docs(arap): B-41, the bookspec examples, and the four registers (P4b S7)

rules.md B-41 states the write-off: the direct method the owner chose
(A-5), Dr 6990 / Cr 1200 with the receivable tagged, at most what is
owed and at most the least owed from that day on (a partial write-off as
§1.166-3(a) allows), refused on cash-basis books (§1.166-1(e)), its
evidence filed in the same call (§1.166-2(a)); bills are never written
off (ASC 405-20-40-1); and a recovery is not a new movement (D-49): the
same year, reverse the write-off and record the payment; a later year, a
plain entry to a bad-debt-recoveries revenue account, the invoice staying
written off (IRC §111).

bookspec states B-41 for the first time and gives B-38 its example: two
new examples, bad-debt-direct-write-off (two partial write-offs of one
invoice, the balances and the trial balance worked by hand) and
arap-hand-control-posting-refused (a hand line an earlier version wrote
replays, the same line written today is refused). The example schema
gains the dated write_off event, lets a refused entry say so (an entry
posts whole or not at all; older and refused never combine), and its
refusal vocabulary gains untagged_control_line, B-38's control guard.

The registers: docs/architecture.md names the new tool group;
docs/receipt-store.md lists invoice.written_off and what replay does with
it; docs/parity.md records the slice (no row changes status, the floor
stands); docs/testing.md records every test and what P12 must mutate;
docs/verification.md the two Lean theorems and what they cover.

No figure moves: no golden file changed.

checker/src/rules.rs

@@ -165,6 +165,7 @@ pub fn rule_for_refusal(reason: &str) -> Option<&'static Rule> {
         | "already_disposed"
         | "invalid_depreciation_period" => 15,
         "invalid_schedule" => 16,
+        "untagged_control_line" => 38,
         _ => return None,
     };
     rule(b)
@@ -529,7 +530,7 @@ const SPEC: Spec = &[
         Area::Arap,
         "A document's figures are its ledger lines that stand; a control account is its documents",
         Some(Status::Choice),
-        &[],
+        &["arap-hand-control-posting-refused"],
     ),
     (
         39,
@@ -548,9 +549,9 @@ const SPEC: Spec = &[
     (
         41,
         Area::Arap,
-        "Write-offs (allocated, not yet stated)",
-        None,
-        &[],
+        "A debt that will not be collected is written off, and a recovery is income",
+        Some(Status::Choice),
+        &["bad-debt-direct-write-off"],
     ),
     (
         42,