members' equity: split undistributed earnings cumulatively

A capital account is one running balance (Form 1065 Schedule K-1
instructions, Item L: beginning and ending capital "based on the
partnership's books and records"), but the statement split prior
earnings and the period's income separately, so a member's ending on one
statement could differ by a cent from their beginning on the next.

Now each member's share of undistributed earnings is allocated as of a
date (largest remainder, as before): beginning as of the day before the
period, ending as of its last day. A member's period income is the
roll-forward's remainder (their share within a rounding cent); incomes
still sum to net income. New property
each_members_capital_chains_across_statements (random books, odd-cent
shares, closes to members or not, any split date) fails on the old code
and passes now. The hand-computed test is recomputed: the old split gave
two cents off an even 50/50 to date.

Also: rules.md B-13 quotes Item L; docs/testing.md #7 and #8 marked
changed; the CPA-question list is replaced by the rule that wanderbooks
settles questions from the sources and makes real choices per-company
settings.

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

crates/ledger-core/src/reports.rs

@@ -823,8 +823,17 @@ pub struct MembersEquityStatement {
 ///   1. Each row MUST roll forward exactly: beginning + contributions +
 ///      income - distributions + other = ending.
 ///   2. The total ending MUST equal balance-sheet equity at `end`.
-///   3. Unclosed earnings and the period's income MUST be split by share,
-///      to the cent, by largest remainder (DECISION, Stephen 2026-10-13).
+///   3. Undistributed earnings MUST be split by share, to the cent, by
+///      largest remainder (DECISION, Stephen 2026-10-13), cumulatively as
+///      of each date: a member's beginning is their capital and share as
+///      of the day before `start`, their ending as of `end`.
+///   3a. A member's ending on one statement MUST equal their beginning on
+///      the next, exactly (a capital account is one running balance: Form
+///      1065 Schedule K-1 instructions, Item L, "beginning capital account
+///      and ending capital account ... based on the partnership's books").
+///   3b. A member's income is the roll-forward's remainder: their share of
+///      the period's income within a rounding cent; the members' incomes
+///      MUST sum to the period's net income.
 ///   4. NEVER hide an unexplained change: it goes in "other".
 ///   5. An entry dated `start` is period activity, not beginning capital.
 /// SCENARIOS:
@@ -924,10 +933,39 @@ pub fn members_equity(
         .collect();
 
     // Everything in equity that isn't a capital account is partnership
-    // earnings not yet distributed: allocate it by share.
-    let undistributed = begin_bs.total_equity - capital.iter().sum::<Decimal>();
-    let begin_alloc = allocate(undistributed, &shares);
-    let income_alloc = allocate(pnl.net_income(), &shares);
+    // earnings not yet distributed. Each member's share of it is allocated
+    // cumulatively, as of a date, so a member's capital on a date never
+    // depends on which statement shows it: one statement's ending is the
+    // next one's beginning, to the cent (a capital account is one running
+    // balance: Form 1065 Schedule K-1 instructions, Item L).
+    let capital_through = |id: crate::AccountId, through: NaiveDate| -> Decimal {
+        let mut m = Decimal::ZERO;
+        for e in ledger.posted_entries().filter(|e| e.date() <= through) {
+            for l in e.lines().iter().filter(|l| l.account == id) {
+                match l.side {
+                    crate::Side::Credit => m += l.amount.amount,
+                    crate::Side::Debit => m -= l.amount.amount,
+                }
+            }
+        }
+        m
+    };
+    let capital_end: Vec<Decimal> = members
+        .iter()
+        .map(|m| {
+            capital_through(m.capital_account, end)
+                + m.distribution_account
+                    .map_or(Decimal::ZERO, |d| capital_through(d, end))
+        })
+        .collect();
+    let begin_alloc = allocate(
+        begin_bs.total_equity - capital.iter().sum::<Decimal>(),
+        &shares,
+    );
+    let end_alloc = allocate(
+        end_bs.total_equity - capital_end.iter().sum::<Decimal>(),
+        &shares,
+    );
     let explained = flow.iter().map(|(c, d)| c - d).sum::<Decimal>() + pnl.net_income();
     let other_alloc = allocate(
         end_bs.total_equity - begin_bs.total_equity - explained,
@@ -937,13 +975,17 @@ pub fn members_equity(
     let mut cols = Vec::with_capacity(members.len());
     for (i, m) in members.iter().enumerate() {
         let beginning = capital[i] + begin_alloc[i];
+        let ending = capital_end[i] + end_alloc[i];
         let (contributions, distributions) = flow[i];
-        let ending = beginning + contributions - distributions + income_alloc[i] + other_alloc[i];
+        // The member's income is what the roll-forward leaves: their share
+        // of the period's income, give or take the rounding cent that keeps
+        // the running balance exact. The members' incomes sum to net income.
+        let income = ending - beginning - contributions + distributions - other_alloc[i];
         cols.push(MemberEquityColumn {
             name: m.name.clone(),
             beginning: zero_clean(beginning),
             contributions,
-            net_income: zero_clean(income_alloc[i]),
+            net_income: zero_clean(income),
             distributions,
             other: zero_clean(other_alloc[i]),
             ending: zero_clean(ending),

crates/ledger-core/tests/spec_reports.rs

@@ -1004,14 +1004,16 @@ fn me_refuses_bad_shares() {
     }
 }
 
-/// Oracle: ME INVARIANTS 1-3 — hand-computed roll-forward with odd cents
-/// split by largest remainder, ties to the earlier member: prior unclosed
-/// earnings 100.01 -> A 50.01, B 50.00; period income 201.01 -> A 100.51,
-/// B 100.50. Total ending 2251.02 = BS equity.
-///
-/// CHANGE PENDING (docs/testing.md #7): the beginning (unclosed prior earnings) and the period's income
-/// are each split separately (INVARIANT 3 names them separately), not
-/// cumulative-then-differenced.
+/// Oracle: ME INVARIANTS 1-3b — hand-computed roll-forward, cumulative
+/// allocation (docs/testing.md #7; K-1 Item L: one running capital
+/// balance), odd cents by largest remainder, ties to the earlier member.
+/// Undistributed before Feb 1: 100.01 -> A 50.01, B 50.00. Through Mar 31:
+/// 100.01 + 301.01 - 100.00 = 301.02 -> 150.51 each. Endings: A 950.00 +
+/// 150.51 = 1100.51, B 1000.00 + 150.51 = 1150.51. Incomes (the
+/// remainder): A 1100.51 - 1050.01 + 50.00 = 100.50, B 100.51; sum 201.01,
+/// the period's income. Total ending 2251.02 = BS equity. (Splitting the
+/// period's income on its own would give A 150.52 and B 150.50 to date:
+/// two cents off half each.)
 #[test]
 fn me_hand_computed_roll_forward_with_largest_remainder() {
     let mut co = company();
@@ -1059,8 +1061,8 @@ fn me_hand_computed_roll_forward_with_largest_remainder() {
     assert_eq!(
         st.members,
         vec![
-            col("A", 105001, 0, 10051, 5000, 0, 110052),
-            col("B", 5000, 100000, 10050, 0, 0, 115050),
+            col("A", 105001, 0, 10050, 5000, 0, 110051),
+            col("B", 5000, 100000, 10051, 0, 0, 115051),
         ]
     );
     assert_eq!(
@@ -1408,7 +1410,8 @@ fn sorted_amounts(lines: &[ledger_core::CashFlowLine]) -> Vec<Decimal> {
 /// 400; AR up 300 (-300), AP up 80 (+80); CFO 180; financing loan 300 +
 /// contribution 100 = 400; net change 580 = cash 1000 -> 1580.
 ///
-/// CHANGE PENDING (docs/testing.md #8): one working-capital / financing line per account that changed.
+/// Working capital is one line per account that changed; financing is gross per
+/// account (docs/testing.md #8): here each financing account moved one way only.
 #[test]
 fn cf_hand_computed_with_designated_debt() {
     let co = cf_example_books();
@@ -2424,7 +2427,8 @@ proptest! {
     /// NI + depreciation + working capital; with or without a close and a
     /// designated loan.
     ///
-    /// CHANGE PENDING (docs/testing.md #8): with no registered fixed assets, depreciation and investing
+    /// With no registered fixed assets and no investing accounts (docs/testing.md #8),
+    /// depreciation and investing
     /// are zero (receivables are current, so working capital).
     #[test]
     fn prop_cf_sections_sum_to_change_in_cash(gens in arb_books(), (a, _m, e) in three_days(), month in opt_month(), designate in any::<bool>()) {

crates/ledger-core/tests/statements.proptest-regressions

@@ -0,0 +1,7 @@
+# Seeds for failure cases proptest has generated in the past. It is
+# automatically read and these particular cases re-run before any
+# novel cases are generated.
+#
+# It is recommended to check this file in to source control so that
+# everyone who runs the test benefits from these saved cases.
+cc b177aed2b1d69b6a0abb37b170ec5b9efc73d7fae49bace065c15c819ecca711 # shrinks to months = [(0, 0, 0, 507, 37392), (0, 0, 0, 9054, 3952), (0, 0, 0, 34144, 7979)], closes = [false, true, false, false, false, false, false, false, false, false, false, false], split = 14

crates/ledger-core/tests/statements.rs

@@ -471,16 +471,20 @@ fn members_equity_rolls_capital_forward_and_ties_to_the_balance_sheet() {
         );
 
         // February begins where January ended, whether or not January was
-        // closed to retained earnings. 100.01 splits 50.01 / 50.00.
+        // closed to retained earnings (still undistributed either way).
+        // Cumulative split (docs/testing.md #7): everything to date, 666.67
+        // + 100.01 = 766.68, is 383.34 each, so Alice's February share is
+        // 383.34 - 333.34 = 50.00 and Bob's 383.34 - 333.33 = 50.01.
         let feb = members_equity(&l, d(2, 1), d(2, 28), &members).unwrap();
+        let (alice, bob) = (("50.00", "983.34"), ("50.01", "683.34"));
         assert_eq!(
             row(&feb.members[0]),
             (
                 cents("933.34"),
                 cents("0"),
-                cents("50.01"),
+                cents(alice.0),
                 cents("0"),
-                cents("983.35")
+                cents(alice.1)
             )
         );
         assert_eq!(
@@ -488,9 +492,9 @@ fn members_equity_rolls_capital_forward_and_ties_to_the_balance_sheet() {
             (
                 cents("733.33"),
                 cents("0"),
-                cents("50.00"),
+                cents(bob.0),
                 cents("100"),
-                cents("683.33")
+                cents(bob.1)
             )
         );
         assert_eq!(feb.total.ending, cents("1666.68"));
@@ -1405,3 +1409,116 @@ fn an_entry_that_nets_to_nothing_on_an_account_adds_no_line() {
     assert_eq!(cf.cash_from_financing, dec(600));
     assert_eq!(cf.financing.len(), 4);
 }
+
+mod chaining {
+    use super::*;
+    use ledger_core::{CloseTo, MemberClose};
+    use proptest::prelude::*;
+
+    /// One month of activity: (member, contribution cents, distribution
+    /// cents, revenue cents, expense cents).
+    type Month = (usize, i64, i64, i64, i64);
+
+    fn month() -> impl Strategy<Value = Month> {
+        (
+            0usize..3,
+            0i64..50_000,
+            0i64..20_000,
+            0i64..100_000,
+            0i64..80_000,
+        )
+    }
+
+    proptest! {
+        #![proptest_config(ProptestConfig { cases: 256, ..ProptestConfig::default() })]
+
+        /// Oracle: members' equity INVARIANT 3a (docs/testing.md #7; Form
+        /// 1065 Schedule K-1 instructions, Item L: one running capital
+        /// balance per member). For random books, shares with odd cents,
+        /// months closed to the members or not, and any split date: each
+        /// member's ending on the first statement is their beginning on
+        /// the second, and the two statements together roll to the
+        /// one-statement figures; every member's incomes sum to net income.
+        #[test]
+        fn each_members_capital_chains_across_statements(
+            months in prop::collection::vec(month(), 1..12),
+            closes in prop::collection::vec(any::<bool>(), 12),
+            split in 1u32..330,
+        ) {
+            let mut l = Ledger::new(Currency::USD);
+            let mut add = |code: &str, t| l.add_account(code, code, t, None, false).unwrap();
+            let cash = add("1000", AccountType::Asset);
+            let caps = [
+                add("3000", AccountType::Equity),
+                add("3001", AccountType::Equity),
+                add("3002", AccountType::Equity),
+            ];
+            let rev = add("4000", AccountType::Revenue);
+            let exp = add("6000", AccountType::Expense);
+            let shares = [
+                Decimal::from_str("0.3333").unwrap(),
+                Decimal::from_str("0.3333").unwrap(),
+                Decimal::from_str("0.3334").unwrap(),
+            ];
+            let cents = |n: i64| Money::new(Decimal::new(n, 2), Currency::USD);
+            let post2 = |l: &mut Ledger, date, dr, cr, n: i64| {
+                if n > 0 {
+                    let e = l.create_entry(date, "x");
+                    l.add_line(e, dr, Side::Debit, cents(n)).unwrap();
+                    l.add_line(e, cr, Side::Credit, cents(n)).unwrap();
+                    l.post_entry(e).unwrap();
+                }
+            };
+            for (i, (who, contrib, dist, sales, costs)) in months.iter().enumerate() {
+                let m = i as u32 + 1;
+                post2(&mut l, d(m, 3), cash, caps[*who], *contrib);
+                post2(&mut l, d(m, 10), cash, rev, *sales);
+                post2(&mut l, d(m, 15), exp, cash, *costs);
+                post2(&mut l, d(m, 20), caps[*who], cash, *dist);
+                if closes[i] {
+                    let end = if m == 12 { d(12, 31) } else { d(m + 1, 1).pred_opt().unwrap() };
+                    let p = l.create_period(&format!("2026-{m:02}"), d(m, 1), end).unwrap();
+                    let to = CloseTo::Members(
+                        caps.iter()
+                            .zip(shares)
+                            .map(|(&capital, share)| MemberClose { capital, share, distributions: None })
+                            .collect(),
+                    );
+                    // Closes must go in order; a refused close just leaves
+                    // the month open.
+                    let _ = l.close_period_to(p, &to);
+                }
+            }
+            let members: Vec<MemberCapital> = caps
+                .iter()
+                .zip(shares)
+                .enumerate()
+                .map(|(i, (&capital_account, share))| MemberCapital {
+                    name: format!("M{i}"),
+                    capital_account,
+                    distribution_account: None,
+                    share,
+                })
+                .collect();
+            let mid = d(1, 1) + chrono::Days::new(u64::from(split));
+            let first = members_equity(&l, d(1, 1), mid, &members).unwrap();
+            let second = members_equity(&l, mid.succ_opt().unwrap(), d(12, 31), &members).unwrap();
+            let whole = members_equity(&l, d(1, 1), d(12, 31), &members).unwrap();
+            for i in 0..3 {
+                prop_assert_eq!(first.members[i].ending, second.members[i].beginning);
+                prop_assert_eq!(second.members[i].ending, whole.members[i].ending);
+                prop_assert_eq!(first.members[i].beginning, whole.members[i].beginning);
+            }
+            for st in [&first, &second, &whole] {
+                let incomes: Decimal = st.members.iter().map(|m| m.net_income).sum();
+                prop_assert_eq!(incomes, st.total.net_income);
+                for m in &st.members {
+                    prop_assert_eq!(
+                        m.beginning + m.contributions + m.net_income - m.distributions + m.other,
+                        m.ending
+                    );
+                }
+            }
+        }
+    }
+}

docs/spec/rules.md

@@ -217,10 +217,20 @@ closed period).
 - **No authority** says how to round a share to the cent. Largest
   remainder, ties to the earlier member: DECISION (Stephen, 2026-10-13).
   Closes made before then replay with the last member absorbing it.
+- A capital account is one running balance: Form 1065 Schedule K-1
+  instructions, Item L: "The partnership must report your beginning
+  capital account and ending capital account for the year", "based on the
+  partnership's books and records." So a statement of members' equity
+  splits undistributed earnings cumulatively, as of each date (beginning
+  as of the day before the period, ending as of its last day), never one
+  period at a time: a member's ending on one statement is their beginning
+  on the next, to the cent, and a member's period income is the
+  roll-forward's remainder (their share within a rounding cent).
 
 **Enforced:** `CloseTo::Members`, `periods::allocate`,
 `kernel::apportion`, `members_equity`. **Checked:** Kani
-`apportion_is_exact`, `apportion_is_fair`; properties `prop_split_*`;
+`apportion_is_exact`, `apportion_is_fair`; properties `prop_split_*`,
+`each_members_capital_chains_across_statements`;
 `closes_journaled_under_the_old_rule_replay_with_it`.
 
 ## B-14 Statements: P&L for a period; cash flow by the indirect method

docs/testing.md

@@ -73,20 +73,17 @@ accounting question), CHANGE (a source says otherwise; work pending).
 | 4 | Closing a period with nothing to close still locks it | CONVENTION | A close is a lock (B-12); a dormant month must still lock and count for close-in-order |
 | 5 | Draws and distributions are closed into capital at period end | CONFIRMED | OpenStax 5.1: dividends "are closed to the permanent account"; drawing accounts close to owner's capital. Monthly closes mean the year's K-1 Item L withdrawals sum across months |
 | 6 | Reconciliation balances | CONFIRMED | Signed by the account's normal side (a card reads as owed), as statements show it; `reconciling_a_card_reads_its_normal_side_...` |
-| 7 | A member's ending on one equity statement may differ by a cent from the next statement's beginning | CHANGE (pending) | A capital account is one running balance (Form 1065 K-1 instructions, Item L: beginning and ending capital "based on the partnership's books and records"). Allocate cumulatively so beginning equals the prior ending per member. CPA question below |
-| 8 | Cash flow nets one line per account; investing comes only from registered assets | CHANGE (pending) | ASC 230-10-45-7: gross receipts and payments "more relevant" than net; 45-8 limits netting to quick-turnover items. Financing: contributions apart from distributions, borrowings apart from repayments. ASC 230-10-20/45-13: loans made and investments bought are investing, so classify by account role |
+| 7 | A member's ending on one equity statement may differ by a cent from the next statement's beginning | CHANGED 2026-10-13 | A capital account is one running balance (Form 1065 K-1 instructions, Item L). Undistributed earnings now split cumulatively as of each date, so each member's capital chains exactly (`each_members_capital_chains_across_statements`; it fails on the old code); rules.md B-13 |
+| 8 | Cash flow nets one line per account; investing comes only from registered assets | CHANGED 2026-10-13 | ASC 230-10-45-7: gross receipts and payments "more relevant" than net; 45-8 limits netting to quick-turnover items. Financing and investing are now gross; loans made and investments bought are investing (230-10-20, 45-13) via `[books] investing_accounts`. Owner-advanced expenses: PwC 6.9.3.1 constructive treatment via `[books] financing_accounts` (rules.md B-14) |
 | 9 | An asset's life ends at purchase + life months, that day not held; day-count proration | CONVENTION | Exactly N months of service; day proration and the mid-month convention are both accepted book policies (ASC 360-10-35-4 not read: login) |
 | 10 | A payroll entry has one line per account total | CONFIRMED | The per-employee detail the IRS requires ("Amounts and dates of all wage ... payments", Employment Tax Recordkeeping) is kept in the run; a summary entry is standard |
 | 11 | A period with exactly the dates of an existing one is allowed | DESIGN | Nothing governs duplicate periods; harmless (the second close locks only). Refusing exact duplicates is an option |
 
-Questions for Krista Baker (CPA):
-
-1. Interim members' equity: is a per-member allocation of unclosed
-   earnings acceptable on interim statements, or should the books close
-   monthly so the capital accounts carry it?
-2. How should 2100 Due to Shareholders, and expenses the owners paid
-   personally, appear on the cash flow statement: operating, financing,
-   or as a non-cash disclosure (ASC 230-10-50-3, not yet read)?
+Questions are settled from the sources, not by any one company's CPA
+(wanderbooks is general software). Where the standards leave a real
+choice, it is a per-company setting with a sourced default, for that
+company's accountant to review: the cash flow account roles (rules.md
+B-14) are the first.
 
 ## Gap list: what isn't covered, and what would bring it in