fix(of): correct vigil_feast's justification for of-nativity-vigil

The prior comment claimed of-nativity-vigil is 'not a distinct celebration' -
wrong: Temporal_of.named (temporal_of.ml:230) constructs it as its own
Sollemnitas-rank candidate on 24 December, a genuine contestant in
band/Precedence.resolve.

The real reason None is safe is structural, not that. The Nativity is
Tabula entry 2 (band 20); only entry 1, the Paschal Triduum (band 10),
bands lower. The Triduum's Easter-2..Easter window is confined to 20
March-25 April because Gregorian Easter never falls outside [22 March, 25
April] over the whole 1583-9999 domain (measured exhaustively in
test_computus.ml, not assumed), so it can never reach 25 December. The
Nativity therefore always keeps its own day and its vigil can never be
orphaned by a transfer or reduction.

Behaviour is unchanged: vigil_feast still returns None unconditionally.
RG 33 (EF-only) and Normae nn. 11/13 remain the reason the hook exists at
all and returns None for every other candidate.

2 files changed, 32 insertions, 9 deletions

diff --git a/lib/rites/rite_of/precedence_of.ml b/lib/rites/rite_of/precedence_of.ml
index fb26d64..5d32ee2 100644
--- a/lib/rites/rite_of/precedence_of.ml
+++ b/lib/rites/rite_of/precedence_of.ml
@@ -226,13 +226,27 @@ let admit ~(observed : Vocab_of.rank Precedence.candidate)
    can be orphaned by its feast moving: Normae n. 11 gives solemnities First
    Vespers and n. 13 denies them to feasts, but neither creates a separate
    celebration that could survive or fail independently of the day it precedes.
-   The one OF celebration whose slug says "vigil" -- the Nativity's, which
-   Temporal_of emits as "of-nativity-vigil" -- is a MASS FORMULARY of the
-   solemnity itself (IGMR n. 346's own Christmas-Mass series: ad vigiliam, in
-   nocte, in aurora, in die), not a distinct celebration.
+   This is why the hook exists at all and why it returns [None] for every
+   OTHER candidate -- there is no OF office this rule could ever apply to.
 
-   So [None] unconditionally, and Calendar's RG 33 suppression pass never
-   fires for this rite. *)
+   "of-nativity-vigil" itself needs a narrower, structural argument, not that
+   general one: Temporal_of.named (temporal_of.ml:230) DOES construct it as
+   its own Sollemnitas-rank candidate on 24 December, independent of
+   "of-nativity" on the 25th -- it is a genuine contestant in [band]/[resolve],
+   not merely a Mass formulary with no life of its own on the precedence axis.
+
+   What makes [None] safe here is that the feast it precedes can never be
+   orphaned. The Nativity is Tabula entry 2 (band 20); the only entry that
+   bands lower is entry 1, the Paschal Triduum (band 10, [is_triduum] above).
+   Gregorian Easter falls in [22 March, 25 April] for EVERY year 1583-9999 --
+   measured exhaustively, not assumed (test_computus.ml's
+   [test_gregorian_invariants_exhaustive]) -- so the Triduum's own band-10
+   window (Easter-2 .. Easter) is confined to 20 March-25 April and can never
+   reach 25 December. Nothing else in the Tabula bands below entry 2. So
+   "of-nativity" is unconditionally the observed office on its own day, its
+   vigil can never be orphaned by a transfer or reduction, and [None] is the
+   correct answer for it too -- not because it lacks standing as a candidate,
+   but because the day it precedes can never lose. *)
 let vigil_feast (_ : Vocab_of.rank Precedence.candidate) : Slug.t option = None
 
 (* The assembled record Precedence.resolve consumes. Kept here rather than in
diff --git a/lib/rites/rite_of/precedence_of.mli b/lib/rites/rite_of/precedence_of.mli
index 6b30dad..e81d35e 100644
--- a/lib/rites/rite_of/precedence_of.mli
+++ b/lib/rites/rite_of/precedence_of.mli
@@ -69,9 +69,18 @@ val admit :
   (Vocab_of.rank Precedence.candidate * Precedence.privilege) list
 
 (** [vigil_feast]: always [None]. RG 33's third omission trigger is EF-only;
-    the OF has no vigil OFFICE that its feast's movement could orphan. The
-    Nativity's "of-nativity-vigil" is a Mass formulary of the solemnity, not a
-    separate celebration. *)
+    the OF has no vigil OFFICE that its feast's movement could orphan --
+    Normae nn. 11/13 create no such independent celebration for anything
+    other than "of-nativity-vigil". THAT candidate is not exempt by lacking
+    standing: {!Rite_of.Temporal_of.named} constructs it as its own
+    Sollemnitas-rank candidate on 24 December, a genuine contestant in
+    {!band}/{!Colitur_kernel.Precedence.resolve}. It is exempt structurally
+    instead -- the Nativity (Tabula entry 2, band 20) can only ever be beaten
+    by the Triduum (entry 1, band 10), whose window (Easter-2..Easter) is
+    confined to 20 March-25 April because Gregorian Easter never falls outside
+    [22 March, 25 April] (measured exhaustively, 1583-9999, not assumed), so
+    it can never reach 25 December. The Nativity therefore always keeps its
+    own day, and its vigil can never be orphaned. *)
 val vigil_feast : Vocab_of.rank Precedence.candidate -> Slug.t option
 
 (** The four functions assembled for {!Colitur_kernel.Precedence.resolve}. *)