Splitting $10.00 three ways loses a cent (#26)

[Param-Harrison]

Closes #26

Summary

splitCents rounded every share down and dropped the leftover, so 1000 cents split 3 ways came to 333/333/333 (999 in total). It now applies the remainder rule from .claude/skills/handling-money/references/rules.md: base = floor(total / n), and the first total - base * n members, in the order passed in, each get base + 1. Shares now always add up to the total. Only src/money/cents.ts and tests/money.test.ts changed.

Acceptance criteria

AC	Evidence (command / test)	Result
AC-1	bun test tests/money.test.ts: splitCents > gives the leftover cent to the first member when splitting 1000 three ways (1000 → {a:334,b:333,c:333})	pass
AC-2	bun test tests/money.test.ts: splitCents > assigns leftover cents so the shares sum to the total (101/5 → {a:21,b:20,c:20,d:20,e:20})	pass
AC-3	bun test tests/money.test.ts: splitCents > gives leftover cents to the first members in member order (["c","a","d","b"], 1002 → {c:251,a:251,d:250,b:250})	pass
AC-4	bun test tests/money.test.ts: splitCents > splits a total smaller than the member count one cent at a time (2/5 → {a:1,b:1,c:0,d:0,e:0})	pass
AC-5	The 6 original tests pass unmodified, and git diff main -- tests/money.test.ts only adds lines. The zero-member throw was checked directly with bun -e "splitCents(100, [])", which printed cannot split among zero members	pass
AC-6	bun run .claude/skills/handling-money/scripts/check-cents.ts: [ok ] for all 4 cases, exit 0	pass
AC-7	make check: tsc clean, 30 pass / 0 fail, all 9 skills valid, exit 0	pass

Full evidence is in the verdict comment on #26.

Non-goals respected

• NG-1: No signature or return-type changes. formatCents, parseCents and sumCents were not edited.
• NG-2: No edits to src/expenses.ts, src/balances.ts, src/routes/**, src/db.ts or the schema.
• NG-3: No protected paths touched.
• NG-4: No new handling or validation for negative or non-integer totals.
• NG-5: Tests were only added. None were deleted or weakened.
• NG-6: Expense shares already in the database are not repaired or migrated.
• NG-7: Leftover cents are assigned only by position in the input array (i < remainder), not by payer, amount or ID.

The test that bites

• Test: splitCents > splits a total smaller than the member count one cent at a time
• Fails on main: with main's src/money/cents.ts and this branch's tests, bun test tests/money.test.ts gives 6 pass / 4 fail. This test expected a: 1, b: 1 and got a: 0, b: 0, and the other three new tests fail too.
• Passes here: bun test tests/money.test.ts gives 10 pass / 0 fail.

Gate line

FACTORY_GATES: status=GREEN passed=3 failed=0 skipped=1 failed_gates=audit

audit is required: false in .factory/config.json. It fails because of Hono advisories that already exist on main, not because of this diff.

Protected paths touched

none

Reviewer findings addressed

Both findings are non-blocking, predate this diff and were left out of scope:

• splitCents stores shares in a Record keyed by member ID, so duplicate member IDs collapse into one entry and the shares no longer add up to the total. This needs its own follow-up issue.
• No test asserts that a split among zero members throws. It was checked by hand for AC-5 (see above). Adding that test could go in the same follow-up.

Human checklist

• AC table has real evidence, not placeholders
• Non-goals respected
• Gate line is GREEN
• Protected paths are "none", or the change to them is expected and reviewed
• I ran the test that bites myself

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