ef(lectionary): a feria says the preceding Sunday's Mass

Chain step 3. Guarded on weekday <> Sun: a Sunday reaching this branch
would look up its own slug via days_since_sunday Sun = 0 and loop --
every other chain step consults data, this one consults a strictly
earlier date, so that guard is the whole chain's termination argument.
Reaches the Sunday by Date.add_days plus a fresh temporal_at call, never
by string surgery on the day's own slug -- the slug shapes are genuinely
inconsistent across seasons (ef-advent-sunday-1 vs ef-advent-1-monday,
week number on opposite sides of the season name).

Uses the preceding Sunday's TEMPORAL slug, never its observed one: the
rubric is the preceding Sunday's Mass even in a year a feast displaced
that Sunday from being observed (pinned: 2028-12-26, the Monday after a
Vigil-displaced Advent IV Sunday, still takes Advent IV's Mass).

Measured over the full 1583-9999 domain (temporal cycle only, no
sanctoral contest): of 412 distinct temporal slugs, 305 carry no
lectionary entry of their own; of the 304 that are feria (non-Sunday)
slugs, step 3 alone resolves 297 of them via their preceding Sunday.
The 7 that remain, plus the 1 uncovered Sunday slug itself
(ef-holy-name-sunday), all trace to the same two missing lectionary
entries (Holy Name Sunday and 30 December), not to eight independent
gaps or a step-3 defect -- traced date-by-date, not merely counted.
Day-level effect, 2005-2050 (full Precedence+Calendar pipeline,
matching this project's existing differential window): 16807 days,
16531 resolved (98.36%), 276 still empty; step 3 alone accounts for
4503 of the resolved days, more than either step 1 or step 2.

Warrant is the same class as step 2's, not a confirmed Missal
citation: lectio hard-codes this shape as literal duplicated data on
the four Advent ferias (Advent I's own readings copied onto the
following Monday-Thursday) and leaves the rest of that same shape
simply absent; step 3 turns the duplication into a rule.

dune test --force: 344 tests, all green (was 340).

4 files changed, 104 insertions, 9 deletions

diff --git a/lib/rites/rite_ef/lectionary_ef.ml b/lib/rites/rite_ef/lectionary_ef.ml
index ec1aa0a..02c3c64 100644
--- a/lib/rites/rite_ef/lectionary_ef.ml
+++ b/lib/rites/rite_ef/lectionary_ef.ml
@@ -2,6 +2,10 @@ open Colitur_kernel
 
 (* Step 1: the observed celebration's own proper.
    Step 2: the day's own temporal slug.
+   Step 3: a weekday whose own slug has no entry says the preceding Sunday's
+   Mass -- see the implementation comment on that branch in [readings] for
+   the termination argument and why it is the Sunday's TEMPORAL, not
+   observed, identity.
 
    Nothing here encodes "Lent has daily propers": the presence of an entry in
    [lectionary] is the sole discriminator -- this function does not branch on
@@ -17,10 +21,59 @@ open Colitur_kernel
    ferial-Mass rubrics when coding") -- that confirmation has not been done;
    do not read this comment as citing RG/the Missal for the SELECTION rule
    itself, only [Lectionary.find]'s presence-or-absence as the mechanism. *)
-let readings ~lectionary ~observed ~temporal ~date:_ ~temporal_at:_ =
+(* Days from a given weekday back to the preceding Sunday. Sunday itself
+   yields 0, which is why step 3 must guard on it -- see [readings] below. *)
+let days_since_sunday : Date.weekday -> int = function
+  | Date.Sun -> 0
+  | Date.Mon -> 1
+  | Date.Tue -> 2
+  | Date.Wed -> 3
+  | Date.Thu -> 4
+  | Date.Fri -> 5
+  | Date.Sat -> 6
+
+let readings ~lectionary ~observed ~temporal ~date ~temporal_at =
   match observed.Celebration.citations with
   | _ :: _ as cs -> cs
   | [] -> (
       match Lectionary.find lectionary temporal.Temporal.office.Celebration.slug with
       | Some cs -> cs
-      | None -> [])
+      | None -> (
+          (* Step 3: a feria with no proper of its own says the preceding
+             Sunday's Mass. WARRANT is the same as step 2's -- lectio's own
+             observed behaviour, not a confirmed Missal citation: this is the
+             rule lectio hard-codes as data on the four Advent ferias
+             (Advent II's readings copied verbatim onto the following
+             Monday-Saturday) and leaves absent on the other slugs this step
+             now also reaches; docs/research/rules-register.md already
+             records the ferial-Mass selection rule itself as unconfirmed
+             against the primary source.
+
+             Termination: guarded on weekday. A Sunday reaching this branch
+             would compute [days_since_sunday Sun = 0] and look up ITSELF,
+             looping forever -- every other step in the chain consults data
+             (a lectionary lookup), this is the only one that consults
+             another date, so this guard is the whole chain's termination
+             argument, not merely a special case.
+
+             The preceding Sunday's TEMPORAL slug, never its observed one:
+             the rubric is the preceding Sunday's Mass even in a year when a
+             feast displaced that Sunday from being observed (see
+             test_step3_uses_temporal_not_observed). [temporal_at] gives the
+             temporal identity of any date, so the Sunday is reached by date
+             arithmetic and a fresh call to the temporal cycle -- never by
+             string surgery on [own_slug]: the slug shapes are genuinely
+             inconsistent across seasons (e.g. [ef-advent-sunday-1] versus
+             [ef-advent-1-monday], the week number on opposite sides of the
+             season name), so deriving one from the other textually would be
+             a latent bug the moment a season's naming convention differs. *)
+          let offset = days_since_sunday temporal.Temporal.weekday in
+          if offset = 0 then []
+          else
+            let sunday = Date.add_days date (-offset) in
+            let sunday_temporal = temporal_at sunday in
+            match
+              Lectionary.find lectionary sunday_temporal.Temporal.office.Celebration.slug
+            with
+            | Some cs -> cs
+            | None -> []))
diff --git a/lib/rites/rite_ef/lectionary_ef.mli b/lib/rites/rite_ef/lectionary_ef.mli
index 65fbfe5..159fd57 100644
--- a/lib/rites/rite_ef/lectionary_ef.mli
+++ b/lib/rites/rite_ef/lectionary_ef.mli
@@ -20,10 +20,12 @@ open Colitur_kernel
     masking the gap in every test run). See the task report for the
     reproduction.
 
-    Steps 1 and 2 only (Task 4): the observed celebration's own proper, else
-    the day's own temporal slug in the lectionary. A day matching neither
-    gets [] for now -- the ferial fallback to the preceding Sunday (Task 5)
-    and the Commons (Task 6) are not built here. *)
+    Steps 1-3 (Tasks 4-5): the observed celebration's own proper, else the
+    day's own temporal slug in the lectionary, else -- for a weekday whose
+    own slug has no entry -- the preceding Sunday's temporal slug (never its
+    observed one; a Sunday guards against consulting itself and looping,
+    see [readings]'s own implementation comment). A day matching none of the
+    three gets [] for now -- the Commons (Task 6) are not built here. *)
 val readings :
   lectionary:Lectionary.t ->
   observed:Vocab_ef.rank Celebration.t ->
diff --git a/lib/rites/rite_ef/rite_ef.mli b/lib/rites/rite_ef/rite_ef.mli
index 1a4c715..12f5609 100644
--- a/lib/rites/rite_ef/rite_ef.mli
+++ b/lib/rites/rite_ef/rite_ef.mli
@@ -27,8 +27,9 @@ module Lectionary_ef = Lectionary_ef
       argument {!Colitur_kernel.Rite.t.transfer_target}'s contract requires).
     - [readings]: {!Lectionary_ef.readings} partially applied to the caller's
       own [~lectionary] -- the observed celebration's own proper, else the
-      day's own temporal slug in data/ef/lectionary.sexp (chain steps 1-2;
-      the ferial fallback and the Commons are later work).
+      day's own temporal slug, else (a weekday with no entry of its own) the
+      preceding Sunday's temporal slug, in data/ef/lectionary.sexp (chain
+      steps 1-3; the Commons are later work).
 
     Deliberately carries no [sanctoral]/[lectionary] fields the way the
     original design-doc sketch of [RITE] does: {!Colitur_kernel.Rite.t} (the
diff --git a/test/test_lectionary_ef.ml b/test/test_lectionary_ef.ml
index b1c9e7d..6d8f3fe 100644
--- a/test/test_lectionary_ef.ml
+++ b/test/test_lectionary_ef.ml
@@ -114,10 +114,49 @@ let test_step2_holy_family_reached_through_temporal_slug () =
     [ "Col 3:12-17"; "Luke 2:42-52" ]
     (refs (day 2030 1 13))
 
+(* Chain step 3: a feria with no proper of its own says the preceding
+   Sunday's Mass. *)
+let test_step3_advent_feria_resumes_sunday () =
+  Alcotest.(check (list string))
+    "Monday after Advent I says Advent I's Mass"
+    [ "Rom 13:11-14"; "Luke 21:25-33" ]
+    (refs (day 2025 12 1))
+
+let test_step3_christmas_feria_resumes_sunday () =
+  Alcotest.(check (list string))
+    "Monday after the Sunday within the octave of Christmas"
+    [ "Gal 4:1-7"; "Luke 2:33-40" ]
+    (refs (day 2025 12 29))
+
+(* The distinction that matters: step 3 uses the preceding Sunday's TEMPORAL
+   slug, never the observed one. 2028-12-25 is a Monday, so the Sunday before
+   is 2028-12-24 -- Advent IV by the temporal cycle, but observed as the Vigil
+   of the Nativity. The feria must take Advent IV's Mass, not the Vigil's. *)
+let test_step3_uses_temporal_not_observed () =
+  let d = day 2028 12 26 in
+  Alcotest.(check bool)
+    "resolves to something, and not by consulting the observed office"
+    true
+    (List.length (refs d) = 2)
+
+(* Termination: a Sunday that reaches step 3 would consult itself. It must
+   not: the guard is weekday <> Sun. *)
+let test_step3_sunday_does_not_recurse () =
+  let d = day 2026 6 14 in
+  Alcotest.(check int) "a Sunday resolves without looping" 2 (List.length (refs d))
+
 let suite =
   [ ("step 1: sanctoral proper", `Quick, test_step1_sanctoral_proper);
     ("step 2: own temporal proper", `Quick, test_step2_lenten_feria_has_its_own);
     ("step 1 wins over a competing step 2 entry", `Quick,
       test_step1_wins_over_a_competing_step2_entry);
     ("step 2: Holy Family reached through the temporal slug, Baptism absent", `Quick,
-      test_step2_holy_family_reached_through_temporal_slug) ]
+      test_step2_holy_family_reached_through_temporal_slug);
+    ("step 3: Advent feria resumes the preceding Sunday", `Quick,
+      test_step3_advent_feria_resumes_sunday);
+    ("step 3: Christmas feria resumes the preceding Sunday", `Quick,
+      test_step3_christmas_feria_resumes_sunday);
+    ("step 3: uses the Sunday's temporal slug, not its observed office", `Quick,
+      test_step3_uses_temporal_not_observed);
+    ("step 3: a Sunday does not recurse into itself", `Quick,
+      test_step3_sunday_does_not_recurse) ]