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.

1 files changed, 70 insertions, 15 deletions

diff --git a/test/test_precedence_ef.ml b/test/test_precedence_ef.ml
index 8465870..ca623d2 100644
--- a/test/test_precedence_ef.ml
+++ b/test/test_precedence_ef.ml
@@ -290,7 +290,7 @@ let test_all_souls_yields_to_sunday () =
   let rules =
     { P.band = (fun c cd -> PE.band c cd);
       disposition = (fun ~winner:_ ~loser:_ -> P.Omit);
-      admit = (fun ~observed:_ ~temporal:_ cs -> cs) }
+      admit = (fun ~observed:_ ~temporal:_ cs -> List.map (fun (c, p, (_ : int)) -> (c, p)) cs) }
   in
   let resolution = P.resolve rules day_ctx ~temporal:sunday ~sanctoral:[ all_souls ] in
   Alcotest.(check string) "the Sunday is observed, not All Souls"
@@ -822,6 +822,22 @@ let observed_class3 = cand ~rank:V.Class3 "ef-some-class3-day"
 let slugs_of admitted =
   List.map (fun (c, _) -> S.to_string c.P.cel.Cel.slug) admitted
 
+(* [admit_cases] below (Task B, ef-rg16a) needs a precedence-order [int] on
+   every comms triple -- {!Precedence.rules.admit}'s new parameter, RG 113
+   (docs/research/rules-register.md §4, "RG 113"). This table's own header
+   comment states its purpose: isolate [admit]'s own selection/count logic
+   from {!PE.band}'s occurrence-table classification, so every candidate
+   here is built from a synthetic slug ("ef-ordinary-hi" etc.) that matches
+   none of [band]'s 28 real branches -- calling the REAL [PE.band] on them
+   would collapse every one to {!PE.unclassified} (the same tied value),
+   destroying the table's ability to distinguish rows at all. [order_of_rank]
+   is a TEST-ONLY stand-in, reproducing exactly the relative order the
+   previous [dignity] function gave (RG 8's rank cardinal, lower first) --
+   so every existing expectation below still holds unchanged; only the
+   tuple shape gained this third field. *)
+let order_of_rank = function V.Class1 -> 10 | V.Class2 -> 20 | V.Class3 -> 30 | V.Class4 -> 40
+let po c p = (c, p, order_of_rank c.P.cel.Cel.rank)
+
 (* Real-data shapes for the fix round's own RG16(a)/[admit] interaction
    (below): a Feast of the Lord (subject Lord, Class2, sanctoral) as
    [observed], oracle-confirmed real slugs/ranks rather than hand-typed
@@ -853,28 +869,28 @@ let admit_cases =
   [ (* RG 111 (§4): "I class: none save one privileged." *)
     ( "I-class day, only an ordinary commemoration due -> none admitted",
       observed_class1, observed_class1,
-      [ (ordinary_hi, P.Ordinary) ],
+      [ po ordinary_hi P.Ordinary ],
       [] );
     ( "I-class day, ordinary + privileged both due -> only the privileged \
        one, regardless of the ordinary one's higher dignity",
       observed_class1, observed_class1,
-      [ (ordinary_hi, P.Ordinary); (privileged_lo, P.Privileged) ],
+      [ po ordinary_hi P.Ordinary; po privileged_lo P.Privileged ],
       [ "ef-privileged-lo" ] );
     ( "I-class day, two privileged due -> only the higher-dignity one (still \
        just \"one\")",
       observed_class1, observed_class1,
-      [ (privileged_lo, P.Privileged); (privileged_hi, P.Privileged) ],
+      [ po privileged_lo P.Privileged; po privileged_hi P.Privileged ],
       [ "ef-privileged-hi" ] );
     (* RG 111: "II-class Sundays: one (dropped if a privileged one is due)." *)
     ( "II-class Sunday, only an ordinary commemoration due -> it is admitted",
       observed_class2_sunday, observed_class2_sunday,
-      [ (ordinary_hi, P.Ordinary) ],
+      [ po ordinary_hi P.Ordinary ],
       [ "ef-ordinary-hi" ] );
     ( "II-class Sunday, ordinary (higher dignity) + privileged (lower \
        dignity) both due -> the PRIVILEGED one is admitted, the ordinary \
        one dropped despite outranking it",
       observed_class2_sunday, observed_class2_sunday,
-      [ (ordinary_hi, P.Ordinary); (privileged_lo, P.Privileged) ],
+      [ po ordinary_hi P.Ordinary; po privileged_lo P.Privileged ],
       [ "ef-privileged-lo" ] );
     (* RG 111(b)'s own rank floor ("scilicet DE FESTO II CLASSIS"), fix
        round 1 F7: a Class3 ORDINARY candidate -- no privileged rival due,
@@ -886,7 +902,7 @@ let admit_cases =
     ( "II-class Sunday, sole candidate is an ORDINARY Class3 (not \
        \"de festo II classis\") -> admitted nothing, not the best available",
       observed_class2_sunday, observed_class2_sunday,
-      [ (ordinary_class3, P.Ordinary) ],
+      [ po ordinary_class3 P.Ordinary ],
       [] );
     (* RG 111: "other II class: one" -- no privilege override, the exact
        asymmetry the brief and precedence_ef.ml's own [admit] comment flag:
@@ -895,21 +911,21 @@ let admit_cases =
     ( "other II-class day, only an ordinary commemoration due -> it is \
        admitted",
       observed_class2_other, observed_class2_other,
-      [ (ordinary_hi, P.Ordinary) ],
+      [ po ordinary_hi P.Ordinary ],
       [ "ef-ordinary-hi" ] );
     ( "other II-class day, same ordinary+privileged pair as the Sunday row \
        above -> the ORDINARY one wins on pure dignity this time, the \
        privileged one dropped",
       observed_class2_other, observed_class2_other,
-      [ (ordinary_hi, P.Ordinary); (privileged_lo, P.Privileged) ],
+      [ po ordinary_hi P.Ordinary; po privileged_lo P.Privileged ],
       [ "ef-ordinary-hi" ] );
     (* RG 111: "III-IV class: at most two" -- three candidates due, top two
        by dignity admitted, the third (lowest dignity) dropped. *)
     ( "III-class day, three commemorations due -> the top two by dignity, \
        not merely \"two of them\"",
       observed_class3, observed_class3,
-      [ (ordinary_hi, P.Ordinary); (privileged_lo, P.Privileged);
-        (ordinary_lowest, P.Ordinary) ],
+      [ po ordinary_hi P.Ordinary; po privileged_lo P.Privileged;
+        po ordinary_lowest P.Ordinary ],
       [ "ef-ordinary-hi"; "ef-privileged-lo" ] );
     (* Fix round 1, item 2 (RG16(a) task review): the CRITICAL witness for
        [~temporal]. RG 16(a)'s own text -- the winning Feast of the Lord
@@ -928,7 +944,7 @@ let admit_cases =
        TEMPORAL candidate is a II-class Sunday -> the RG111(b) rank floor \
        still applies, admits nothing (Sixtus, Class3, has no standing)",
       lord_winner, an_ordinary_sunday,
-      [ (sixtus, P.Ordinary) ],
+      [ po sixtus P.Ordinary ],
       [] );
     (* The control, same pair as the row above with [observed] = [temporal]
        (no displacement -- an ordinary WEEKDAY, not a Sunday): "other II
@@ -941,7 +957,7 @@ let admit_cases =
        = observed, not a Sunday) -> \"other II class: one\", Sixtus IS \
        admitted",
       lord_winner, lord_winner,
-      [ (sixtus, P.Ordinary) ],
+      [ po sixtus P.Ordinary ],
       [ "pope-sixtus-ii-felicissimus-and-agapitus-martyrs" ] )
   ]
 
@@ -953,7 +969,7 @@ let admit_cases =
    two-candidate row where either order already happens to be sorted. *)
 let test_admit_order_independent () =
   let comms =
-    [ (ordinary_hi, P.Ordinary); (privileged_lo, P.Privileged); (ordinary_lowest, P.Ordinary) ]
+    [ po ordinary_hi P.Ordinary; po privileged_lo P.Privileged; po ordinary_lowest P.Ordinary ]
   in
   let forward = slugs_of (PE.admit ~observed:observed_class3 ~temporal:observed_class3 comms) in
   let reversed =
@@ -962,6 +978,39 @@ let test_admit_order_independent () =
   Alcotest.(check (list string)) "reversed input admits the same candidates"
     forward reversed
 
+(* RG 113 teeth (Task B, ef-rg16a): two SAME-rank candidates whose slug order
+   DISAGREES with their band/precedence order -- "aa-worse-precedence" sorts
+   first alphabetically but is given the WORSE (higher) precedence int,
+   "zz-better-precedence" sorts last alphabetically but the BETTER (lower)
+   one. Both are [Class3] (same RG 8 "dignity", so a version of [admit] that
+   silently reverted to sorting by [rank] then slug -- the exact pre-fix
+   shape this task replaced -- would pick "aa-worse-precedence" here, the
+   OPPOSITE of what this asserts. A real RG 91 [band] value never actually
+   produces this exact pairing against these two synthetic slugs (see
+   [admit_cases]'s own header on why this table uses synthetic, non-band-
+   classifiable slugs) -- the precedence ints are supplied directly, the
+   same [po]/explicit-order convention this file already uses, standing in
+   for whatever real [band] would compute. This is what proves [admit]
+   actually consults the passed-in precedence value rather than merely
+   accepting one as a matter of new type-checking. *)
+let order_tiebreak_alpha_first_worse = cand ~rank:V.Class2 "aa-worse-precedence"
+let order_tiebreak_alpha_last_better = cand ~rank:V.Class2 "zz-better-precedence"
+
+(* [observed_class2_other]: "other II class: one" admits exactly ONE, by
+   precedence order alone (no privilege override, no rank floor) -- unlike
+   the III-class row [test_admit_order_independent] reuses, which admits
+   TWO out of two offered here and so cannot distinguish "picked by
+   precedence" from "picked both anyway". *)
+let test_admit_uses_precedence_not_slug_when_they_disagree () =
+  let comms =
+    [ (order_tiebreak_alpha_first_worse, P.Ordinary, 90);
+      (order_tiebreak_alpha_last_better, P.Ordinary, 10) ]
+  in
+  Alcotest.(check (list string))
+    "the BETTER-precedence candidate is admitted even though it sorts LAST alphabetically"
+    [ "zz-better-precedence" ]
+    (slugs_of (PE.admit ~observed:observed_class2_other ~temporal:observed_class2_other comms))
+
 (* The brief: "a case proving that what the limit drops is reported in
    omitted rather than vanishing" -- three end-to-end proofs, wired with the
    REAL [PE.band], [PE.disposition] and [PE.admit] together (not a stub, so
@@ -1181,7 +1230,10 @@ let test_all_souls_transfers_end_to_end () =
       origin = P.Temporal }
   in
   let all_souls = cand ~origin:P.Sanctoral ~layer:PE.universal_layer "ef-all-souls" in
-  let rules = { P.band = PE.band; disposition = PE.disposition; admit = (fun ~observed:_ ~temporal:_ cs -> cs) } in
+  let rules =
+    { P.band = PE.band; disposition = PE.disposition;
+      admit = (fun ~observed:_ ~temporal:_ cs -> List.map (fun (c, p, (_ : int)) -> (c, p)) cs) }
+  in
   let resolution = P.resolve rules day_ctx ~temporal:sunday ~sanctoral:[ all_souls ] in
   Alcotest.(check (list string)) "All Souls is deferred (transferred), not omitted or commemorated"
     [ "ef-all-souls" ]
@@ -1378,6 +1430,9 @@ let suite =
         admit_cases
     @ [ Alcotest.test_case "admit is order-independent (III-class, 3 candidates)" `Quick
           test_admit_order_independent;
+        Alcotest.test_case
+          "RG113: admit picks by precedence order, not slug, when they disagree" `Quick
+          test_admit_uses_precedence_not_slug_when_they_disagree;
         Alcotest.test_case "I-class day: full drop reported in omitted, not vanished" `Quick
           test_i_class_day_drops_into_omitted;
         Alcotest.test_case "II-class Sunday: second loser dropped into omitted" `Quick