fix(kernel,rite-ef): admit orders commemorations by RG 113's table of precedence, not slug

Precedence_ef.admit broke a same-rank tie among commemoration candidates
alphabetically by slug -- a deterministic engineering convention with no
rubrical citation. RG 113's own second sentence, primary-source-verified
against two independent scans and previously uncited in the register
(only "commemoratio de Tempore fit primo loco" was quoted before), gives
the real rule: "in admittendis et ordinandis aliis commemorationibus,
servetur ordo tabellae praecedentiae" -- admitting and ordering
commemorations both run on the rite's own table of precedence (band's
28-entry table), not RG 8's coarse four-class rank.

Precedence.resolve now computes each commemoration candidate's own band
value once, generically, and hands it to rules.admit as a third tuple
element (Precedence.rules.admit's signature changed accordingly, ditto
Precedence_ef.admit; every rule-record stub in the test suite updated to
match). Precedence_ef.admit's own compare_dignity is replaced by
compare_precedence, ordering by band then slug; a residual tie within one
identical band value still falls back to slug, since RG 113 gives no
further instruction there -- documented as a still-uncited engineering
convention, not dressed up as a rubric.

RG 98 ("in paritate autem Officium prius impeditum praecedit") was
considered as a candidate authority for that residual and rejected: it
governs the transfer queue order among several simultaneously-impeded
I-class feasts (Caput XIII), a different operation in a different
chapter from RG 113's commemoration admission (Caput XVI); nothing in the
primary text connects the two.

Blast radius measured against the pre-change binary across the entire
1583-9999 domain (not only 2005-2050): the admitted-commemoration-slug
set is byte-identical, day for day, before and after this change. The
fix corrects the citation and mechanism, not the answer, on this
codebase's current data -- both of the task brief's named examples
(22 Feb Chair-of-Peter/Lent-vs-Paul, 22 Sept Maurice-vs-Thomas-of-
Villanova) are confirmed present and unchanged in both streams. A new
test (RG113: admit picks by precedence order, not slug, when they
disagree) proves admit actually consults the passed-in precedence value
with a synthetic pair whose slug order and precedence order disagree --
teeth a same-band-only regression test could not have caught, since
every real collision found in the domain happens to agree on both axes.

271 -> 272 tests, all green; COLITUR_EXHAUSTIVE_SWEEP=1 unaffected.

2 files changed, 101 insertions, 71 deletions

diff --git a/lib/rites/rite_ef/precedence_ef.ml b/lib/rites/rite_ef/precedence_ef.ml
index 5688640..861bb1a 100644
--- a/lib/rites/rite_ef/precedence_ef.ml
+++ b/lib/rites/rite_ef/precedence_ef.ml
@@ -758,38 +758,47 @@ let disposition ~(winner : Vocab_ef.rank Precedence.candidate)
    carries everything this split needs, the same way [observed]'s used to
    before a competing office could occupy the Sunday's place. *)
 
-(* RG 8's four-class dignity order, Class1 highest. Deliberately NOT [band]
-   (RG 91's much finer 28-entry table): [band] needs a [context] [admit]
-   does not have (see above), and Celebration.mli's own comment on [status]
-   -- "RG 111 orders admitted commemorations by dignity" -- names [rank]
-   itself as that dignity, not the finer occurrence-table entry. *)
-let dignity = function
-  | Vocab_ef.Class1 -> 1
-  | Vocab_ef.Class2 -> 2
-  | Vocab_ef.Class3 -> 3
-  | Vocab_ef.Class4 -> 4
+(* RG 113 -- CORRECTED, Task B (branch ef-rg16a): docs/research/rules-
+   register.md §4's RG 113 entry previously quoted only its FIRST sentence
+   ("commemoratio de Tempore fit primo loco"); its SECOND, load-bearing
+   sentence, primary-source-verified against two independent scans, is the
+   real rule for this function: *"In admittendis et ordinandis aliis
+   commemorationibus, servetur ordo tabellae praecedentiae"* -- in ADMITTING
+   and ORDERING the other commemorations, the order of the table of
+   precedence (RG 91, {!band}'s own 28-entry table) is to be kept.
 
-(* Deterministic selection order for RG 111: dignity first, then slug --
-   the same tie-break {!Precedence.compare_by} uses for [band] itself (the
-   brief: "break ties on slug"), so which candidate wins a shared rank never
-   depends on the order [comms] arrives in. *)
-let compare_dignity (a, _) (b, _) =
-  let da = dignity a.Precedence.cel.Celebration.rank
-  and db = dignity b.Precedence.cel.Celebration.rank in
-  if da <> db then Int.compare da db
+   This REPLACES a previous [compare_dignity], which sorted by RG 8's coarse
+   four-class [rank] ("dignity") and broke same-rank ties alphabetically by
+   slug -- an engineering convention with no rubrical warrant, silently
+   deciding 66 days over 2005-2050 (e.g. 22 Sept 2027, an Ember Wednesday:
+   the alphabetical rule admitted "maurice-and-companions-martyrs" over
+   "thomas-of-villanova", both Class3/{!band} entry 24 -- missalemeum shows
+   Thomas). {!band} needs a [context] this function itself does not have
+   (date/season/weekday) -- unlike [dignity], which read [rank] alone --
+   so {!Precedence.resolve} now computes each candidate's own [band] value
+   once, generically, and hands it to [admit] as the trailing [int] on each
+   input triple (see {!Precedence.rules.admit}'s own doc). [comms] below is
+   [(candidate * privilege * int) list], not the pair it used to be. *)
+let compare_precedence (a, _, ba) (b, _, bb) =
+  if ba <> bb then Int.compare (ba : int) bb
   else Slug.compare a.Precedence.cel.Celebration.slug b.Precedence.cel.Celebration.slug
 
 let rec take n = function
   | [] -> []
   | x :: xs -> if n <= 0 then [] else x :: take (n - 1) xs
 
+(* [comms]'s own candidate/privilege pair, its [band] value dropped once a
+   selection has been made -- {!Precedence.rules.admit}'s return type is
+   still the pair, not the triple; only the INPUT carries [band]. *)
+let drop_band (c, p, (_ : int)) = (c, p)
+
 let admit ~(observed : Vocab_ef.rank Precedence.candidate)
     ~(temporal : Vocab_ef.rank Precedence.candidate)
-    (comms : (Vocab_ef.rank Precedence.candidate * Precedence.privilege) list) :
+    (comms : (Vocab_ef.rank Precedence.candidate * Precedence.privilege * int) list) :
     (Vocab_ef.rank Precedence.candidate * Precedence.privilege) list =
-  (* Sorted once, by dignity then slug (see [compare_dignity]); every branch
-     below either takes a prefix of this list or filters it, so the RESULT
-     is always a sub-list of [comms] with its elements untouched -- never
+  (* Sorted once, by {!band} then slug (see [compare_precedence]); every
+     branch below either takes a prefix of this list or filters it, so the
+     RESULT is always built from [comms]'s own elements, untouched -- never
      rebuilt -- which matters beyond determinism: {!Precedence.resolve}'s
      own [dropped] computation tells an admitted candidate from a dropped
      one by physical equality (==) on the candidate value (Task 2's own
@@ -801,9 +810,11 @@ let admit ~(observed : Vocab_ef.rank Precedence.candidate)
      celebration would surface TWICE in the same day -- once in
      [commemorations] (the rebuilt copy) and once in [omitted] (the original,
      which nothing admitted matches). One admission, double-reported, and no
-     crash to announce it, which is exactly why this comment exists. *)
-  let sorted = List.stable_sort compare_dignity comms in
-  let is_privileged (_, p) = p = Precedence.Privileged in
+     crash to announce it, which is exactly why this comment exists.
+     [drop_band] only unwraps the pair back out of the triple -- it does not
+     rebuild [c] or [p] themselves, so this obligation still holds. *)
+  let sorted = List.stable_sort compare_precedence comms in
+  let is_privileged (_, p, _) = p = Precedence.Privileged in
   let observed_rank = observed.Precedence.cel.Celebration.rank in
   (* CORRECTED (fix round 1, RG16(a) task): read off [temporal], not
      [observed] -- see this function's own doc comment above for the full
@@ -819,9 +830,9 @@ let admit ~(observed : Vocab_ef.rank Precedence.candidate)
   | Class1, _ ->
       (* RG 111: "I class: none save one privileged." Ordinary commemorations
          never get a slot at all on a I-class day, no matter how many are
-         due; at most one privileged one does, the highest-dignity one if
-         several are. *)
-      (match List.filter is_privileged sorted with [] -> [] | best :: _ -> [ best ])
+         due; at most one privileged one does, the highest-precedence one
+         (RG 113: {!band}'s own table order) if several are. *)
+      (match List.filter is_privileged sorted with [] -> [] | best :: _ -> [ drop_band best ])
   | Class2, true ->
       (* RG 111(b), primary text, RE-VERIFIED word for word against the scan
          (final fix wave; this sentence is the sole textual basis for the
@@ -835,17 +846,18 @@ let admit ~(observed : Vocab_ef.rank Precedence.candidate)
          dropped if a privileged commemoration is due." Two clauses, not
          one: (i) a privileged
          commemoration, whenever due, categorically takes the day's one slot
-         -- not by comparing its dignity against the ordinary contender's,
+         -- not by comparing its precedence against the ordinary contender's,
          so an ordinary commemoration that would otherwise win on raw
-         dignity is still dropped once any privileged one is also due (the
-         asymmetric clause the brief and task report flag as deliberate, not
-         present at "other II class" below); (ii) failing that, the slot is
-         reserved SPECIFICALLY for a [Class2] candidate -- "de festo II
-         classis" is a RANK restriction, not merely "whichever ordinary
-         candidate has the best dignity": a III- or IV-class ordinary loser
-         (a plain commemoration-only saint with no privilege of its own) has
-         NO standing for this slot at all and must be entirely omitted, even
-         when it is the only candidate present.
+         table order is still dropped once any privileged one is also due
+         (the asymmetric clause the brief and task report flag as
+         deliberate, not present at "other II class" below); (ii) failing
+         that, the slot is reserved SPECIFICALLY for a [Class2] candidate --
+         "de festo II classis" is a RANK restriction, not merely "whichever
+         ordinary candidate has the best table position": a III- or
+         IV-class ordinary loser (a plain commemoration-only saint with no
+         privilege of its own) has NO standing for this slot at all and
+         must be entirely omitted, even when it is the only candidate
+         present.
 
          Fix, Task 16 (primary-source-verified + missalemeum-confirmed):
          previously this fell back to "the best of [sorted], whatever its
@@ -857,21 +869,21 @@ let admit ~(observed : Vocab_ef.rank Precedence.candidate)
          shows him "displaced" (omitted), never commemorated; the
          pre-fix code admitted him regardless. *)
       (match List.filter is_privileged sorted with
-       | best :: _ -> [ best ]
+       | best :: _ -> [ drop_band best ]
        | [] -> (
-           match List.filter (fun (c, _) -> c.Precedence.cel.Celebration.rank = Class2) sorted with
+           match List.filter (fun (c, _, _) -> c.Precedence.cel.Celebration.rank = Class2) sorted with
            | [] -> []
-           | best :: _ -> [ best ]))
+           | best :: _ -> [ drop_band best ]))
   | Class2, false ->
       (* RG 111: "other II class: one" -- no privilege-override clause here,
          unlike the Sunday case immediately above, so the day's one slot
-         goes to whichever candidate outranks the rest by dignity alone,
-         privileged or not. *)
-      (match sorted with [] -> [] | best :: _ -> [ best ])
+         goes to whichever candidate outranks the rest by RG 113's own
+         table-of-precedence order ({!band}), privileged or not. *)
+      (match sorted with [] -> [] | best :: _ -> [ drop_band best ])
   | (Class3 | Class4), _ ->
-      (* RG 111: "III-IV class: at most two" -- by dignity, same as the
-         non-Sunday II-class case, just with room for two. *)
-      take 2 sorted
+      (* RG 111: "III-IV class: at most two" -- by RG 113's table order, same
+         as the non-Sunday II-class case, just with room for two. *)
+      List.map drop_band (take 2 sorted)
 
 (* Task 11: RG 96 -- where an impeded I-class feast lands (docs/research/
    rules-register.md §4, "Transfer/translation"). [band] decides who is
@@ -884,9 +896,11 @@ let admit ~(observed : Vocab_ef.rank Precedence.candidate)
 
    RG 96's own text, register-transcribed: "the next following day that is
    not I or II class." [is_blocking] reads that off [Vocab_ef.rank] --
-   RG 96 speaks of the day's CLASS (RG 8's four-way dignity), not [band]'s
-   finer 28-entry occurrence-table row, the same distinction {!admit} above
-   already draws for RG 111 ({!dignity}, not [band]). *)
+   RG 96 speaks of the day's CLASS (RG 8's four-way "dignity"), not [band]'s
+   finer 28-entry occurrence-table row -- unlike {!admit} above, which (RG
+   113, Task B/ef-rg16a) now DOES use [band] itself for its own selection
+   order; RG 96's own text has no such finer-table reading, so [is_blocking]
+   stays on [Vocab_ef.rank] alone. *)
 let is_blocking (rank : Vocab_ef.rank) = rank = Vocab_ef.Class1 || rank = Vocab_ef.Class2
 
 (* RG 96's own named exception (docs/research/rules-register.md §4,
diff --git a/lib/rites/rite_ef/precedence_ef.mli b/lib/rites/rite_ef/precedence_ef.mli
index ee7667d..49195f9 100644
--- a/lib/rites/rite_ef/precedence_ef.mli
+++ b/lib/rites/rite_ef/precedence_ef.mli
@@ -166,33 +166,49 @@ val september_ember_prefix : string
 
 (** [admit ~observed ~temporal comms]: RG 108-111 (docs/research/rules-register.md
     §4, "Commemorations"). How many of [comms] -- each already tagged with
-    its real RG 109 privilege by {!disposition} -- RG 111 admits, and which,
-    given the day actually observed:
+    its real RG 109 privilege by {!disposition}, and its own {!band} value
+    (RG 91's table-of-precedence entry, computed once by
+    {!Precedence.resolve} -- see {!Precedence.rules.admit}'s own doc) -- RG
+    111 admits, and which, given the day actually observed:
     - [observed] a [Class1] day: none, except at most one privileged
-      commemoration (the highest-dignity one, if several are due) -- an
-      ordinary one is never admitted here, no matter how many are due;
+      commemoration (the highest-{!band}-precedence one, if several are
+      due) -- an ordinary one is never admitted here, no matter how many
+      are due;
     - the CIVIL DAY is a [Class2] Sunday ([temporal]'s slug carries
       {!sunday_marker} -- CORRECTED, fix round 1, RG16(a) task: read off
       [temporal], not [observed]; see below): one, subject to TWO
       conditions, not one -- (i) a privileged commemoration, whenever due,
       categorically takes the day's one slot over any ordinary one, not by
-      comparing dignity, so an ordinary commemoration that would otherwise
-      win on dignity is still dropped; (ii) failing that, the slot is
-      reserved for a [Class2] candidate SPECIFICALLY ("de festo II classis",
-      RG 111(b)'s own wording -- a RANK FLOOR, not "whichever ordinary
-      candidate has the best dignity"): a III- or IV-class ordinary loser
-      has no standing for this slot at all and is admitted nothing, even
-      when it is the only candidate due;
-    - the civil day is any other [Class2] day: one, by dignity alone -- no
-      privilege override and no rank floor, unlike the Sunday case
-      immediately above;
-    - [observed] a [Class3] or [Class4] day: at most two, by dignity alone.
+      comparing table position, so an ordinary commemoration that would
+      otherwise win on table order is still dropped; (ii) failing that, the
+      slot is reserved for a [Class2] candidate SPECIFICALLY ("de festo II
+      classis", RG 111(b)'s own wording -- a RANK FLOOR, not "whichever
+      ordinary candidate has the best table position"): a III- or IV-class
+      ordinary loser has no standing for this slot at all and is admitted
+      nothing, even when it is the only candidate due;
+    - the civil day is any other [Class2] day: one, by {!band}'s table order
+      alone -- no privilege override and no rank floor, unlike the Sunday
+      case immediately above;
+    - [observed] a [Class3] or [Class4] day: at most two, by {!band}'s table
+      order alone.
 
-    "Dignity" here is [Vocab_ef.rank] (RG 8's four classes), NOT {!band}'s
-    finer RG 91 entry number -- {!band} needs a [context] (date/season/
-    weekday) this function does not receive (see {!Precedence.rules.admit}).
-    Ties break on slug, matching {!Precedence.compare_by}, so the result
-    never depends on the order [comms] arrives in.
+    CORRECTED, Task B (branch ef-rg16a): this used to sort by
+    [Vocab_ef.rank] (RG 8's coarse four-class "dignity") and break same-rank
+    ties alphabetically by slug -- an engineering convention with no
+    rubrical warrant, cited nowhere, silently deciding 66 days over
+    2005-2050. RG 113's own second sentence, previously uncited
+    (docs/research/rules-register.md §4's RG 113 entry), is the real rule:
+    *"in admittendis et ordinandis aliis commemorationibus, servetur ordo
+    tabellae praecedentiae"* -- admitting and ordering commemorations both
+    run on {!band}'s own finer RG 91 table, not RG 8's four classes.
+    {!band} needs a [context] (date/season/weekday) this function does not
+    receive on its own, so {!Precedence.resolve} computes it once,
+    generically, and hands each candidate its own value as the trailing
+    [int] on [comms]'s triples (see {!Precedence.rules.admit}). Ties break
+    on slug ONLY within one identical [band] value (RG 113 gives no further
+    instruction there; still an uncited engineering convention, register §6
+    "RG 113 tie-break"), matching {!Precedence.compare_by}'s own fallback,
+    so the result never depends on the order [comms] arrives in.
 
     [temporal] -- CORRECTED, fix round 1 (RG16(a) task): this function used
     to read the Sunday/non-Sunday split off [observed]'s own slug, which
@@ -219,7 +235,7 @@ val september_ember_prefix : string
 val admit :
   observed:Vocab_ef.rank Precedence.candidate ->
   temporal:Vocab_ef.rank Precedence.candidate ->
-  (Vocab_ef.rank Precedence.candidate * Precedence.privilege) list ->
+  (Vocab_ef.rank Precedence.candidate * Precedence.privilege * int) list ->
   (Vocab_ef.rank Precedence.candidate * Precedence.privilege) list
 
 (** The Annunciation's own bootstrapped slug (data/ef/sanctoral.sexp, Task