feat(render): Roman week numbers and date spans, as data

The ordo booklet's week header repeated the month name on every week
even though the heading above already established it -- pure noise.
Replace it with a Roman week number plus the span of dates the week
covers, e.g. "Hebdomada I (Ian 1-2)", following the project's own rule
that a presentation choice is data, not code.

lang/{la,en}.ini gain a [month_abbr] section (three-letter month
abbreviations); Lang.month_abbr follows Lang.month's exact shape,
including the out-of-range and miss-returns-the-key contracts. The
coverage test now fails loudly if an abbreviation goes missing, the
same as [month] already does.

Every week object in the view gains num_roman (Roman numeral, num
stays as the arabic original -- Roman is a presentation choice, not an
engine change), first_dom/last_dom (the day-of-month of the week's
first and last IN-MONTH days, padding excluded), month_abbr (resolved
through Lang.month_abbr), and single_day (true when the week holds
exactly one in-month day). single_day is a flag, not a preformatted
span string: the engine is logic-less and cannot itself decide between
"Ian 1" and "Ian 1-2", so a template makes that call from the flag
instead -- the same "shape the data, not the template" discipline
in_month and last already follow.

Weeks are built per month with padding only at the two ends, so a
week's in-month days never cross a month boundary -- verified, not
assumed: every week always has at least one real day since no month is
shorter than a single week.

Covered by three new View tests, including a real single-day-week
witness (January 2027's own trailing week is a lone Sunday, the 31st).

3 files changed, 71 insertions, 0 deletions

diff --git a/test/test_lang.ml b/test/test_lang.ml
index b54e85b..c9b7f1a 100644
--- a/test/test_lang.ml
+++ b/test/test_lang.ml
@@ -14,6 +14,8 @@ let sample =
    monday = Feria II\n\
    [month]\n\
    1 = Ianuarius\n\
+   [month_abbr]\n\
+   1 = Ian\n\
    [season]\n\
    lent = Quadragesima\n\
    [rank]\n\
@@ -34,6 +36,7 @@ let test_lookups () =
     (L.celebration t "ef-lent-3-monday");
   Alcotest.(check string) "weekday 0 is Sunday" "Dominica" (L.weekday t 0);
   Alcotest.(check string) "month 1" "Ianuarius" (L.month t 1);
+  Alcotest.(check string) "month_abbr 1" "Ian" (L.month_abbr t 1);
   Alcotest.(check string) "season" "Quadragesima" (L.season t "lent");
   Alcotest.(check string) "rank" "I classis" (L.rank t "class-1");
   Alcotest.(check string) "colour" "albus" (L.colour t "white");
diff --git a/test/test_lang_coverage.ml b/test/test_lang_coverage.ml
index 9ed633c..b4de5be 100644
--- a/test/test_lang_coverage.ml
+++ b/test/test_lang_coverage.ml
@@ -78,6 +78,9 @@ let test_vocabularies_are_complete () =
   done;
   for n = 1 to 12 do
     if L.month t n = string_of_int n then Alcotest.failf "no Latin month for %d" n
+  done;
+  for n = 1 to 12 do
+    if L.month_abbr t n = string_of_int n then Alcotest.failf "no Latin month abbreviation for %d" n
   done
 
 (* Defect 1: the booklet used to print the bare rite id ("ef") because no
diff --git a/test/test_view.ml b/test/test_view.ml
index 24e1d85..37fb284 100644
--- a/test/test_view.ml
+++ b/test/test_view.ml
@@ -182,6 +182,68 @@ let latin () =
 
 let view_named y = V.of_days ~lang:(latin ()) ~vocab:Rite_ef.Vocab_ef.vocab ~rite:"ef" ~year:y (days_of_year y)
 
+(* The ordo booklet's week header (Hebdomada I (Ian 1-2)): a Roman numeral
+   beside the existing arabic one, and month_num/month_name/month_abbr
+   carried onto every week the same way (there is no {{../}} parent-path
+   syntax to reach the enclosing month otherwise). January 2027 has six
+   weeks (1 Jan 2027 is a Friday, 31 Jan a lone trailing Sunday), so I-VI
+   is a real witness, not a guess capped at a small sample. *)
+let test_week_num_roman_and_month_fields () =
+  let v = view_named 2027 in
+  let jan = List.hd (as_list (get [ "months" ] v)) in
+  let weeks = as_list (get [ "weeks" ] jan) in
+  Alcotest.(check int) "January 2027 has six weeks" 6 (List.length weeks);
+  Alcotest.(check (list string)) "I..VI" [ "I"; "II"; "III"; "IV"; "V"; "VI" ]
+    (List.map (fun w -> as_str (get [ "num_roman" ] w)) weeks);
+  List.iter
+    (fun w ->
+      Alcotest.(check string) "month_num" "1" (as_str (get [ "month_num" ] w));
+      Alcotest.(check string) "month_name" "Ianuarius" (as_str (get [ "month_name" ] w));
+      Alcotest.(check string) "month_abbr" "Ian" (as_str (get [ "month_abbr" ] w)))
+    weeks
+
+(* The date-span fields a template needs to print "(Ian 1-2)" without ever
+   being handed a preformatted string (spec: the engine is logic-less, so a
+   punctuation choice between "Ian 1" and "Ian 1-2" must stay data the
+   template or a language file can still change). Verified against real
+   1 January 2027 = Friday / 31 January 2027 = Sunday arithmetic: the
+   month's first week holds only its own leading two in-month days (1-2),
+   and its own LAST week -- a lone trailing Sunday, 31 -- is this whole
+   suite's single-day-week witness. *)
+let test_week_date_span () =
+  let v = view_named 2027 in
+  let jan = List.hd (as_list (get [ "months" ] v)) in
+  let weeks = as_list (get [ "weeks" ] jan) in
+  let first_week = List.hd weeks in
+  Alcotest.(check string) "week 1 first_dom" "1" (as_str (get [ "first_dom" ] first_week));
+  Alcotest.(check string) "week 1 last_dom" "2" (as_str (get [ "last_dom" ] first_week));
+  Alcotest.(check bool) "week 1 is not a single day" false (as_bool (get [ "single_day" ] first_week));
+  let last_week = List.nth weeks (List.length weeks - 1) in
+  Alcotest.(check string) "week 6 first_dom" "31" (as_str (get [ "first_dom" ] last_week));
+  Alcotest.(check string) "week 6 last_dom" "31" (as_str (get [ "last_dom" ] last_week));
+  Alcotest.(check bool) "week 6 IS a single day" true (as_bool (get [ "single_day" ] last_week))
+
+(* Property, not a one-off sample: over every week of every month of a whole
+   year, [single_day] must agree exactly with [first_dom] = [last_dom], and
+   the count of in-month cells in [days] must match what [single_day] claims
+   -- proves the flag is computed FROM the same in-month cells a template
+   walks, not from a separately-derived (and possibly drifting) count. *)
+let test_single_day_agrees_with_span_and_cells () =
+  let v = view_of 2027 in
+  List.iter
+    (fun m ->
+      List.iter
+        (fun w ->
+          let first_dom = as_str (get [ "first_dom" ] w) and last_dom = as_str (get [ "last_dom" ] w) in
+          let single = as_bool (get [ "single_day" ] w) in
+          Alcotest.(check bool) "single_day iff first_dom = last_dom" (first_dom = last_dom) single;
+          let real_cells =
+            List.filter (fun c -> as_bool (get [ "in_month" ] c)) (as_list (get [ "days" ] w))
+          in
+          if single then Alcotest.(check int) "single day: exactly one real cell" 1 (List.length real_cells))
+        (as_list (get [ "weeks" ] m)))
+    (as_list (get [ "months" ] v))
+
 (* The defect this whole branch exists to fix: no rendered day may show a slug
    where a name exists. Asserted over a whole year, not a sample. *)
 let test_no_day_shows_a_slug () =
@@ -227,6 +289,9 @@ let suite =
       Alcotest.test_case "padding cells flagged" `Quick test_padding_cells_are_flagged;
       Alcotest.test_case "first week flagged" `Quick test_first_week_flag;
       Alcotest.test_case "padding and real days share key set" `Quick test_padding_and_real_share_key_set;
+      Alcotest.test_case "week num_roman and month fields" `Quick test_week_num_roman_and_month_fields;
+      Alcotest.test_case "week date span" `Quick test_week_date_span;
+      Alcotest.test_case "single_day agrees with span and cells" `Quick test_single_day_agrees_with_span_and_cells;
       Alcotest.test_case "no day shows a slug" `Quick test_no_day_shows_a_slug;
       Alcotest.test_case "slug unchanged by naming" `Quick test_slug_is_unchanged_by_naming;
       Alcotest.test_case "raw name equals slug" `Quick test_raw_name_equals_slug;