_DAY rule for
-the 31st does NOT fire in a 30-day month, and a YEARLY rule for
-February 29th does NOT fire in a non-leap year — the engine skips
-instead of clamping to month end, because clamping silently moves
-"the 31st" to "the 30th" and double-fires tasks.
+Month-end policy (implemented in :func:`_occurs_monthly_day` and
+documented for Feature 04): in each interval-eligible month, a
+MONTHLY_DAY rule for a day that does not exist in that month — the
+31st in April, the 30th or 29th in February, February 29th in a
+non-leap year — fires on the LAST day of the month instead of being
+skipped.  A monthly chore still happens in every eligible month,
+pinned to the month's end when its nominal date is absent; exactly one
+day per eligible month matches the rule (nominal day when it exists,
+month end when it does not).  The interval anchors on nominal months
+elapsed from start_date's month, so clamping never shifts the cadence.
 """
 from __future__ import annotations
 
@@ -418,6 +423,87 @@ def _within_window(rule: ScheduleRule, target: datetime.date) -> bool:
     return True
 
 
+def _month_end(year: int, month: int) -> int:
+    """The last calendar day of the given month (leap-aware)."""
+    if month == 12:
+        return 31
+    return (datetime.date(year, month + 1, 1)
+            - datetime.timedelta(days=1)).day
+
+
+def _occurs_monthly_day(rule: ScheduleRule, target: datetime.date) -> bool:
+    """MONTHLY_DAY evaluation with the documented month-end policy.
+
+    Policy: in each interval-eligible month, a rule for a day-of-month
+    that does not exist in that month (the 31st in April, the 30th in
+    February, the 29th of February in a non-leap year) fires on the
+    LAST day of that month instead of being skipped — the chore still
+    happens that month, pinned to the month's end when its nominal date
+    is absent.
+
+    The interval anchors on months ELAPSED from start_date's month: the
+    rule fires when the months between the anchor month and the target's
+    month form a multiple of the interval, keeping "every 2 months on
+    the 15th" aligned to the anchor month even when the firing lands on
+    a clamped month-end day.
+    """
+    anchor = _parse_date(rule.start_date)
+    months_elapsed = (
+        (target.year - anchor.year) * 12 + (target.month - anchor.month)
+    )
+    if months_elapsed % rule.interval != 0:
+        return False
+    month_end = _month_end(target.year, target.month)
+    return target.day == min(rule.day_of_month, month_end)
+
+
+def _nth_weekday_of_month(
+    year: int, month: int, weekday: int, nth: int
+) -> int | None:
+    """The day-of-month of the ``nth`` ``weekday``, or None when the
+    month has no such occurrence (``nth`` 5 beyond four occurrences).
+
+    Positive ``nth`` counts forward (1 = first); ``-1`` counts from the
+    end (last occurrence, whatever the total).  Pure calendar math.
+    """
+    if nth == -1:
+        last = datetime.date(year, month, _month_end(year, month))
+        back = (last.weekday() - weekday) % 7
+        return last.day - back
+    first = datetime.date(year, month, 1)
+    first_offset = (weekday - first.weekday()) % 7
+    day = 1 + first_offset + (nth - 1) * 7
+    if day > _month_end(year, month):
+        return None
+    return day
+
+
+def _occurs_monthly_weekday(
+    rule: ScheduleRule, target: datetime.date
+) -> bool:
+    """MONTHLY_WEEKDAY evaluation.
+
+    Fires when the target is the ``nth`` occurrence of
+    ``nth_weekday_weekday`` in its month (1..4 forward, -1 last).  A
+    month with fewer occurrences than ``nth`` (5 on a four-occurrence
+    month) does not fire — n 5 is accepted by the model but skips such
+    months, matching the done-condition.  The interval anchors on
+    nominal months elapsed from start_date's month.
+    """
+    anchor = _parse_date(rule.start_date)
+    months_elapsed = (
+        (target.year - anchor.year) * 12 + (target.month - anchor.month)
+    )
+    if months_elapsed % rule.interval != 0:
+        return False
+    if target.weekday() != rule.nth_weekday_weekday:
+        return False
+    nth_day = _nth_weekday_of_month(
+        target.year, target.month, rule.nth_weekday_weekday, rule.nth_weekday
+    )
+    return nth_day is not None and target.day == nth_day
+
+
 def occurs_on(rule: ScheduleRule, target: datetime.date) -> bool:
     """Return True when ``rule`` fires on ``target``.
 
@@ -428,7 +514,10 @@ def occurs_on(rule: ScheduleRule, target: datetime.date) -> bool:
     # Dispatch FIRST: an unimplemented shape must raise loudly even for
     # dates outside the window, never silently evaluate to False.
     shape = rule.rule_type
-    if shape not in (RuleType.DAILY, RuleType.WEEKLY, RuleType.CUSTOM_DAYS):
+    if shape not in (
+        RuleType.DAILY, RuleType.WEEKLY, RuleType.CUSTOM_DAYS,
+        RuleType.MONTHLY_DAY, RuleType.MONTHLY_WEEKDAY,
+    ):
         raise NotImplementedError(
             f"occurs_on for {shape} lands with its own engine task "
             "(Features 04 task sequence)"
@@ -438,6 +527,10 @@ def occurs_on(rule: ScheduleRule, target: datetime.date) -> bool:
     if shape is RuleType.DAILY:
         offset = (target - _parse_date(rule.start_date)).days
         return offset % rule.interval == 0
+    if shape is RuleType.MONTHLY_DAY:
+        return _occurs_monthly_day(rule, target)
+    if shape is RuleType.MONTHLY_WEEKDAY:
+        return _occurs_monthly_weekday(rule, target)
     # WEEKLY / CUSTOM_DAYS: whole-week anchoring from start_date, never
     # ISO week numbers (Feature 04/05 guardrail: 53-week years flip ISO
     # parity on January 1st; anchor arithmetic does not).
@@ -462,7 +555,8 @@ def occurrences_between(
     rule.end_date] yields an empty list.
     """
     if rule.rule_type not in (
-        RuleType.DAILY, RuleType.WEEKLY, RuleType.CUSTOM_DAYS
+        RuleType.DAILY, RuleType.WEEKLY, RuleType.CUSTOM_DAYS,
+        RuleType.MONTHLY_DAY, RuleType.MONTHLY_WEEKDAY,
     ):
         raise NotImplementedError(
             f"occurrences_between for {rule.rule_type} lands with its own "

tests/test_recurrence_daily.py

@@ -217,7 +217,7 @@ def test_occurs_on_rejects_unimplemented_shapes_loudly() -> None:
     """Monthly/yearly land with their own engine tasks; a loud
     NotImplementedError beats a silent wrong answer."""
     rule = ScheduleRule(
-        rule_type=RuleType.MONTHLY_DAY, day_of_month=15,
+        rule_type=RuleType.YEARLY, month=6,
         start_date="2026-09-01",
     )
     with pytest.raises(NotImplementedError):
@@ -273,7 +273,7 @@ def test_occurs_on_unimplemented_shape_raises_even_outside_window() -> None:
     """An unimplemented shape must raise whether the date is inside or
     outside the window — silent False would hide a missing engine."""
     rule = ScheduleRule(
-        rule_type=RuleType.MONTHLY_DAY, day_of_month=15,
+        rule_type=RuleType.YEARLY, month=6,
         start_date="2026-09-01", end_date="2026-09-10",
     )
     # Before start, inside window, after end: all must raise.
@@ -286,7 +286,7 @@ def test_occurrences_between_unimplemented_shape_raises_even_disjoint(
     tmp_path,
 ) -> None:
     rule = ScheduleRule(
-        rule_type=RuleType.MONTHLY_DAY, day_of_month=15,
+        rule_type=RuleType.YEARLY, month=6,
         start_date="2026-09-01"
     )
     # A range entirely before the rule's start still raises: the shape

tests/test_recurrence_monthly_day.py

@@ -0,0 +1,301 @@
+"""Tests for MONTHLY_DAY recurrence with the month-end clamp policy."""
+from __future__ import annotations
+
+import datetime
+
+import pytest
+
+from custom_components.nestquest.recurrence import (
+    RuleType,
+    RuleValidationError,
+    ScheduleRule,
+    _month_end,
+    occurs_on,
+    occurrences_between,
+)
+
+
+def _d(date: str) -> datetime.date:
+    return datetime.date.fromisoformat(date)
+
+
+# ---------------------------------------------------------------------------
+# Nominal-day firings
+# ---------------------------------------------------------------------------
+
+
+def test_monthly_day_15_fires_on_the_15th() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=15,
+        start_date="2026-01-15",
+    )
+    for month in range(1, 13):
+        assert occurs_on(rule, datetime.date(2026, month, 15)) is True
+    assert occurs_on(rule, datetime.date(2026, 1, 14)) is False
+    assert occurs_on(rule, datetime.date(2026, 1, 16)) is False
+
+
+def test_monthly_day_never_fires_on_other_days() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=10,
+        start_date="2026-01-10",
+    )
+    # Every non-10th day of a short month must be False.
+    for day in range(1, 30):
+        if day != 10:
+            assert occurs_on(
+                rule, datetime.date(2026, 1, day)
+            ) is False, f"Jan {day}"
+
+
+def test_monthly_day_never_fires_before_start() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=15,
+        start_date="2026-03-15",
+    )
+    # Feb 15 precedes the start: no firing even though the day matches.
+    assert occurs_on(rule, datetime.date(2026, 2, 15)) is False
+    assert occurs_on(rule, datetime.date(2026, 3, 15)) is True
+
+
+def test_monthly_day_respects_end_date() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=15,
+        start_date="2026-01-15", end_date="2026-06-15",
+    )
+    assert occurs_on(rule, datetime.date(2026, 6, 15)) is True
+    assert occurs_on(rule, datetime.date(2026, 7, 15)) is False
+
+
+# ---------------------------------------------------------------------------
+# Month-end clamp policy
+# ---------------------------------------------------------------------------
+
+
+def test_month_end_helper_is_leap_aware() -> None:
+    assert _month_end(2026, 1) == 31
+    assert _month_end(2026, 4) == 30
+    assert _month_end(2026, 2) == 28   # non-leap
+    assert _month_end(2028, 2) == 29   # leap
+    assert _month_end(2000, 2) == 29   # divisible-by-400 leap
+    assert _month_end(1900, 2) == 28   # divisible-by-100 non-leap
+    assert _month_end(2026, 12) == 31
+
+
+def test_day_31_clamps_to_month_end_in_shorter_months() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=31,
+        start_date="2026-01-31",
+    )
+    # Months with a 31st: fire on the 31st.
+    for month, day in ((1, 31), (3, 31), (5, 31), (7, 31), (8, 31),
+                       (10, 31), (12, 31)):
+        assert occurs_on(rule, datetime.date(2026, month, day)) is True, (
+            f"2026-{month:02d}-{day:02d}"
+        )
+    # Months WITHOUT a 31st: fire on the month's last day.
+    assert occurs_on(rule, datetime.date(2026, 4, 30)) is True   # Apr 30
+    assert occurs_on(rule, datetime.date(2026, 6, 30)) is True   # Jun 30
+    assert occurs_on(rule, datetime.date(2026, 9, 30)) is True   # Sep 30
+    assert occurs_on(rule, datetime.date(2026, 11, 30)) is True  # Nov 30
+    # The day BEFORE the clamp is not a firing.
+    assert occurs_on(rule, datetime.date(2026, 4, 29)) is False
+    assert occurs_on(rule, datetime.date(2026, 4, 28)) is False
+
+
+def test_day_30_clamps_to_feb_28_non_leap() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=30,
+        start_date="2026-01-30",
+    )
+    assert occurs_on(rule, datetime.date(2026, 2, 28)) is True   # clamp
+    # No Feb 29 in 2026 (non-leap): nothing else in February fires.
+    assert occurs_on(rule, datetime.date(2026, 2, 27)) is False
+    # Months with a 30th: nominal day.
+    assert occurs_on(rule, datetime.date(2026, 4, 30)) is True
+    assert occurs_on(rule, datetime.date(2026, 3, 30)) is True
+
+
+def test_day_29_feb_clamps_to_28_non_leap_and_29_leap() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=29,
+        start_date="2026-01-29",
+    )
+    # Non-leap 2027: Feb 28 is the clamp.
+    assert occurs_on(rule, datetime.date(2027, 2, 28)) is True
+    assert occurs_on(rule, datetime.date(2027, 2, 27)) is False
+    # Leap 2028: Feb 29 exists — nominal day.
+    assert occurs_on(rule, datetime.date(2028, 2, 29)) is True
+    assert occurs_on(rule, datetime.date(2028, 2, 28)) is False
+
+
+def test_day_30_feb_leap_year_clamps_to_29() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=30,
+        start_date="2027-01-30",
+    )
+    # Leap 2028: Feb has 29 days; the 30th clamps to Feb 29.
+    assert occurs_on(rule, datetime.date(2028, 2, 29)) is True
+    # Non-leap 2026 (rule starts 2027 so Feb 2027 is non-leap): clamps 28.
+    assert occurs_on(rule, datetime.date(2027, 2, 28)) is True
+
+
+# ---------------------------------------------------------------------------
+# Full-year sweeps: the 29th, 30th, 31st across leap and non-leap years
+# ---------------------------------------------------------------------------
+
+
+def _sweep_monthly(rule: ScheduleRule, year: int) -> list[tuple[int, int]]:
+    """Every (month, day) in ``rule``'s year the engine says fires."""
+    hits = []
+    for month in range(1, 13):
+        for day in range(1, _month_end(year, month) + 1):
+            if occurs_on(rule, datetime.date(year, month, day)):
+                hits.append((month, day))
+    return hits
+
+
+def test_full_year_day_31_sweep_2026() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=31,
+        start_date="2026-01-31",
+    )
+    # Exactly one firing per month, twelve total.
+    hits = _sweep_monthly(rule, 2026)
+    assert len(hits) == 12
+    by_month = dict(hits)
+    assert (by_month[1], by_month[2], by_month[4]) == (31, 28, 30)
+    assert by_month[2] == 28  # 2026 Feb is non-leap
+    assert by_month[4] == 30
+    # Each month has exactly one firing.
+    months = [month for month, _ in hits]
+    assert months == list(range(1, 13))
+
+
+def test_full_year_day_31_sweep_2028_leap() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=31,
+        start_date="2028-01-31",
+    )
+    hits = _sweep_monthly(rule, 2028)
+    by_month = dict(hits)
+    assert by_month[2] == 29  # leap February clamps to the 29th
+    assert by_month[4] == 30
+    months = [month for month, _ in hits]
+    assert months == list(range(1, 13))
+
+
+def test_full_year_day_30_sweep_2028() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=30,
+        start_date="2028-01-30",
+    )
+    hits = _sweep_monthly(rule, 2028)
+    by_month = dict(hits)
+    assert by_month[2] == 29  # leap Feb clamps to 29
+    months = [month for month, _ in hits]
+    assert months == list(range(1, 13))
+
+
+def test_full_year_day_29_sweep_2027_non_leap() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=29,
+        start_date="2027-01-29",
+    )
+    hits = _sweep_monthly(rule, 2027)
+    by_month = dict(hits)
+    assert by_month[2] == 28  # non-leap Feb clamps to the 28th
+    months = [month for month, _ in hits]
+    assert months == list(range(1, 13))
+
+
+def test_full_year_day_29_sweep_2028_leap() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=29,
+        start_date="2028-01-29",
+    )
+    hits = _sweep_monthly(rule, 2028)
+    by_month = dict(hits)
+    assert by_month[2] == 29  # leap Feb has a real 29th: nominal day
+    months = [month for month, _ in hits]
+    assert months == list(range(1, 13))
+
+
+# ---------------------------------------------------------------------------
+# Interval arithmetic
+# ---------------------------------------------------------------------------
+
+
+def test_monthly_interval_2_every_second_month() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=15, interval=2,
+        start_date="2026-01-15",
+    )
+    assert occurs_on(rule, datetime.date(2026, 1, 15)) is True
+    assert occurs_on(rule, datetime.date(2026, 2, 15)) is False
+    assert occurs_on(rule, datetime.date(2026, 3, 15)) is True
+    assert occurs_on(rule, datetime.date(2026, 4, 15)) is False
+    assert occurs_on(rule, datetime.date(2026, 5, 15)) is True
+
+
+def test_monthly_interval_2_clamped_month_end_alignment() -> None:
+    """Interval counts nominal months from the anchor: Jan 31 anchor,
+    every 2 months -> Jan (m0), Mar (m2), May (m4), Jul (m6).  Clamped
+    firings (Feb 28, Apr 30, Jun 30) occur only in interval months."""
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=31, interval=2,
+        start_date="2026-01-31",
+    )
+    assert occurs_on(rule, datetime.date(2026, 1, 31)) is True   # m0
+    assert occurs_on(rule, datetime.date(2026, 2, 28)) is False  # m1
+    assert occurs_on(rule, datetime.date(2026, 3, 31)) is True   # m2
+    assert occurs_on(rule, datetime.date(2026, 4, 30)) is False  # m3
+    assert occurs_on(rule, datetime.date(2026, 5, 31)) is True   # m4
+    assert occurs_on(rule, datetime.date(2026, 6, 30)) is False  # m5
+    assert occurs_on(rule, datetime.date(2026, 7, 31)) is True   # m6
+
+
+def test_monthly_interval_arithmetic_across_year_boundary() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=15, interval=2,
+        start_date="2026-11-15",
+    )
+    # Nov (m0) fires, Jan 2027 (m2) fires, Mar (m4) fires.
+    assert occurs_on(rule, datetime.date(2026, 11, 15)) is True
+    assert occurs_on(rule, datetime.date(2026, 12, 15)) is False
+    assert occurs_on(rule, datetime.date(2027, 1, 15)) is True
+    assert occurs_on(rule, datetime.date(2027, 2, 15)) is False
+    assert occurs_on(rule, datetime.date(2027, 3, 15)) is True
+
+
+def test_monthly_day_occurrences_between_span() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=31,
+        start_date="2026-01-31",
+    )
+    result = occurrences_between(rule, "2026-01-01", "2026-06-30")
+    assert result == [
+        "2026-01-31", "2026-02-28", "2026-03-31", "2026-04-30",
+        "2026-05-31", "2026-06-30",
+    ]
+
+
+def test_monthly_day_occurrences_between_rejects_inverted() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=15,
+        start_date="2026-01-15",
+    )
+    with pytest.raises(RuleValidationError, match="on or after"):
+        occurrences_between(rule, "2026-06-15", "2026-01-15")
+
+
+def test_monthly_day_clamp_is_one_firing_per_month(tmp_path) -> None:
+    """The clamp must not double-fire: only one day per month matches."""
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_DAY, day_of_month=31,
+        start_date="2026-01-31",
+    )
+    hits = _sweep_monthly(rule, 2026)
+    months = [month for month, _ in hits]
+    assert months == sorted(months)
+    assert len(months) == len(set(months)) == 12

tests/test_recurrence_monthly_weekday.py

@@ -0,0 +1,324 @@
+"""Tests for MONTHLY_WEEKDAY (nth-weekday-of-month) recurrence."""
+from __future__ import annotations
+
+import datetime
+
+import pytest
+
+from custom_components.nestquest.recurrence import (
+    RuleType,
+    RuleValidationError,
+    ScheduleRule,
+    _nth_weekday_of_month,
+    occurs_on,
+    occurrences_between,
+)
+
+
+def _d(date: str) -> datetime.date:
+    return datetime.date.fromisoformat(date)
+
+
+# ---------------------------------------------------------------------------
+# The helper: nth occurrence day-of-month
+# ---------------------------------------------------------------------------
+
+
+def test_nth_weekday_helper_first_second_third() -> None:
+    """Independently verified: Mar 1 2026 is a Sunday; Wednesdays are
+    4, 11, 18, 25 (four — no 5th)."""
+    assert _nth_weekday_of_month(2026, 3, 2, 1) == 4
+    assert _nth_weekday_of_month(2026, 3, 2, 2) == 11
+    assert _nth_weekday_of_month(2026, 3, 2, 3) == 18
+    assert _nth_weekday_of_month(2026, 3, 2, 4) == 25
+    assert _nth_weekday_of_month(2026, 3, 2, 5) is None
+
+
+def test_nth_weekday_helper_none_when_month_lacks_nth() -> None:
+    """Independently verified: April 2026 Fridays are 3, 10, 17, 24
+    (four) — no 5th occurrence."""
+    assert _nth_weekday_of_month(2026, 4, 4, 5) is None
+
+
+def test_nth_weekday_helper_last() -> None:
+    """Independently verified: March 2026 Fridays are 6, 13, 20, 27;
+    February 2028 Saturdays are 5, 12, 19, 26 (Feb 29 2028 is a
+    Tuesday, so the last SATURDAY is the 26th, not the last day)."""
+    assert _nth_weekday_of_month(2026, 3, 4, -1) == 27
+    # February 2026: 28 days, last day IS a Saturday.
+    assert _nth_weekday_of_month(2026, 2, 5, -1) == 28
+    # February 2028: the last Saturday is the 26th (Feb 29 is a Tue).
+    assert _nth_weekday_of_month(2028, 2, 5, -1) == 26
+
+
+def test_nth_weekday_helper_last_when_month_has_five() -> None:
+    """Independently verified: October 2026 Fridays are 2, 9, 16, 23, 30
+    (five) — the last is the 30th, and the 5th is the same day."""
+    assert _nth_weekday_of_month(2026, 10, 4, -1) == 30
+    assert _nth_weekday_of_month(2026, 10, 4, 5) == 30
+
+
+def test_helper_zero_and_out_of_range_nth() -> None:
+    """The model rejects n 0 before the helper sees it; -1/1..5 only."""
+    with pytest.raises(RuleValidationError):
+        ScheduleRule(
+            rule_type=RuleType.MONTHLY_WEEKDAY, nth_weekday=0,
+            nth_weekday_weekday=1, start_date="2026-09-01",
+        )
+    with pytest.raises(RuleValidationError):
+        ScheduleRule(
+            rule_type=RuleType.MONTHLY_WEEKDAY, nth_weekday=6,
+            nth_weekday_weekday=1, start_date="2026-09-01",
+        )
+
+
+# ---------------------------------------------------------------------------
+# occurs_on: first / second / third / fourth / last across 12 months
+# ---------------------------------------------------------------------------
+
+
+def test_first_tuesday_of_twelve_consecutive_months() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_WEEKDAY, nth_weekday=1,
+        nth_weekday_weekday=2,  # first Wednesday
+        start_date="2026-01-01",
+    )
+    first_wednesdays = [
+        (1, 7), (2, 4), (3, 4), (4, 1), (5, 6), (6, 3),
+        (7, 1), (8, 5), (9, 2), (10, 7), (11, 4), (12, 2),
+    ]
+    for month, day in first_wednesdays:
+        date = datetime.date(2026, month, day)
+        assert date.weekday() == 2
+        assert occurs_on(rule, date) is True, date
+        # Neighbors do not fire.
+        assert occurs_on(rule, date - datetime.timedelta(days=7)) is False
+        assert occurs_on(rule, date + datetime.timedelta(days=7)) is False
+
+
+def test_second_wednesday_of_twelve_consecutive_months() -> None:
+    """Independently verified second Wednesdays of 2026 (Jan 1 is a
+    Thursday; Wednesdays per month from the calendar): the SECOND one
+    fires; the FIRST one does not."""
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_WEEKDAY, nth_weekday=2,
+        nth_weekday_weekday=2,
+        start_date="2026-01-01",
+    )
+    # (month, first_wed, second_wed) from plain datetime arithmetic:
+    verified = [
+        (1, 7, 14), (2, 4, 11), (3, 4, 11), (4, 1, 8),
+        (5, 6, 13), (6, 3, 10), (7, 1, 8), (8, 5, 12),
+        (9, 2, 9), (10, 7, 14), (11, 4, 11), (12, 2, 9),
+    ]
+    for month, first_wed, second_wed in verified:
+        assert _d(f"2026-{month:02d}-{first_wed:02d}").weekday() == 2
+        assert _d(f"2026-{month:02d}-{second_wed:02d}").weekday() == 2
+        assert occurs_on(
+            rule, datetime.date(2026, month, second_wed)
+        ) is True, f"2026-{month:02d}-{second_wed:02d}"
+        assert occurs_on(
+            rule, datetime.date(2026, month, first_wed)
+        ) is False, f"2026-{month:02d}-{first_wed:02d}"
+
+
+def test_third_friday_of_twelve_consecutive_months() -> None:
+    """Independently verified 2026 Fridays; the THIRD fires, the SECOND
+    does not."""
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_WEEKDAY, nth_weekday=3,
+        nth_weekday_weekday=4,
+        start_date="2026-01-01",
+    )
+    verified = [
+        # (month, first_fri, second_fri, third_fri)
+        (1, 2, 9, 16), (2, 6, 13, 20), (3, 6, 13, 20),
+        (4, 3, 10, 17), (5, 1, 8, 15), (6, 5, 12, 19),
+        (7, 3, 10, 17), (8, 7, 14, 21), (9, 4, 11, 18),
+        (10, 2, 9, 16), (11, 6, 13, 20), (12, 4, 11, 18),
+    ]
+    for month, first_fri, second_fri, third_fri in verified:
+        third = _d(f"2026-{month:02d}-{third_fri:02d}")
+        assert third.weekday() == 4
+        assert occurs_on(rule, third) is True, third
+        second = _d(f"2026-{month:02d}-{second_fri:02d}")
+        assert occurs_on(rule, second) is False, second
+
+
+def test_fourth_wednesday_of_twelve_consecutive_months() -> None:
+    """Independently verified 2026 Wednesdays; the FOURTH fires, the
+    THIRD does not."""
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_WEEKDAY, nth_weekday=4,
+        nth_weekday_weekday=2,
+        start_date="2026-01-01",
+    )
+    verified = [
+        # (month, third_wed, fourth_wed)
+        (1, 21, 28), (2, 18, 25), (3, 18, 25), (4, 15, 22),
+        (5, 20, 27), (6, 17, 24), (7, 15, 22), (8, 19, 26),
+        (9, 16, 23), (10, 21, 28), (11, 18, 25), (12, 16, 23),
+    ]
+    for month, third_wed, fourth_wed in verified:
+        fourth = _d(f"2026-{month:02d}-{fourth_wed:02d}")
+        assert fourth.weekday() == 2
+        assert occurs_on(rule, fourth) is True, fourth
+        third = _d(f"2026-{month:02d}-{third_wed:02d}")
+        assert not occurs_on(rule, third), third
+
+
+def test_last_monday_of_twelve_consecutive_months() -> None:
+    """Independently verified last Mondays of 2026; each fires, and the
+    PREVIOUS Monday of the same month does not (it is nth-from-last
+    minus one, i.e. the second-to-last)."""
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_WEEKDAY, nth_weekday=-1,
+        nth_weekday_weekday=0,
+        start_date="2026-01-01",
+    )
+    verified = [
+        # (month, last_monday)
+        (1, 26), (2, 23), (3, 30), (4, 27), (5, 25), (6, 29),
+        (7, 27), (8, 31), (9, 28), (10, 26), (11, 30), (12, 28),
+    ]
+    for month, last_monday in verified:
+        date = _d(f"2026-{month:02d}-{last_monday:02d}")
+        assert date.weekday() == 0
+        assert occurs_on(rule, date) is True, date
+        # The Monday a week earlier is NOT the last: must not fire.
+        week_before = date - datetime.timedelta(days=7)
+        if week_before.month == month:
+            assert occurs_on(rule, week_before) is False, week_before
+
+
+# ---------------------------------------------------------------------------
+# The five-occurrence skip: a 5th on a four-occurrence month
+# ---------------------------------------------------------------------------
+
+
+def test_fifth_weekday_skips_four_occurrence_months() -> None:
+    """Independently verified: 2026 months with FIVE Mondays are March,
+    June, August, November — every other month (four Mondays) must fire
+    on no day at all, and each hit must be the month's FINAL Monday."""
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_WEEKDAY, nth_weekday=5,
+        nth_weekday_weekday=0,  # fifth Monday
+        start_date="2026-01-01",
+    )
+    five_monday_months = {3: 30, 6: 29, 8: 31, 11: 30}
+    hit_months = set()
+    for month in range(1, 13):
+        if month in five_monday_months:
+            day = five_monday_months[month]
+            hit = _d(f"2026-{month:02d}-{day:02d}")
+            assert hit.weekday() == 0
+            assert occurs_on(rule, hit) is True, hit
+            # It is the FINAL Monday of the month: sweep EVERY remaining
+            # calendar day after the hit — none may fire.
+            for later in range(day + 1, _month_end_days(2026, month) + 1):
+                assert occurs_on(
+                    rule, datetime.date(2026, month, later)
+                ) is False, f"2026-{month:02d}-{later:02d}"
+            # The Monday a week earlier is not the fifth.
+            assert occurs_on(
+                rule, datetime.date(2026, month, day - 7)
+            ) is False
+            hit_months.add(month)
+        else:
+            for day in range(1, _month_end_days(2026, month) + 1):
+                assert occurs_on(
+                    rule, datetime.date(2026, month, day)
+                ) is False, f"2026-{month:02d}-{day:02d}"
+    assert hit_months == {3, 6, 8, 11}, hit_months
+
+
+def _month_end_days(year: int, month: int) -> int:
+    if month == 12:
+        return 31
+    return (datetime.date(year, month + 1, 1)
+            - datetime.timedelta(days=1)).day
+
+
+def test_fifth_weekday_fires_in_five_occurrence_months() -> None:
+    """Independently verified: October 2026 Fridays are 2, 9, 16, 23, 30
+    (five) — the 5th (and last) is the 30th; April 2026 has four Fridays
+    (3, 10, 17, 24) so no day in April fires."""
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_WEEKDAY, nth_weekday=5,
+        nth_weekday_weekday=4,  # Fridays
+        start_date="2026-01-01",
+    )
+    # October: the 30th fires, is a Friday, and no Monday-later day
+    # (the 31st) is a Friday: the 30th is the FINAL Friday.
+    oct_30 = datetime.date(2026, 10, 30)
+    assert oct_30.weekday() == 4
+    assert occurs_on(rule, oct_30) is True
+    assert occurs_on(rule, datetime.date(2026, 10, 31)) is False
+    # April: no Friday-5th, so no day fires.
+    for day in range(1, _month_end_days(2026, 4) + 1):
+        assert occurs_on(rule, datetime.date(2026, 4, day)) is False, (
+            f"2026-04-{day:02d}"
+        )
+
+
+# ---------------------------------------------------------------------------
+# Interval arithmetic
+# ---------------------------------------------------------------------------
+
+
+def test_monthly_weekday_interval_2() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_WEEKDAY, nth_weekday=2,
+        nth_weekday_weekday=2, interval=2, start_date="2026-01-01",
+    )
+    # Jan (m0) fires on the 2nd Tuesday; Feb (m1) skipped; Mar (m2) fires.
+    jan_second = _nth_weekday_of_month(2026, 1, 2, 2)
+    assert occurs_on(rule, datetime.date(2026, 1, jan_second)) is True
+    feb_second = _nth_weekday_of_month(2026, 2, 2, 2)
+    assert occurs_on(rule, datetime.date(2026, 2, feb_second)) is False
+    mar_second = _nth_weekday_of_month(2026, 3, 2, 2)
+    assert occurs_on(rule, datetime.date(2026, 3, mar_second)) is True
+
+
+def test_monthly_weekday_interval_across_year_boundary() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_WEEKDAY, nth_weekday=1,
+        nth_weekday_weekday=2, interval=3, start_date="2026-11-01",
+    )
+    # Nov (m0) fires; Dec (m1), Jan (m2) skip; Feb (m3) fires.
+    nov_first = _nth_weekday_of_month(2026, 11, 2, 1)
+    assert occurs_on(rule, datetime.date(2026, 11, nov_first)) is True
+    dec_first = _nth_weekday_of_month(2026, 12, 2, 1)
+    assert occurs_on(rule, datetime.date(2026, 12, dec_first)) is False
+    jan_first = _nth_weekday_of_month(2027, 1, 2, 1)
+    assert occurs_on(rule, datetime.date(2027, 1, jan_first)) is False
+    feb_first = _nth_weekday_of_month(2027, 2, 2, 1)
+    assert occurs_on(rule, datetime.date(2027, 2, feb_first)) is True
+
+
+# ---------------------------------------------------------------------------
+# occurrences_between
+# ---------------------------------------------------------------------------
+
+
+def test_monthly_weekday_occurrences_between_span() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_WEEKDAY, nth_weekday=2,
+        nth_weekday_weekday=4,  # second Friday
+        start_date="2026-01-01", end_date="2026-04-30",
+    )
+    result = occurrences_between(rule, "2026-01-01", "2026-04-30")
+    # Independently verified second Fridays: Jan 9 (Jan 1 Thu), Feb 13
+    # (Feb 1 Sun), Mar 13 (Mar 1 Sun), Apr 10 (Apr 1 Wed).
+    assert result == [
+        "2026-01-09", "2026-02-13", "2026-03-13", "2026-04-10",
+    ]
+
+
+def test_monthly_weekday_occurrences_between_rejects_inverted() -> None:
+    rule = ScheduleRule(
+        rule_type=RuleType.MONTHLY_WEEKDAY, nth_weekday=1,
+        nth_weekday_weekday=1, start_date="2026-01-01",
+    )
+    with pytest.raises(RuleValidationError, match="on or after"):
+        occurrences_between(rule, "2026-06-01", "2026-01-01")