feat(core): prove the accounting laws (Kani + Lean); fix three engine gaps

The money arithmetic every invariant rests on now lives in one kernel,
ledger-core/src/kernel.rs: signing a line, totals, net, per-account
movements, reversal, normal balances, trial-balance columns, closing
lines, and the rounding plug for member splits. It is generic over a
checked `Amount` trait. The engine runs it on Decimal (validate,
movements, reverse_entry, account_balance, close_period_to, allocate,
trial_balance): there is one copy of the arithmetic, and it is the one
under proof.

Three layers, docs/verification.md maps every law to its proofs:

- Kani (src/proofs.rs): 17 harnesses prove the kernel at i64 for every
  input up to 4 lines over 3 accounts. An entry is accepted exactly
  when it is two or more positive, in-range lines whose debits equal
  credits; accepted entries net to zero; grouping by account loses
  nothing; a reversal mirrors and cancels its original; trial-balance
  columns balance iff the books net to zero; closing lines zero their
  accounts and a close balances however the net is split; the plug
  makes parts sum to the whole. No panics, no overflow. kani::cover!
  shows the proofs are not vacuous.
- Lean 4 (verify/lean): 24 headline theorems for books of any size. The
  ledger is a state machine (add account, draft, post, reverse, open,
  close), and in every reachable state the books net to zero, the trial
  balance balances (as of any date), and the accounting equation holds.
  Posting only appends ("posted is forever"), closed periods are
  frozen, a close zeroes revenue and expenses and credits exactly the net
  income, and period statements add up. Audit.lean shows standard axioms
  only, no sorry.
- Bridge (tests/kernel_bridge.rs): the Decimal and i64 kernels agree.

What the proofs found (each one missed by every test, fuzzer, and
mutant):

- The engine accepted negative line amounts; only MCP refused them. Now
  NegativeAmountLine: direction is the side's job.
- Summing lines near Decimal::MAX panicked. Lines are now capped at one
  quadrillion and ten decimal places (AmountOutOfRange), which keeps
  every realistic sum exact, and the kernel's sums are checked.
- FX conversion (foreign_amount * fx_rate) could panic the same way; it
  is now a checked multiply.
- Kani itself: 0.68 mis-models symbolic-length copy_from_slice
  (model-checking/kani#4904) and reported a reversal that doesn't net to
  zero. The counterexample, replayed natively, passes, and a 15-line
  standalone crate reproduces the bug. Harnesses avoid bulk copies, and
  a should_panic canary will flag the upstream fix.

`just prove` runs it all (Kani memory- and time-capped, fails on an
unsatisfiable cover or a non-standard Lean axiom). AGENTS.md now makes
formal coverage part of every core change.

Also, docs: GnuCash is *an* oracle, never *the* oracle (the owner). The
spec is accounting principles, proved. Golden files are recomputed from
principles. External implementations (GnuCash, the old Sheet, QBO/Xero)
are cross-checks whose disagreements get adjudicated, never obeyed.
docs/oracle.md gains "Who is right"; AGENTS, README, architecture,
roadmap, parity, and STATUS are reworded to match.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01GWVo7x3UHw5kwCUaWxiejX

crates/ledger-core/src/journal.rs

@@ -4,6 +4,7 @@
 //! total credits. Entries are born as drafts, validated, then posted. Posting
 //! is one-way; a posted entry can only be corrected by a reversing entry.
 
+use crate::kernel::{self, LineError};
 use crate::{AccountId, ChartOfAccounts, ClassId, Currency, LedgerError, Money, Side};
 use chrono::NaiveDate;
 use rust_decimal::Decimal;
@@ -126,14 +127,11 @@ impl JournalEntry {
     }
 
     /// Validate the entry against the chart of accounts. This is the heart of
-    /// R-1: at least two lines, no zero amounts, no placeholder or unknown
-    /// accounts, one currency throughout, and debits exactly equal to credits.
+    /// R-1: at least two lines, every amount positive and within line range,
+    /// no placeholder or unknown accounts, one currency throughout, and
+    /// debits exactly equal to credits. The arithmetic is
+    /// [`kernel::check_lines`].
     pub fn validate(&self, chart: &ChartOfAccounts) -> Result<(), LedgerError> {
-        if self.lines.len() < 2 {
-            return Err(LedgerError::TooFewLines);
-        }
-        let mut debits = Decimal::ZERO;
-        let mut credits = Decimal::ZERO;
         let mut currency: Option<Currency> = None;
         for line in &self.lines {
             let account = chart
@@ -142,9 +140,6 @@ impl JournalEntry {
             if account.placeholder {
                 return Err(LedgerError::PlaceholderAccount(account.code.clone()));
             }
-            if line.amount.is_zero() {
-                return Err(LedgerError::ZeroAmountLine);
-            }
             match currency {
                 None => currency = Some(line.amount.currency),
                 Some(c) if c != line.amount.currency => {
@@ -161,28 +156,33 @@ impl JournalEntry {
                     found: line.amount.currency.code().to_string(),
                 });
             }
-            match line.side {
-                Side::Debit => debits += line.amount.amount,
-                Side::Credit => credits += line.amount.amount,
+        }
+        let sides: Vec<(Side, Decimal)> = self
+            .lines
+            .iter()
+            .map(|l| (l.side, l.amount.amount))
+            .collect();
+        kernel::check_lines(&sides).map_err(|e| match e {
+            LineError::TooFewLines => LedgerError::TooFewLines,
+            LineError::ZeroAmount => LedgerError::ZeroAmountLine,
+            LineError::NegativeAmount => LedgerError::NegativeAmountLine,
+            LineError::OutOfRange => LedgerError::AmountOutOfRange,
+            LineError::Unbalanced { debits, credits } => {
+                LedgerError::UnbalancedEntry { debits, credits }
             }
-        }
-        if debits != credits {
-            return Err(LedgerError::UnbalancedEntry { debits, credits });
-        }
-        Ok(())
+        })
     }
 
     /// Net movement per account within this entry: debits minus credits.
     /// Sums to zero across accounts for any valid entry.
     pub fn movements(&self) -> HashMap<AccountId, Decimal> {
-        let mut out = HashMap::new();
-        for line in &self.lines {
-            let delta = match line.side {
-                Side::Debit => line.amount.amount,
-                Side::Credit => -line.amount.amount,
-            };
-            *out.entry(line.account).or_insert(Decimal::ZERO) += delta;
-        }
-        out
+        kernel::movements(
+            self.lines
+                .iter()
+                .map(|l| (l.account, l.side, l.amount.amount)),
+        )
+        .expect("posted lines are in range, so their sums are")
+        .into_iter()
+        .collect()
     }
 }