fix(splits): make every split account for 100%

A 50/50 arrangement was stored as a single row saying "Sonu 50%". The
arithmetic was never wrong — `myShare` resolves the payer's share as
`100 - SUM(everyone else)`, so balances and per-user spend were correct
throughout. It was still a bug, because a ledger is read as well as
computed: on screen that row is a 50% share against a blank, which looks
like half the money is unallocated and is indistinguishable from a split
somebody abandoned half-finished.

It also leaked. `getSharedTransactions` filters by participant with an
EXISTS on an explicit split row, so filtering the Shared view by the
payer silently dropped every transaction where their share was only ever
implied.

Four write paths could produce it, three of them unguarded:

  - the Slack nudge's share button, which inserted one row
  - `POST /api/transactions`, where the add form shows an amber total
    under 100 but saves anyway — this is how Lawn Mowing and Hedge
    Pruning were stored
  - `applyRuleActions`, where ten of the fourteen live split rules name
    only the other person

`completeSplit` is now the single place that writes the remainder, and
every one of those paths ends in it. The remainder goes to the
transaction's *owner*, never to "me": the owner's row on their own
transaction is excluded from both halves of the balance query, so it
cannot create, enlarge or discharge a debt, whereas a row for me on
someone else's transaction is a real obligation. That distinction is
what makes this safe to apply to existing data.

Also fixes the order panel's "Shared 50/50" toggle, which was inert in
both directions: it posted a lone 50% row to share (rejected — must
total 100%) and an empty array to un-share (rejected — array required),
because no way to clear a split existed. DELETE on the splits route is
that way.

Backfill: 7 rows, verified against a row-level dump diff — 2549 -> 2556
rows, none removed, none modified — and participant balances byte
identical before and after (Molina 19556.07, Sonu 20913.35). Every split
in the database now totals 100%.

Not done: a database-level constraint. Enforcing the sum needs a
deferred constraint trigger, and the rule path commits its DELETE and
INSERT as separate statements, so the trigger would reject the
intermediate state. Making it work means wrapping every write path in a
transaction, which is a larger change than the defect warrants.

src/__tests__/integration/splits.test.ts

@@ -0,0 +1,304 @@
+import { describe, it, expect, beforeAll, afterAll, beforeEach } from "vitest";
+import type { Pool } from "pg";
+import {
+  createPool,
+  mockDbWithPool,
+  resetDB,
+  seedParticipants,
+  insertTransaction,
+} from "./helpers";
+
+/**
+ * Every split adds up to 100%.
+ *
+ * The failure this guards against is not an arithmetic one — `myShare` has
+ * always treated the payer's share as the remainder, so the numbers were right.
+ * It is that the remainder was never written down, so a 50/50 arrangement was
+ * stored as a single row reading "Sonu 50%" and displayed as half a split.
+ */
+describe("completeSplit", () => {
+  let pool: Pool;
+  let completeSplit: (id: number) => Promise<void>;
+
+  beforeAll(async () => {
+    pool = createPool();
+    mockDbWithPool(pool);
+    ({ completeSplit } = await import("@/lib/splits"));
+  });
+
+  afterAll(async () => {
+    await pool.end();
+  });
+
+  beforeEach(async () => {
+    await resetDB(pool);
+  });
+
+  const sharesOf = async (txId: number) => {
+    const r = await pool.query(
+      `SELECT participant_id, share_percent::float FROM transaction_splits
+        WHERE transaction_id = $1 ORDER BY participant_id`,
+      [txId]
+    );
+    return r.rows as { participant_id: number; share_percent: number }[];
+  };
+
+  it("writes the payer's half of a 50/50 recorded as one row", async () => {
+    const { ownerId, otherId } = await seedParticipants(pool);
+    const txId = await insertTransaction(pool, ownerId);
+    await pool.query(
+      `INSERT INTO transaction_splits (transaction_id, participant_id, share_percent)
+       VALUES ($1, $2, 50)`,
+      [txId, otherId]
+    );
+
+    await completeSplit(txId);
+
+    expect(await sharesOf(txId)).toEqual([
+      { participant_id: ownerId, share_percent: 50 },
+      { participant_id: otherId, share_percent: 50 },
+    ]);
+  });
+
+  it("leaves an unsplit transaction unsplit", async () => {
+    // A transaction nobody shares is not a 100% split of itself. Writing one
+    // would put every row in the Shared view.
+    const { ownerId } = await seedParticipants(pool);
+    const txId = await insertTransaction(pool, ownerId);
+
+    await completeSplit(txId);
+
+    expect(await sharesOf(txId)).toEqual([]);
+  });
+
+  it("adds nothing when the other party owes all of it", async () => {
+    const { ownerId, otherId } = await seedParticipants(pool);
+    const txId = await insertTransaction(pool, ownerId);
+    await pool.query(
+      `INSERT INTO transaction_splits (transaction_id, participant_id, share_percent)
+       VALUES ($1, $2, 100)`,
+      [txId, otherId]
+    );
+
+    await completeSplit(txId);
+
+    expect(await sharesOf(txId)).toEqual([
+      { participant_id: otherId, share_percent: 100 },
+    ]);
+  });
+
+  it("removes the owner's row when the others grow to cover the whole amount", async () => {
+    // A 50/50 revised to "they owe all of it". The owner's share becomes zero,
+    // and a 0% row cannot be stored anyway — `share_percent > 0` is a CHECK
+    // constraint — so the row has to go rather than be zeroed.
+    const { ownerId, otherId } = await seedParticipants(pool);
+    const txId = await insertTransaction(pool, ownerId);
+    await pool.query(
+      `INSERT INTO transaction_splits (transaction_id, participant_id, share_percent)
+       VALUES ($1, $2, 100), ($1, $3, 50)`,
+      [txId, otherId, ownerId]
+    );
+
+    await completeSplit(txId);
+
+    expect(await sharesOf(txId)).toEqual([
+      { participant_id: otherId, share_percent: 100 },
+    ]);
+  });
+
+  it("fills the remainder for a three-way split, not a half", async () => {
+    const { ownerId, otherId } = await seedParticipants(pool);
+    const third = (
+      await pool.query(`INSERT INTO participants (name) VALUES ('Carol') RETURNING id`)
+    ).rows[0].id as number;
+    const txId = await insertTransaction(pool, ownerId);
+    await pool.query(
+      `INSERT INTO transaction_splits (transaction_id, participant_id, share_percent)
+       VALUES ($1, $2, 50), ($1, $3, 25)`,
+      [txId, otherId, third]
+    );
+
+    await completeSplit(txId);
+
+    expect(await sharesOf(txId)).toEqual([
+      { participant_id: ownerId, share_percent: 25 },
+      { participant_id: otherId, share_percent: 50 },
+      { participant_id: third, share_percent: 25 },
+    ]);
+  });
+
+  it("leaves an over-allocated split alone instead of trimming someone's share", async () => {
+    // >100% is a caller's mistake. Silently deleting a share to force the total
+    // down would destroy the evidence of it.
+    // No single row may exceed 100 (CHECK constraint), but two can add up past
+    // it — 60 + 60 is how an over-allocated split actually arrives.
+    const { ownerId, otherId } = await seedParticipants(pool);
+    const third = (
+      await pool.query(`INSERT INTO participants (name) VALUES ('Dave') RETURNING id`)
+    ).rows[0].id as number;
+    const txId = await insertTransaction(pool, ownerId);
+    await pool.query(
+      `INSERT INTO transaction_splits (transaction_id, participant_id, share_percent)
+       VALUES ($1, $2, 60), ($1, $3, 60)`,
+      [txId, otherId, third]
+    );
+
+    await completeSplit(txId);
+
+    expect(await sharesOf(txId)).toEqual([
+      { participant_id: otherId, share_percent: 60 },
+      { participant_id: third, share_percent: 60 },
+    ]);
+  });
+
+  it("gives the remainder to the statement's owner when the row has none", async () => {
+    // Statement rows carry no owner_id of their own; it comes from the
+    // statement. Transaction 3828 was one of these.
+    const { ownerId, otherId } = await seedParticipants(pool);
+    const stmt = await pool.query(
+      `INSERT INTO statements (owner_id, filename, bank_name, account_number, billing_start_date, billing_end_date)
+       VALUES ($1, 'test.pdf', 'Test Bank', '0001', '2026-06-01', '2026-06-30') RETURNING id`,
+      [ownerId]
+    );
+    const tx = await pool.query(
+      `INSERT INTO transactions (owner_id, statement_id, transaction_date, description, amount, transaction_type, row_index)
+       VALUES (NULL, $1, '2026-06-15', 'Statement row', 29.17, 'debit', 0) RETURNING id`,
+      [stmt.rows[0].id]
+    );
+    const txId = tx.rows[0].id as number;
+    await pool.query(
+      `INSERT INTO transaction_splits (transaction_id, participant_id, share_percent)
+       VALUES ($1, $2, 50)`,
+      [txId, otherId]
+    );
+
+    await completeSplit(txId);
+
+    expect(await sharesOf(txId)).toEqual([
+      { participant_id: ownerId, share_percent: 50 },
+      { participant_id: otherId, share_percent: 50 },
+    ]);
+  });
+
+  it("never puts my share on someone else's transaction", async () => {
+    // The remainder goes to the transaction's owner, never to "me". A row for
+    // me on a transaction I do not own is a debt I owe, and this helper must
+    // not invent one.
+    const { ownerId, otherId } = await seedParticipants(pool);
+    const txId = await insertTransaction(pool, otherId); // they paid
+    await pool.query(
+      `INSERT INTO transaction_splits (transaction_id, participant_id, share_percent)
+       VALUES ($1, $2, 50)`,
+      [txId, ownerId]
+    );
+
+    await completeSplit(txId);
+
+    const shares = await sharesOf(txId);
+    expect(shares).toEqual([
+      { participant_id: ownerId, share_percent: 50 },
+      { participant_id: otherId, share_percent: 50 },
+    ]);
+    // My share is unchanged — the new row belongs to the payer.
+    expect(shares.find((s) => s.participant_id === ownerId)?.share_percent).toBe(50);
+  });
+
+  it("does not disturb a settled split", async () => {
+    // Adding the payer's row must not touch anyone else's `settled` flag —
+    // that is how $37k of discharged debt gets resurrected.
+    const { ownerId, otherId } = await seedParticipants(pool);
+    const txId = await insertTransaction(pool, ownerId);
+    await pool.query(
+      `INSERT INTO transaction_splits (transaction_id, participant_id, share_percent, settled)
+       VALUES ($1, $2, 50, true)`,
+      [txId, otherId]
+    );
+
+    await completeSplit(txId);
+
+    const r = await pool.query(
+      `SELECT settled FROM transaction_splits
+        WHERE transaction_id = $1 AND participant_id = $2`,
+      [txId, otherId]
+    );
+    expect(r.rows[0].settled).toBe(true);
+  });
+
+  it("is idempotent", async () => {
+    const { ownerId, otherId } = await seedParticipants(pool);
+    const txId = await insertTransaction(pool, ownerId);
+    await pool.query(
+      `INSERT INTO transaction_splits (transaction_id, participant_id, share_percent)
+       VALUES ($1, $2, 50)`,
+      [txId, otherId]
+    );
+
+    await completeSplit(txId);
+    const once = await sharesOf(txId);
+    await completeSplit(txId);
+    expect(await sharesOf(txId)).toEqual(once);
+  });
+});
+
+/**
+ * The rule path, which is where ten of the live rules write a single share.
+ */
+describe("applyRuleActions completes the split", () => {
+  let pool: Pool;
+  let applyRuleActions: (
+    id: number,
+    actions: { apply_split?: { participant_id: number; share_percent: number }[] }
+  ) => Promise<void>;
+
+  beforeAll(async () => {
+    pool = createPool();
+    mockDbWithPool(pool);
+    ({ applyRuleActions } = await import("@/lib/rule-actions"));
+  });
+
+  afterAll(async () => {
+    await pool.end();
+  });
+
+  beforeEach(async () => {
+    await resetDB(pool);
+  });
+
+  it("writes the payer's half for a rule that names only the other person", async () => {
+    const { ownerId, otherId } = await seedParticipants(pool);
+    const txId = await insertTransaction(pool, ownerId, { description: "Woolworths" });
+
+    await applyRuleActions(txId, {
+      apply_split: [{ participant_id: otherId, share_percent: 50 }],
+    });
+
+    const r = await pool.query(
+      `SELECT participant_id, share_percent::float FROM transaction_splits
+        WHERE transaction_id = $1 ORDER BY participant_id`,
+      [txId]
+    );
+    expect(r.rows).toEqual([
+      { participant_id: ownerId, share_percent: 50 },
+      { participant_id: otherId, share_percent: 50 },
+    ]);
+  });
+
+  it("leaves a rule that already names both alone", async () => {
+    const { ownerId, otherId } = await seedParticipants(pool);
+    const txId = await insertTransaction(pool, ownerId);
+
+    await applyRuleActions(txId, {
+      apply_split: [
+        { participant_id: ownerId, share_percent: 50 },
+        { participant_id: otherId, share_percent: 50 },
+      ],
+    });
+
+    const r = await pool.query(
+      `SELECT sum(share_percent)::float AS total, count(*)::int AS n
+         FROM transaction_splits WHERE transaction_id = $1`,
+      [txId]
+    );
+    expect(r.rows[0]).toEqual({ total: 100, n: 2 });
+  });
+});