FA-58151 / Double-entry ledger accounting / Open access
Cost pool allocation entry: remainder tie-break · case 01
The spare cent goes to the last of several equally entitled centers.
ROOT CAUSE
Equal remainders are broken in reverse listing order.
VERIFIED REPAIR
Break remainder ties by listing order, earlier first.
Unsuccessful approach: Breaking ties by center name only matches listing order by accident.
Case contract
x = {'amount': signed cents, 'weights': [[center, non-negative weight]] (some positive), 'source': account}. The pool magnitude is split across positive-weight centers by the largest remainder method: floor shares, then one extra cent to the largest remainders, ties to the earlier-listed center. A non-negative amount credits the source and debits centers; a negative amount (reversal) debits the source and credits centers, all amounts positive. Return lines [[source, side, magnitude]] + [[center, side, share]] for nonzero shares in listing order.
Why this case matters
Ledger software must keep debits equal to credits and apply normal-balance, period and cutoff rules exactly; small sign or boundary slips silently misstate financial statements.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
amt = x['amount']
side_src, side_dst = ('C', 'D') if amt >= 0 else ('D', 'C')
mag = abs(amt)
ws = [(c, w) for c, w in x['weights'] if w > 0]
total = sum(w for _, w in ws)
base = [mag * w // total for _, w in ws]
rems = [mag * w % total for _, w in ws]
left = mag - sum(base)
order = sorted(range(len(ws)), key=lambda i: (-rems[i], -i))
for i in order[:left]:
base[i] += 1
lines = [[x['source'], side_src, mag]]
for (c, w), share in zip(ws, base):
if share:
lines.append([c, side_dst, share])
return lines
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: remainder tie-break', {'amount': 7, 'weights': [['fin', 0], ['it', 7], ['hr', 2], ['lab', 3], ['ops', 2]], 'source': 'pool'}, [['pool', 'C', 7], ['it', 'D', 4], ['hr', 'D', 1], ['lab', 'D', 1], ['ops', 'D', 1]]], ['regression: remainder tie-break, partial-repair probe', {'amount': 10, 'weights': [['mkt', 1], ['ops', 7], ['lab', 1], ['it', 5], ['hr', 1]], 'source': 'pool'}, [['pool', 'C', 10], ['mkt', 'D', 1], ['ops', 'D', 5], ['lab', 'D', 1], ['it', 'D', 3]]], ['control 1', {'amount': 7, 'weights': [['mkt', 0], ['fin', 1]], 'source': 'pool'}, [['pool', 'C', 7], ['fin', 'D', 7]]], ['control 2', {'amount': 99999, 'weights': [['hr', 1], ['it', 0]], 'source': 'pool'}, [['pool', 'C', 99999], ['hr', 'D', 99999]]], ['control 3', {'amount': 0, 'weights': [['ops', 3], ['mkt', 7], ['fin', 3], ['lab', 5]], 'source': 'pool'}, [['pool', 'C', 0]]], ['control 4', {'amount': 100, 'weights': [['ops', 5], ['it', 5]], 'source': 'pool'}, [['pool', 'C', 100], ['ops', 'D', 50], ['it', 'D', 50]]], ['control 5', {'amount': 0, 'weights': [['ops', 5], ['hr', 5], ['mkt', 7], ['fin', 3]], 'source': 'pool'}, [['pool', 'C', 0]]]], [['regression: remainder tie-break', {'amount': 3, 'weights': [['it', 0], ['hr', 0], ['fin', 2], ['ops', 2]], 'source': 'pool'}, [['pool', 'C', 3], ['fin', 'D', 2], ['ops', 'D', 1]]], ['regression: remainder tie-break, partial-repair probe', {'amount': 101, 'weights': [['it', 3], ['mkt', 0], ['lab', 7], ['hr', 7]], 'source': 'pool'}, [['pool', 'C', 101], ['it', 'D', 18], ['lab', 'D', 42], ['hr', 'D', 41]]], ['control 1', {'amount': 7, 'weights': [['mkt', 0], ['it', 7], ['ops', 2], ['fin', 2], ['lab', 1]], 'source': 'pool'}, [['pool', 'C', 7], ['it', 'D', 4], ['ops', 'D', 1], ['fin', 'D', 1], ['lab', 'D', 1]]], ['control 2', {'amount': 0, 'weights': [['it', 3], ['lab', 1], ['mkt', 0]], 'source': 'pool'}, [['pool', 'C', 0]]], ['control 3', {'amount': 101, 'weights': [['lab', 7], ['hr', 5]], 'source': 'pool'}, [['pool', 'C', 101], ['lab', 'D', 59], ['hr', 'D', 42]]], ['control 4', {'amount': 10, 'weights': [['lab', 1], ['it', 3], ['hr', 1], ['ops', 7], ['mkt', 0]], 'source': 'pool'}, [['pool', 'C', 10], ['lab', 'D', 1], ['it', 'D', 2], ['hr', 'D', 1], ['ops', 'D', 6]]], ['control 5', {'amount': 10, 'weights': [['mkt', 1], ['it', 2], ['fin', 1], ['hr', 7]], 'source': 'pool'}, [['pool', 'C', 10], ['mkt', 'D', 1], ['it', 'D', 2], ['fin', 'D', 1], ['hr', 'D', 6]]]], [['regression: remainder tie-break', {'amount': 1000, 'weights': [['ops', 7], ['mkt', 5], ['fin', 7]], 'source': 'pool'}, [['pool', 'C', 1000], ['ops', 'D', 369], ['mkt', 'D', 263], ['fin', 'D', 368]]], ['control 1', {'amount': 7, 'weights': [['fin', 1], ['mkt', 5]], 'source': 'pool'}, [['pool', 'C', 7], ['fin', 'D', 1], ['mkt', 'D', 6]]], ['control 2', {'amount': 7, 'weights': [['it', 0], ['lab', 7], ['mkt', 1], ['hr', 3]], 'source': 'pool'}, [['pool', 'C', 7], ['lab', 'D', 4], ['mkt', 'D', 1], ['hr', 'D', 2]]], ['control 3', {'amount': 3, 'weights': [['it', 7], ['hr', 1]], 'source': 'pool'}, [['pool', 'C', 3], ['it', 'D', 3]]], ['control 4', {'amount': 10, 'weights': [['ops', 3], ['lab', 5]], 'source': 'pool'}, [['pool', 'C', 10], ['ops', 'D', 4], ['lab', 'D', 6]]], ['control 5', {'amount': 10, 'weights': [['ops', 1], ['lab', 5]], 'source': 'pool'}, [['pool', 'C', 10], ['ops', 'D', 2], ['lab', 'D', 8]]], ['control 6', {'amount': 0, 'weights': [['it', 7], ['ops', 7], ['lab', 5], ['hr', 7]], 'source': 'pool'}, [['pool', 'C', 0]]]], [['regression: remainder tie-break', {'amount': -101, 'weights': [['fin', 7], ['mkt', 0], ['hr', 3], ['it', 7], ['ops', 7]], 'source': 'pool'}, [['pool', 'D', 101], ['fin', 'C', 30], ['hr', 'C', 13], ['it', 'C', 29], ['ops', 'C', 29]]], ['regression: remainder tie-break, partial-repair probe', {'amount': 1000, 'weights': [['fin', 7], ['mkt', 3], ['it', 3], ['lab', 1], ['hr', 2]], 'source': 'pool'}, [['pool', 'C', 1000], ['fin', 'D', 438], ['mkt', 'D', 188], ['it', 'D', 187], ['lab', 'D', 62], ['hr', 'D', 125]]], ['control 1', {'amount': -7, 'weights': [['lab', 2], ['ops', 7], ['mkt', 2]], 'source': 'pool'}, [['pool', 'D', 7], ['lab', 'C', 1], ['ops', 'C', 5], ['mkt', 'C', 1]]], ['control 2', {'amount': -101, 'weights': [['it', 5], ['ops', 7]], 'source': 'pool'}, [['pool', 'D', 101], ['it', 'C', 42], ['ops', 'C', 59]]], ['control 3', {'amount': 100, 'weights': [['it', 7], ['fin', 3], ['mkt', 7], ['hr', 1]], 'source': 'pool'}, [['pool', 'C', 100], ['it', 'D', 39], ['fin', 'D', 17], ['mkt', 'D', 39], ['hr', 'D', 5]]], ['control 4', {'amount': 10, 'weights': [['lab', 2], ['it', 5], ['hr', 7], ['mkt', 0], ['ops', 7]], 'source': 'pool'}, [['pool', 'C', 10], ['lab', 'D', 1], ['it', 'D', 3], ['hr', 'D', 3], ['ops', 'D', 3]]], ['control 5', {'amount': 3, 'weights': [['it', 3], ['lab', 3], ['hr', 7]], 'source': 'pool'}, [['pool', 'C', 3], ['it', 'D', 1], ['lab', 'D', 1], ['hr', 'D', 1]]]], [['regression: remainder tie-break', {'amount': 101, 'weights': [['fin', 2], ['hr', 2]], 'source': 'pool'}, [['pool', 'C', 101], ['fin', 'D', 51], ['hr', 'D', 50]]], ['regression: remainder tie-break, partial-repair probe', {'amount': -101, 'weights': [['ops', 2], ['hr', 2], ['lab', 7], ['it', 1], ['fin', 1]], 'source': 'pool'}, [['pool', 'D', 101], ['ops', 'C', 16], ['hr', 'C', 15], ['lab', 'C', 54], ['it', 'C', 8], ['fin', 'C', 8]]], ['control 1', {'amount': 100, 'weights': [['fin', 2], ['hr', 0], ['it', 0], ['mkt', 0]], 'source': 'pool'}, [['pool', 'C', 100], ['fin', 'D', 100]]], ['control 2', {'amount': 10, 'weights': [['ops', 3], ['it', 1], ['mkt', 3], ['hr', 0]], 'source': 'pool'}, [['pool', 'C', 10], ['ops', 'D', 4], ['it', 'D', 2], ['mkt', 'D', 4]]], ['control 3', {'amount': -7, 'weights': [['fin', 3], ['mkt', 1]], 'source': 'pool'}, [['pool', 'D', 7], ['fin', 'C', 5], ['mkt', 'C', 2]]], ['control 4', {'amount': 7, 'weights': [['mkt', 1], ['it', 0]], 'source': 'pool'}, [['pool', 'C', 7], ['mkt', 'D', 7]]], ['control 5', {'amount': 10, 'weights': [['mkt', 1], ['it', 7], ['fin', 0], ['ops', 1]], 'source': 'pool'}, [['pool', 'C', 10], ['mkt', 'D', 1], ['it', 'D', 8], ['ops', 'D', 1]]]]]
for label, args, expected in fixtures[N-1]:
try:
actual = solve(args)
except Exception as exc:
actual = 'raised ' + type(exc).__name__
check(label, actual, expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: remainder tie-break | [['pool', 'C', 7], ['it', 'D', 3], ['hr', 'D', 1], ['lab', 'D', 2], ['ops', 'D', 1]] | [['pool', 'C', 7], ['it', 'D', 4], ['hr', 'D', 1], ['lab', 'D', 1], ['ops', 'D', 1]] | Failed |
| regression: remainder tie-break, partial-repair probe | [['pool', 'C', 10], ['ops', 'D', 5], ['lab', 'D', 1], ['it', 'D', 3], ['hr', 'D', 1]] | [['pool', 'C', 10], ['mkt', 'D', 1], ['ops', 'D', 5], ['lab', 'D', 1], ['it', 'D', 3]] | Failed |
| control 1 | [['pool', 'C', 7], ['fin', 'D', 7]] | [['pool', 'C', 7], ['fin', 'D', 7]] | Passed |
| control 2 | [['pool', 'C', 99999], ['hr', 'D', 99999]] | [['pool', 'C', 99999], ['hr', 'D', 99999]] | Passed |
| control 3 | [['pool', 'C', 0]] | [['pool', 'C', 0]] | Passed |
| control 4 | [['pool', 'C', 100], ['ops', 'D', 50], ['it', 'D', 50]] | [['pool', 'C', 100], ['ops', 'D', 50], ['it', 'D', 50]] | Passed |
| control 5 | [['pool', 'C', 0]] | [['pool', 'C', 0]] | Passed |
SHA-256 / 0f1dcb374faae944d8ebac2866f494307043bcb4224d6f5f8548c0bb0500456e
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
amt = x['amount']
side_src, side_dst = ('C', 'D') if amt >= 0 else ('D', 'C')
mag = abs(amt)
ws = [(c, w) for c, w in x['weights'] if w > 0]
total = sum(w for _, w in ws)
base = [mag * w // total for _, w in ws]
rems = [mag * w % total for _, w in ws]
left = mag - sum(base)
order = sorted(range(len(ws)), key=lambda i: (-rems[i], ws[i][0]))
for i in order[:left]:
base[i] += 1
lines = [[x['source'], side_src, mag]]
for (c, w), share in zip(ws, base):
if share:
lines.append([c, side_dst, share])
return lines
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: remainder tie-break', {'amount': 7, 'weights': [['fin', 0], ['it', 7], ['hr', 2], ['lab', 3], ['ops', 2]], 'source': 'pool'}, [['pool', 'C', 7], ['it', 'D', 4], ['hr', 'D', 1], ['lab', 'D', 1], ['ops', 'D', 1]]], ['regression: remainder tie-break, partial-repair probe', {'amount': 10, 'weights': [['mkt', 1], ['ops', 7], ['lab', 1], ['it', 5], ['hr', 1]], 'source': 'pool'}, [['pool', 'C', 10], ['mkt', 'D', 1], ['ops', 'D', 5], ['lab', 'D', 1], ['it', 'D', 3]]], ['control 1', {'amount': 7, 'weights': [['mkt', 0], ['fin', 1]], 'source': 'pool'}, [['pool', 'C', 7], ['fin', 'D', 7]]], ['control 2', {'amount': 99999, 'weights': [['hr', 1], ['it', 0]], 'source': 'pool'}, [['pool', 'C', 99999], ['hr', 'D', 99999]]], ['control 3', {'amount': 0, 'weights': [['ops', 3], ['mkt', 7], ['fin', 3], ['lab', 5]], 'source': 'pool'}, [['pool', 'C', 0]]], ['control 4', {'amount': 100, 'weights': [['ops', 5], ['it', 5]], 'source': 'pool'}, [['pool', 'C', 100], ['ops', 'D', 50], ['it', 'D', 50]]], ['control 5', {'amount': 0, 'weights': [['ops', 5], ['hr', 5], ['mkt', 7], ['fin', 3]], 'source': 'pool'}, [['pool', 'C', 0]]]], [['regression: remainder tie-break', {'amount': 3, 'weights': [['it', 0], ['hr', 0], ['fin', 2], ['ops', 2]], 'source': 'pool'}, [['pool', 'C', 3], ['fin', 'D', 2], ['ops', 'D', 1]]], ['regression: remainder tie-break, partial-repair probe', {'amount': 101, 'weights': [['it', 3], ['mkt', 0], ['lab', 7], ['hr', 7]], 'source': 'pool'}, [['pool', 'C', 101], ['it', 'D', 18], ['lab', 'D', 42], ['hr', 'D', 41]]], ['control 1', {'amount': 7, 'weights': [['mkt', 0], ['it', 7], ['ops', 2], ['fin', 2], ['lab', 1]], 'source': 'pool'}, [['pool', 'C', 7], ['it', 'D', 4], ['ops', 'D', 1], ['fin', 'D', 1], ['lab', 'D', 1]]], ['control 2', {'amount': 0, 'weights': [['it', 3], ['lab', 1], ['mkt', 0]], 'source': 'pool'}, [['pool', 'C', 0]]], ['control 3', {'amount': 101, 'weights': [['lab', 7], ['hr', 5]], 'source': 'pool'}, [['pool', 'C', 101], ['lab', 'D', 59], ['hr', 'D', 42]]], ['control 4', {'amount': 10, 'weights': [['lab', 1], ['it', 3], ['hr', 1], ['ops', 7], ['mkt', 0]], 'source': 'pool'}, [['pool', 'C', 10], ['lab', 'D', 1], ['it', 'D', 2], ['hr', 'D', 1], ['ops', 'D', 6]]], ['control 5', {'amount': 10, 'weights': [['mkt', 1], ['it', 2], ['fin', 1], ['hr', 7]], 'source': 'pool'}, [['pool', 'C', 10], ['mkt', 'D', 1], ['it', 'D', 2], ['fin', 'D', 1], ['hr', 'D', 6]]]], [['regression: remainder tie-break', {'amount': 1000, 'weights': [['ops', 7], ['mkt', 5], ['fin', 7]], 'source': 'pool'}, [['pool', 'C', 1000], ['ops', 'D', 369], ['mkt', 'D', 263], ['fin', 'D', 368]]], ['control 1', {'amount': 7, 'weights': [['fin', 1], ['mkt', 5]], 'source': 'pool'}, [['pool', 'C', 7], ['fin', 'D', 1], ['mkt', 'D', 6]]], ['control 2', {'amount': 7, 'weights': [['it', 0], ['lab', 7], ['mkt', 1], ['hr', 3]], 'source': 'pool'}, [['pool', 'C', 7], ['lab', 'D', 4], ['mkt', 'D', 1], ['hr', 'D', 2]]], ['control 3', {'amount': 3, 'weights': [['it', 7], ['hr', 1]], 'source': 'pool'}, [['pool', 'C', 3], ['it', 'D', 3]]], ['control 4', {'amount': 10, 'weights': [['ops', 3], ['lab', 5]], 'source': 'pool'}, [['pool', 'C', 10], ['ops', 'D', 4], ['lab', 'D', 6]]], ['control 5', {'amount': 10, 'weights': [['ops', 1], ['lab', 5]], 'source': 'pool'}, [['pool', 'C', 10], ['ops', 'D', 2], ['lab', 'D', 8]]], ['control 6', {'amount': 0, 'weights': [['it', 7], ['ops', 7], ['lab', 5], ['hr', 7]], 'source': 'pool'}, [['pool', 'C', 0]]]], [['regression: remainder tie-break', {'amount': -101, 'weights': [['fin', 7], ['mkt', 0], ['hr', 3], ['it', 7], ['ops', 7]], 'source': 'pool'}, [['pool', 'D', 101], ['fin', 'C', 30], ['hr', 'C', 13], ['it', 'C', 29], ['ops', 'C', 29]]], ['regression: remainder tie-break, partial-repair probe', {'amount': 1000, 'weights': [['fin', 7], ['mkt', 3], ['it', 3], ['lab', 1], ['hr', 2]], 'source': 'pool'}, [['pool', 'C', 1000], ['fin', 'D', 438], ['mkt', 'D', 188], ['it', 'D', 187], ['lab', 'D', 62], ['hr', 'D', 125]]], ['control 1', {'amount': -7, 'weights': [['lab', 2], ['ops', 7], ['mkt', 2]], 'source': 'pool'}, [['pool', 'D', 7], ['lab', 'C', 1], ['ops', 'C', 5], ['mkt', 'C', 1]]], ['control 2', {'amount': -101, 'weights': [['it', 5], ['ops', 7]], 'source': 'pool'}, [['pool', 'D', 101], ['it', 'C', 42], ['ops', 'C', 59]]], ['control 3', {'amount': 100, 'weights': [['it', 7], ['fin', 3], ['mkt', 7], ['hr', 1]], 'source': 'pool'}, [['pool', 'C', 100], ['it', 'D', 39], ['fin', 'D', 17], ['mkt', 'D', 39], ['hr', 'D', 5]]], ['control 4', {'amount': 10, 'weights': [['lab', 2], ['it', 5], ['hr', 7], ['mkt', 0], ['ops', 7]], 'source': 'pool'}, [['pool', 'C', 10], ['lab', 'D', 1], ['it', 'D', 3], ['hr', 'D', 3], ['ops', 'D', 3]]], ['control 5', {'amount': 3, 'weights': [['it', 3], ['lab', 3], ['hr', 7]], 'source': 'pool'}, [['pool', 'C', 3], ['it', 'D', 1], ['lab', 'D', 1], ['hr', 'D', 1]]]], [['regression: remainder tie-break', {'amount': 101, 'weights': [['fin', 2], ['hr', 2]], 'source': 'pool'}, [['pool', 'C', 101], ['fin', 'D', 51], ['hr', 'D', 50]]], ['regression: remainder tie-break, partial-repair probe', {'amount': -101, 'weights': [['ops', 2], ['hr', 2], ['lab', 7], ['it', 1], ['fin', 1]], 'source': 'pool'}, [['pool', 'D', 101], ['ops', 'C', 16], ['hr', 'C', 15], ['lab', 'C', 54], ['it', 'C', 8], ['fin', 'C', 8]]], ['control 1', {'amount': 100, 'weights': [['fin', 2], ['hr', 0], ['it', 0], ['mkt', 0]], 'source': 'pool'}, [['pool', 'C', 100], ['fin', 'D', 100]]], ['control 2', {'amount': 10, 'weights': [['ops', 3], ['it', 1], ['mkt', 3], ['hr', 0]], 'source': 'pool'}, [['pool', 'C', 10], ['ops', 'D', 4], ['it', 'D', 2], ['mkt', 'D', 4]]], ['control 3', {'amount': -7, 'weights': [['fin', 3], ['mkt', 1]], 'source': 'pool'}, [['pool', 'D', 7], ['fin', 'C', 5], ['mkt', 'C', 2]]], ['control 4', {'amount': 7, 'weights': [['mkt', 1], ['it', 0]], 'source': 'pool'}, [['pool', 'C', 7], ['mkt', 'D', 7]]], ['control 5', {'amount': 10, 'weights': [['mkt', 1], ['it', 7], ['fin', 0], ['ops', 1]], 'source': 'pool'}, [['pool', 'C', 10], ['mkt', 'D', 1], ['it', 'D', 8], ['ops', 'D', 1]]]]]
for label, args, expected in fixtures[N-1]:
try:
actual = solve(args)
except Exception as exc:
actual = 'raised ' + type(exc).__name__
check(label, actual, expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: remainder tie-break | [['pool', 'C', 7], ['it', 'D', 4], ['hr', 'D', 1], ['lab', 'D', 1], ['ops', 'D', 1]] | [['pool', 'C', 7], ['it', 'D', 4], ['hr', 'D', 1], ['lab', 'D', 1], ['ops', 'D', 1]] | Passed |
| regression: remainder tie-break, partial-repair probe | [['pool', 'C', 10], ['mkt', 'D', 1], ['ops', 'D', 4], ['lab', 'D', 1], ['it', 'D', 3], ['hr', 'D', 1]] | [['pool', 'C', 10], ['mkt', 'D', 1], ['ops', 'D', 5], ['lab', 'D', 1], ['it', 'D', 3]] | Failed |
| control 1 | [['pool', 'C', 7], ['fin', 'D', 7]] | [['pool', 'C', 7], ['fin', 'D', 7]] | Passed |
| control 2 | [['pool', 'C', 99999], ['hr', 'D', 99999]] | [['pool', 'C', 99999], ['hr', 'D', 99999]] | Passed |
| control 3 | [['pool', 'C', 0]] | [['pool', 'C', 0]] | Passed |
| control 4 | [['pool', 'C', 100], ['ops', 'D', 50], ['it', 'D', 50]] | [['pool', 'C', 100], ['ops', 'D', 50], ['it', 'D', 50]] | Passed |
| control 5 | [['pool', 'C', 0]] | [['pool', 'C', 0]] | Passed |
SHA-256 / da15b119b9e905b71b1caee209a0e9af91a0787ac597784a7077c03b511107e7
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
amt = x['amount']
side_src, side_dst = ('C', 'D') if amt >= 0 else ('D', 'C')
mag = abs(amt)
ws = [(c, w) for c, w in x['weights'] if w > 0]
total = sum(w for _, w in ws)
base = [mag * w // total for _, w in ws]
rems = [mag * w % total for _, w in ws]
left = mag - sum(base)
order = sorted(range(len(ws)), key=lambda i: (-rems[i], i))
for i in order[:left]:
base[i] += 1
lines = [[x['source'], side_src, mag]]
for (c, w), share in zip(ws, base):
if share:
lines.append([c, side_dst, share])
return lines
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: remainder tie-break', {'amount': 7, 'weights': [['fin', 0], ['it', 7], ['hr', 2], ['lab', 3], ['ops', 2]], 'source': 'pool'}, [['pool', 'C', 7], ['it', 'D', 4], ['hr', 'D', 1], ['lab', 'D', 1], ['ops', 'D', 1]]], ['regression: remainder tie-break, partial-repair probe', {'amount': 10, 'weights': [['mkt', 1], ['ops', 7], ['lab', 1], ['it', 5], ['hr', 1]], 'source': 'pool'}, [['pool', 'C', 10], ['mkt', 'D', 1], ['ops', 'D', 5], ['lab', 'D', 1], ['it', 'D', 3]]], ['control 1', {'amount': 7, 'weights': [['mkt', 0], ['fin', 1]], 'source': 'pool'}, [['pool', 'C', 7], ['fin', 'D', 7]]], ['control 2', {'amount': 99999, 'weights': [['hr', 1], ['it', 0]], 'source': 'pool'}, [['pool', 'C', 99999], ['hr', 'D', 99999]]], ['control 3', {'amount': 0, 'weights': [['ops', 3], ['mkt', 7], ['fin', 3], ['lab', 5]], 'source': 'pool'}, [['pool', 'C', 0]]], ['control 4', {'amount': 100, 'weights': [['ops', 5], ['it', 5]], 'source': 'pool'}, [['pool', 'C', 100], ['ops', 'D', 50], ['it', 'D', 50]]], ['control 5', {'amount': 0, 'weights': [['ops', 5], ['hr', 5], ['mkt', 7], ['fin', 3]], 'source': 'pool'}, [['pool', 'C', 0]]]], [['regression: remainder tie-break', {'amount': 3, 'weights': [['it', 0], ['hr', 0], ['fin', 2], ['ops', 2]], 'source': 'pool'}, [['pool', 'C', 3], ['fin', 'D', 2], ['ops', 'D', 1]]], ['regression: remainder tie-break, partial-repair probe', {'amount': 101, 'weights': [['it', 3], ['mkt', 0], ['lab', 7], ['hr', 7]], 'source': 'pool'}, [['pool', 'C', 101], ['it', 'D', 18], ['lab', 'D', 42], ['hr', 'D', 41]]], ['control 1', {'amount': 7, 'weights': [['mkt', 0], ['it', 7], ['ops', 2], ['fin', 2], ['lab', 1]], 'source': 'pool'}, [['pool', 'C', 7], ['it', 'D', 4], ['ops', 'D', 1], ['fin', 'D', 1], ['lab', 'D', 1]]], ['control 2', {'amount': 0, 'weights': [['it', 3], ['lab', 1], ['mkt', 0]], 'source': 'pool'}, [['pool', 'C', 0]]], ['control 3', {'amount': 101, 'weights': [['lab', 7], ['hr', 5]], 'source': 'pool'}, [['pool', 'C', 101], ['lab', 'D', 59], ['hr', 'D', 42]]], ['control 4', {'amount': 10, 'weights': [['lab', 1], ['it', 3], ['hr', 1], ['ops', 7], ['mkt', 0]], 'source': 'pool'}, [['pool', 'C', 10], ['lab', 'D', 1], ['it', 'D', 2], ['hr', 'D', 1], ['ops', 'D', 6]]], ['control 5', {'amount': 10, 'weights': [['mkt', 1], ['it', 2], ['fin', 1], ['hr', 7]], 'source': 'pool'}, [['pool', 'C', 10], ['mkt', 'D', 1], ['it', 'D', 2], ['fin', 'D', 1], ['hr', 'D', 6]]]], [['regression: remainder tie-break', {'amount': 1000, 'weights': [['ops', 7], ['mkt', 5], ['fin', 7]], 'source': 'pool'}, [['pool', 'C', 1000], ['ops', 'D', 369], ['mkt', 'D', 263], ['fin', 'D', 368]]], ['control 1', {'amount': 7, 'weights': [['fin', 1], ['mkt', 5]], 'source': 'pool'}, [['pool', 'C', 7], ['fin', 'D', 1], ['mkt', 'D', 6]]], ['control 2', {'amount': 7, 'weights': [['it', 0], ['lab', 7], ['mkt', 1], ['hr', 3]], 'source': 'pool'}, [['pool', 'C', 7], ['lab', 'D', 4], ['mkt', 'D', 1], ['hr', 'D', 2]]], ['control 3', {'amount': 3, 'weights': [['it', 7], ['hr', 1]], 'source': 'pool'}, [['pool', 'C', 3], ['it', 'D', 3]]], ['control 4', {'amount': 10, 'weights': [['ops', 3], ['lab', 5]], 'source': 'pool'}, [['pool', 'C', 10], ['ops', 'D', 4], ['lab', 'D', 6]]], ['control 5', {'amount': 10, 'weights': [['ops', 1], ['lab', 5]], 'source': 'pool'}, [['pool', 'C', 10], ['ops', 'D', 2], ['lab', 'D', 8]]], ['control 6', {'amount': 0, 'weights': [['it', 7], ['ops', 7], ['lab', 5], ['hr', 7]], 'source': 'pool'}, [['pool', 'C', 0]]]], [['regression: remainder tie-break', {'amount': -101, 'weights': [['fin', 7], ['mkt', 0], ['hr', 3], ['it', 7], ['ops', 7]], 'source': 'pool'}, [['pool', 'D', 101], ['fin', 'C', 30], ['hr', 'C', 13], ['it', 'C', 29], ['ops', 'C', 29]]], ['regression: remainder tie-break, partial-repair probe', {'amount': 1000, 'weights': [['fin', 7], ['mkt', 3], ['it', 3], ['lab', 1], ['hr', 2]], 'source': 'pool'}, [['pool', 'C', 1000], ['fin', 'D', 438], ['mkt', 'D', 188], ['it', 'D', 187], ['lab', 'D', 62], ['hr', 'D', 125]]], ['control 1', {'amount': -7, 'weights': [['lab', 2], ['ops', 7], ['mkt', 2]], 'source': 'pool'}, [['pool', 'D', 7], ['lab', 'C', 1], ['ops', 'C', 5], ['mkt', 'C', 1]]], ['control 2', {'amount': -101, 'weights': [['it', 5], ['ops', 7]], 'source': 'pool'}, [['pool', 'D', 101], ['it', 'C', 42], ['ops', 'C', 59]]], ['control 3', {'amount': 100, 'weights': [['it', 7], ['fin', 3], ['mkt', 7], ['hr', 1]], 'source': 'pool'}, [['pool', 'C', 100], ['it', 'D', 39], ['fin', 'D', 17], ['mkt', 'D', 39], ['hr', 'D', 5]]], ['control 4', {'amount': 10, 'weights': [['lab', 2], ['it', 5], ['hr', 7], ['mkt', 0], ['ops', 7]], 'source': 'pool'}, [['pool', 'C', 10], ['lab', 'D', 1], ['it', 'D', 3], ['hr', 'D', 3], ['ops', 'D', 3]]], ['control 5', {'amount': 3, 'weights': [['it', 3], ['lab', 3], ['hr', 7]], 'source': 'pool'}, [['pool', 'C', 3], ['it', 'D', 1], ['lab', 'D', 1], ['hr', 'D', 1]]]], [['regression: remainder tie-break', {'amount': 101, 'weights': [['fin', 2], ['hr', 2]], 'source': 'pool'}, [['pool', 'C', 101], ['fin', 'D', 51], ['hr', 'D', 50]]], ['regression: remainder tie-break, partial-repair probe', {'amount': -101, 'weights': [['ops', 2], ['hr', 2], ['lab', 7], ['it', 1], ['fin', 1]], 'source': 'pool'}, [['pool', 'D', 101], ['ops', 'C', 16], ['hr', 'C', 15], ['lab', 'C', 54], ['it', 'C', 8], ['fin', 'C', 8]]], ['control 1', {'amount': 100, 'weights': [['fin', 2], ['hr', 0], ['it', 0], ['mkt', 0]], 'source': 'pool'}, [['pool', 'C', 100], ['fin', 'D', 100]]], ['control 2', {'amount': 10, 'weights': [['ops', 3], ['it', 1], ['mkt', 3], ['hr', 0]], 'source': 'pool'}, [['pool', 'C', 10], ['ops', 'D', 4], ['it', 'D', 2], ['mkt', 'D', 4]]], ['control 3', {'amount': -7, 'weights': [['fin', 3], ['mkt', 1]], 'source': 'pool'}, [['pool', 'D', 7], ['fin', 'C', 5], ['mkt', 'C', 2]]], ['control 4', {'amount': 7, 'weights': [['mkt', 1], ['it', 0]], 'source': 'pool'}, [['pool', 'C', 7], ['mkt', 'D', 7]]], ['control 5', {'amount': 10, 'weights': [['mkt', 1], ['it', 7], ['fin', 0], ['ops', 1]], 'source': 'pool'}, [['pool', 'C', 10], ['mkt', 'D', 1], ['it', 'D', 8], ['ops', 'D', 1]]]]]
for label, args, expected in fixtures[N-1]:
try:
actual = solve(args)
except Exception as exc:
actual = 'raised ' + type(exc).__name__
check(label, actual, expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: remainder tie-break | [['pool', 'C', 7], ['it', 'D', 4], ['hr', 'D', 1], ['lab', 'D', 1], ['ops', 'D', 1]] | [['pool', 'C', 7], ['it', 'D', 4], ['hr', 'D', 1], ['lab', 'D', 1], ['ops', 'D', 1]] | Passed |
| regression: remainder tie-break, partial-repair probe | [['pool', 'C', 10], ['mkt', 'D', 1], ['ops', 'D', 5], ['lab', 'D', 1], ['it', 'D', 3]] | [['pool', 'C', 10], ['mkt', 'D', 1], ['ops', 'D', 5], ['lab', 'D', 1], ['it', 'D', 3]] | Passed |
| control 1 | [['pool', 'C', 7], ['fin', 'D', 7]] | [['pool', 'C', 7], ['fin', 'D', 7]] | Passed |
| control 2 | [['pool', 'C', 99999], ['hr', 'D', 99999]] | [['pool', 'C', 99999], ['hr', 'D', 99999]] | Passed |
| control 3 | [['pool', 'C', 0]] | [['pool', 'C', 0]] | Passed |
| control 4 | [['pool', 'C', 100], ['ops', 'D', 50], ['it', 'D', 50]] | [['pool', 'C', 100], ['ops', 'D', 50], ['it', 'D', 50]] | Passed |
| control 5 | [['pool', 'C', 0]] | [['pool', 'C', 0]] | Passed |
SHA-256 / b080019e34c3561c0d45d44f7efa3bb1c8c02d7168c106252368bd196c9f4350
Verification & scope
A deterministic bounded teaching model with stipulated toy bookkeeping rules stated in the contract; amounts are integer cents; it makes no claim of conformance to any accounting standard or product. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:46:24.021015+00:00.
Case digest / 39403b004a2c09bf4bef7a940d5413a629ce38dd75308db450b49c6ce6cc9ba8