FA-58181 / Double-entry ledger accounting / Open access
VAT invoice journal: half-cent tie · case 01
Tax on exact half-cent amounts is rounded down.
ROOT CAUSE
The rounding helper sends ties down.
VERIFIED REPAIR
Round ties half-up.
Unsuccessful approach: Rounding any remainder up overcharges tax on non-tie amounts.
Case contract
x = {'mode': 'inclusive'|'exclusive', 'rounding': 'line'|'invoice', 'lines': [[amount, rate_bp, account]]}. Exclusive: tax = amount*bp/10000. Inclusive: tax = amount*bp/(10000+bp). Rounding is half-up to the cent, per line ('line', summed per rate) or once per rate on the summed amounts ('invoice'). Tax is keyed by str(rate_bp). Inclusive: receivable = sum amounts, net = receivable - total tax. Exclusive: net = sum amounts, receivable = net + total tax. Return {'receivable', 'net', 'tax'}.
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):
def rnd(n, d):
q, r = divmod(n, d)
return q + (1 if 2 * r > d else 0)
incl = x['mode'] == 'inclusive'
groups = {}
tax = {}
for amount, bp, acct in x['lines']:
denom = 10000 + bp if incl else 10000
key = str(bp)
if x['rounding'] == 'line':
tax[key] = tax.get(key, 0) + rnd(amount * bp, denom)
groups[key] = groups.get(key, 0) + amount
if x['rounding'] == 'invoice':
for key, total in groups.items():
bp = int(key)
tax[key] = rnd(total * bp, 10000 + bp if incl else 10000)
gross_in = sum(groups.values())
total_tax = sum(tax.values())
if incl:
receivable = gross_in
net = gross_in - total_tax
else:
receivable = gross_in + total_tax
net = gross_in
return {'receivable': receivable, 'net': net, 'tax': tax}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: half-cent tie', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[15, 1900, 'services'], [15, 2000, 'services'], [15, 0, 'sales'], [1000, 2100, 'services'], [15, 500, 'sales']]}, {'receivable': 1060, 'net': 880, 'tax': {'1900': 2, '2000': 3, '0': 0, '2100': 174, '500': 1}}], ['control 1', {'mode': 'exclusive', 'rounding': 'line', 'lines': [[2500, 1900, 'sales'], [15, 700, 'sales']]}, {'receivable': 2991, 'net': 2515, 'tax': {'1900': 475, '700': 1}}], ['control 2', {'mode': 'exclusive', 'rounding': 'line', 'lines': [[105, 700, 'services'], [5, 700, 'sales'], [5, 500, 'services'], [105, 1900, 'services'], [15, 500, 'services']]}, {'receivable': 263, 'net': 235, 'tax': {'700': 7, '500': 1, '1900': 20}}], ['control 3', {'mode': 'exclusive', 'rounding': 'line', 'lines': [[1999, 700, 'services'], [999, 0, 'sales']]}, {'receivable': 3138, 'net': 2998, 'tax': {'700': 140, '0': 0}}], ['control 4', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[1999, 2100, 'services'], [12345, 2100, 'sales'], [2500, 500, 'services'], [105, 2100, 'services']]}, {'receivable': 16949, 'net': 14322, 'tax': {'2100': 2508, '500': 119}}], ['control 5', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[1000, 2100, 'services'], [999, 2000, 'sales'], [999, 0, 'sales'], [1999, 2100, 'services'], [1000, 2000, 'services']]}, {'receivable': 7027, 'net': 5997, 'tax': {'2100': 630, '2000': 400, '0': 0}}], ['control 6', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[999, 2100, 'sales'], [105, 500, 'services'], [999, 0, 'services']]}, {'receivable': 2103, 'net': 1925, 'tax': {'2100': 173, '500': 5, '0': 0}}]], [['regression: half-cent tie', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[15, 2100, 'services'], [5, 2000, 'sales'], [12345, 2000, 'sales']]}, {'receivable': 12365, 'net': 10303, 'tax': {'2100': 3, '2000': 2059}}], ['regression: half-cent tie, partial-repair probe', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[2500, 500, 'services'], [105, 500, 'sales']]}, {'receivable': 2605, 'net': 2481, 'tax': {'500': 124}}], ['control 1', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[999, 500, 'services'], [15, 700, 'sales']]}, {'receivable': 1014, 'net': 965, 'tax': {'500': 48, '700': 1}}], ['control 2', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[15, 1900, 'services']]}, {'receivable': 18, 'net': 15, 'tax': {'1900': 3}}], ['control 3', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[12345, 700, 'sales'], [15, 2100, 'sales'], [1000, 700, 'sales'], [2500, 0, 'services']]}, {'receivable': 16797, 'net': 15860, 'tax': {'700': 934, '2100': 3, '0': 0}}], ['control 4', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[1999, 0, 'sales']]}, {'receivable': 1999, 'net': 1999, 'tax': {'0': 0}}], ['control 5', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[15, 700, 'services'], [12345, 700, 'services'], [999, 1900, 'sales'], [1999, 2000, 'sales']]}, {'receivable': 15358, 'net': 14056, 'tax': {'700': 809, '1900': 160, '2000': 333}}]], [['regression: half-cent tie', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[1999, 2100, 'sales'], [105, 2000, 'sales'], [2500, 0, 'services']]}, {'receivable': 4604, 'net': 4239, 'tax': {'2100': 347, '2000': 18, '0': 0}}], ['regression: half-cent tie, partial-repair probe', {'mode': 'exclusive', 'rounding': 'line', 'lines': [[1999, 2100, 'sales'], [5, 2100, 'sales'], [12345, 0, 'services'], [2500, 2000, 'sales']]}, {'receivable': 17770, 'net': 16849, 'tax': {'2100': 421, '0': 0, '2000': 500}}], ['control 1', {'mode': 'exclusive', 'rounding': 'line', 'lines': [[5, 700, 'sales'], [1000, 1900, 'sales'], [15, 2000, 'services'], [1999, 700, 'services'], [15, 0, 'services']]}, {'receivable': 3367, 'net': 3034, 'tax': {'700': 140, '1900': 190, '2000': 3, '0': 0}}], ['control 2', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[1999, 2000, 'sales'], [1999, 1900, 'sales']]}, {'receivable': 4778, 'net': 3998, 'tax': {'2000': 400, '1900': 380}}], ['control 3', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[999, 0, 'sales']]}, {'receivable': 999, 'net': 999, 'tax': {'0': 0}}], ['control 4', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[12345, 700, 'sales'], [105, 700, 'sales']]}, {'receivable': 12450, 'net': 11636, 'tax': {'700': 814}}], ['control 5', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[12345, 2100, 'sales'], [1000, 2100, 'services']]}, {'receivable': 16147, 'net': 13345, 'tax': {'2100': 2802}}]], [['regression: half-cent tie', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[105, 2100, 'sales'], [999, 2000, 'sales'], [105, 2000, 'sales']]}, {'receivable': 1209, 'net': 1006, 'tax': {'2100': 18, '2000': 185}}], ['control 1', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[15, 1900, 'sales'], [2500, 1900, 'services'], [15, 700, 'sales']]}, {'receivable': 3009, 'net': 2530, 'tax': {'1900': 478, '700': 1}}], ['control 2', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[15, 2100, 'sales'], [15, 2100, 'sales'], [105, 0, 'sales'], [1999, 1900, 'sales']]}, {'receivable': 2134, 'net': 1810, 'tax': {'2100': 5, '0': 0, '1900': 319}}], ['control 3', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[5, 0, 'services'], [105, 500, 'sales'], [1000, 700, 'sales'], [5, 2100, 'services'], [5, 0, 'services']]}, {'receivable': 1120, 'net': 1049, 'tax': {'0': 0, '500': 5, '700': 65, '2100': 1}}], ['control 4', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[1999, 700, 'sales']]}, {'receivable': 1999, 'net': 1868, 'tax': {'700': 131}}], ['control 5', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[105, 700, 'services'], [1000, 700, 'sales'], [5, 2100, 'services'], [105, 700, 'services'], [105, 2000, 'services']]}, {'receivable': 1427, 'net': 1320, 'tax': {'700': 85, '2100': 1, '2000': 21}}], ['control 6', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[105, 700, 'services'], [15, 0, 'services'], [1999, 0, 'sales'], [1999, 700, 'services'], [15, 1900, 'sales']]}, {'receivable': 4283, 'net': 4133, 'tax': {'700': 147, '0': 0, '1900': 3}}]], [['regression: half-cent tie', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[105, 2100, 'sales'], [1000, 2000, 'sales'], [1999, 500, 'sales'], [12345, 2000, 'services'], [1000, 500, 'sales']]}, {'receivable': 16449, 'net': 14063, 'tax': {'2100': 18, '2000': 2225, '500': 143}}], ['control 1', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[15, 0, 'sales'], [1999, 0, 'services'], [999, 700, 'services'], [15, 500, 'sales'], [999, 2100, 'sales']]}, {'receivable': 4027, 'net': 3788, 'tax': {'0': 0, '700': 65, '500': 1, '2100': 173}}], ['control 2', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[5, 700, 'services'], [2500, 1900, 'sales'], [1999, 1900, 'services'], [5, 500, 'sales'], [999, 2100, 'sales']]}, {'receivable': 5508, 'net': 4617, 'tax': {'700': 0, '1900': 718, '500': 0, '2100': 173}}], ['control 3', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[1999, 2100, 'services'], [15, 500, 'sales'], [1999, 700, 'sales'], [2500, 2100, 'sales'], [12345, 700, 'services']]}, {'receivable': 18858, 'net': 17138, 'tax': {'2100': 781, '500': 1, '700': 938}}], ['control 4', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[15, 500, 'sales']]}, {'receivable': 16, 'net': 15, 'tax': {'500': 1}}], ['control 5', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[999, 700, 'services']]}, {'receivable': 1069, 'net': 999, 'tax': {'700': 70}}], ['control 6', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[105, 1900, 'sales'], [12345, 500, 'sales'], [1000, 2000, 'sales'], [999, 700, 'services']]}, {'receivable': 15356, 'net': 14449, 'tax': {'1900': 20, '500': 617, '2000': 200, '700': 70}}]]]
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: half-cent tie | {'net': 881, 'receivable': 1060, 'tax': {'0': 0, '1900': 2, '2000': 2, '2100': 174, '500': 1}} | {'net': 880, 'receivable': 1060, 'tax': {'0': 0, '1900': 2, '2000': 3, '2100': 174, '500': 1}} | Failed |
| control 1 | {'net': 2515, 'receivable': 2991, 'tax': {'1900': 475, '700': 1}} | {'net': 2515, 'receivable': 2991, 'tax': {'1900': 475, '700': 1}} | Passed |
| control 2 | {'net': 235, 'receivable': 263, 'tax': {'1900': 20, '500': 1, '700': 7}} | {'net': 235, 'receivable': 263, 'tax': {'1900': 20, '500': 1, '700': 7}} | Passed |
| control 3 | {'net': 2998, 'receivable': 3138, 'tax': {'0': 0, '700': 140}} | {'net': 2998, 'receivable': 3138, 'tax': {'0': 0, '700': 140}} | Passed |
| control 4 | {'net': 14322, 'receivable': 16949, 'tax': {'2100': 2508, '500': 119}} | {'net': 14322, 'receivable': 16949, 'tax': {'2100': 2508, '500': 119}} | Passed |
| control 5 | {'net': 5997, 'receivable': 7027, 'tax': {'0': 0, '2000': 400, '2100': 630}} | {'net': 5997, 'receivable': 7027, 'tax': {'0': 0, '2000': 400, '2100': 630}} | Passed |
| control 6 | {'net': 1925, 'receivable': 2103, 'tax': {'0': 0, '2100': 173, '500': 5}} | {'net': 1925, 'receivable': 2103, 'tax': {'0': 0, '2100': 173, '500': 5}} | Passed |
SHA-256 / be3facde0034c13c1369f2e6549b3cefb3c4bc921f7168a671a8d1354f5ee446
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
def rnd(n, d):
q, r = divmod(n, d)
return q + (1 if r > 0 else 0)
incl = x['mode'] == 'inclusive'
groups = {}
tax = {}
for amount, bp, acct in x['lines']:
denom = 10000 + bp if incl else 10000
key = str(bp)
if x['rounding'] == 'line':
tax[key] = tax.get(key, 0) + rnd(amount * bp, denom)
groups[key] = groups.get(key, 0) + amount
if x['rounding'] == 'invoice':
for key, total in groups.items():
bp = int(key)
tax[key] = rnd(total * bp, 10000 + bp if incl else 10000)
gross_in = sum(groups.values())
total_tax = sum(tax.values())
if incl:
receivable = gross_in
net = gross_in - total_tax
else:
receivable = gross_in + total_tax
net = gross_in
return {'receivable': receivable, 'net': net, 'tax': tax}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: half-cent tie', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[15, 1900, 'services'], [15, 2000, 'services'], [15, 0, 'sales'], [1000, 2100, 'services'], [15, 500, 'sales']]}, {'receivable': 1060, 'net': 880, 'tax': {'1900': 2, '2000': 3, '0': 0, '2100': 174, '500': 1}}], ['control 1', {'mode': 'exclusive', 'rounding': 'line', 'lines': [[2500, 1900, 'sales'], [15, 700, 'sales']]}, {'receivable': 2991, 'net': 2515, 'tax': {'1900': 475, '700': 1}}], ['control 2', {'mode': 'exclusive', 'rounding': 'line', 'lines': [[105, 700, 'services'], [5, 700, 'sales'], [5, 500, 'services'], [105, 1900, 'services'], [15, 500, 'services']]}, {'receivable': 263, 'net': 235, 'tax': {'700': 7, '500': 1, '1900': 20}}], ['control 3', {'mode': 'exclusive', 'rounding': 'line', 'lines': [[1999, 700, 'services'], [999, 0, 'sales']]}, {'receivable': 3138, 'net': 2998, 'tax': {'700': 140, '0': 0}}], ['control 4', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[1999, 2100, 'services'], [12345, 2100, 'sales'], [2500, 500, 'services'], [105, 2100, 'services']]}, {'receivable': 16949, 'net': 14322, 'tax': {'2100': 2508, '500': 119}}], ['control 5', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[1000, 2100, 'services'], [999, 2000, 'sales'], [999, 0, 'sales'], [1999, 2100, 'services'], [1000, 2000, 'services']]}, {'receivable': 7027, 'net': 5997, 'tax': {'2100': 630, '2000': 400, '0': 0}}], ['control 6', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[999, 2100, 'sales'], [105, 500, 'services'], [999, 0, 'services']]}, {'receivable': 2103, 'net': 1925, 'tax': {'2100': 173, '500': 5, '0': 0}}]], [['regression: half-cent tie', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[15, 2100, 'services'], [5, 2000, 'sales'], [12345, 2000, 'sales']]}, {'receivable': 12365, 'net': 10303, 'tax': {'2100': 3, '2000': 2059}}], ['regression: half-cent tie, partial-repair probe', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[2500, 500, 'services'], [105, 500, 'sales']]}, {'receivable': 2605, 'net': 2481, 'tax': {'500': 124}}], ['control 1', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[999, 500, 'services'], [15, 700, 'sales']]}, {'receivable': 1014, 'net': 965, 'tax': {'500': 48, '700': 1}}], ['control 2', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[15, 1900, 'services']]}, {'receivable': 18, 'net': 15, 'tax': {'1900': 3}}], ['control 3', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[12345, 700, 'sales'], [15, 2100, 'sales'], [1000, 700, 'sales'], [2500, 0, 'services']]}, {'receivable': 16797, 'net': 15860, 'tax': {'700': 934, '2100': 3, '0': 0}}], ['control 4', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[1999, 0, 'sales']]}, {'receivable': 1999, 'net': 1999, 'tax': {'0': 0}}], ['control 5', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[15, 700, 'services'], [12345, 700, 'services'], [999, 1900, 'sales'], [1999, 2000, 'sales']]}, {'receivable': 15358, 'net': 14056, 'tax': {'700': 809, '1900': 160, '2000': 333}}]], [['regression: half-cent tie', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[1999, 2100, 'sales'], [105, 2000, 'sales'], [2500, 0, 'services']]}, {'receivable': 4604, 'net': 4239, 'tax': {'2100': 347, '2000': 18, '0': 0}}], ['regression: half-cent tie, partial-repair probe', {'mode': 'exclusive', 'rounding': 'line', 'lines': [[1999, 2100, 'sales'], [5, 2100, 'sales'], [12345, 0, 'services'], [2500, 2000, 'sales']]}, {'receivable': 17770, 'net': 16849, 'tax': {'2100': 421, '0': 0, '2000': 500}}], ['control 1', {'mode': 'exclusive', 'rounding': 'line', 'lines': [[5, 700, 'sales'], [1000, 1900, 'sales'], [15, 2000, 'services'], [1999, 700, 'services'], [15, 0, 'services']]}, {'receivable': 3367, 'net': 3034, 'tax': {'700': 140, '1900': 190, '2000': 3, '0': 0}}], ['control 2', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[1999, 2000, 'sales'], [1999, 1900, 'sales']]}, {'receivable': 4778, 'net': 3998, 'tax': {'2000': 400, '1900': 380}}], ['control 3', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[999, 0, 'sales']]}, {'receivable': 999, 'net': 999, 'tax': {'0': 0}}], ['control 4', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[12345, 700, 'sales'], [105, 700, 'sales']]}, {'receivable': 12450, 'net': 11636, 'tax': {'700': 814}}], ['control 5', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[12345, 2100, 'sales'], [1000, 2100, 'services']]}, {'receivable': 16147, 'net': 13345, 'tax': {'2100': 2802}}]], [['regression: half-cent tie', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[105, 2100, 'sales'], [999, 2000, 'sales'], [105, 2000, 'sales']]}, {'receivable': 1209, 'net': 1006, 'tax': {'2100': 18, '2000': 185}}], ['control 1', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[15, 1900, 'sales'], [2500, 1900, 'services'], [15, 700, 'sales']]}, {'receivable': 3009, 'net': 2530, 'tax': {'1900': 478, '700': 1}}], ['control 2', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[15, 2100, 'sales'], [15, 2100, 'sales'], [105, 0, 'sales'], [1999, 1900, 'sales']]}, {'receivable': 2134, 'net': 1810, 'tax': {'2100': 5, '0': 0, '1900': 319}}], ['control 3', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[5, 0, 'services'], [105, 500, 'sales'], [1000, 700, 'sales'], [5, 2100, 'services'], [5, 0, 'services']]}, {'receivable': 1120, 'net': 1049, 'tax': {'0': 0, '500': 5, '700': 65, '2100': 1}}], ['control 4', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[1999, 700, 'sales']]}, {'receivable': 1999, 'net': 1868, 'tax': {'700': 131}}], ['control 5', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[105, 700, 'services'], [1000, 700, 'sales'], [5, 2100, 'services'], [105, 700, 'services'], [105, 2000, 'services']]}, {'receivable': 1427, 'net': 1320, 'tax': {'700': 85, '2100': 1, '2000': 21}}], ['control 6', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[105, 700, 'services'], [15, 0, 'services'], [1999, 0, 'sales'], [1999, 700, 'services'], [15, 1900, 'sales']]}, {'receivable': 4283, 'net': 4133, 'tax': {'700': 147, '0': 0, '1900': 3}}]], [['regression: half-cent tie', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[105, 2100, 'sales'], [1000, 2000, 'sales'], [1999, 500, 'sales'], [12345, 2000, 'services'], [1000, 500, 'sales']]}, {'receivable': 16449, 'net': 14063, 'tax': {'2100': 18, '2000': 2225, '500': 143}}], ['control 1', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[15, 0, 'sales'], [1999, 0, 'services'], [999, 700, 'services'], [15, 500, 'sales'], [999, 2100, 'sales']]}, {'receivable': 4027, 'net': 3788, 'tax': {'0': 0, '700': 65, '500': 1, '2100': 173}}], ['control 2', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[5, 700, 'services'], [2500, 1900, 'sales'], [1999, 1900, 'services'], [5, 500, 'sales'], [999, 2100, 'sales']]}, {'receivable': 5508, 'net': 4617, 'tax': {'700': 0, '1900': 718, '500': 0, '2100': 173}}], ['control 3', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[1999, 2100, 'services'], [15, 500, 'sales'], [1999, 700, 'sales'], [2500, 2100, 'sales'], [12345, 700, 'services']]}, {'receivable': 18858, 'net': 17138, 'tax': {'2100': 781, '500': 1, '700': 938}}], ['control 4', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[15, 500, 'sales']]}, {'receivable': 16, 'net': 15, 'tax': {'500': 1}}], ['control 5', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[999, 700, 'services']]}, {'receivable': 1069, 'net': 999, 'tax': {'700': 70}}], ['control 6', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[105, 1900, 'sales'], [12345, 500, 'sales'], [1000, 2000, 'sales'], [999, 700, 'services']]}, {'receivable': 15356, 'net': 14449, 'tax': {'1900': 20, '500': 617, '2000': 200, '700': 70}}]]]
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: half-cent tie | {'net': 879, 'receivable': 1060, 'tax': {'0': 0, '1900': 3, '2000': 3, '2100': 174, '500': 1}} | {'net': 880, 'receivable': 1060, 'tax': {'0': 0, '1900': 2, '2000': 3, '2100': 174, '500': 1}} | Failed |
| control 1 | {'net': 2515, 'receivable': 2992, 'tax': {'1900': 475, '700': 2}} | {'net': 2515, 'receivable': 2991, 'tax': {'1900': 475, '700': 1}} | Failed |
| control 2 | {'net': 235, 'receivable': 266, 'tax': {'1900': 20, '500': 2, '700': 9}} | {'net': 235, 'receivable': 263, 'tax': {'1900': 20, '500': 1, '700': 7}} | Failed |
| control 3 | {'net': 2998, 'receivable': 3138, 'tax': {'0': 0, '700': 140}} | {'net': 2998, 'receivable': 3138, 'tax': {'0': 0, '700': 140}} | Passed |
| control 4 | {'net': 14321, 'receivable': 16949, 'tax': {'2100': 2508, '500': 120}} | {'net': 14322, 'receivable': 16949, 'tax': {'2100': 2508, '500': 119}} | Failed |
| control 5 | {'net': 5997, 'receivable': 7027, 'tax': {'0': 0, '2000': 400, '2100': 630}} | {'net': 5997, 'receivable': 7027, 'tax': {'0': 0, '2000': 400, '2100': 630}} | Passed |
| control 6 | {'net': 1924, 'receivable': 2103, 'tax': {'0': 0, '2100': 174, '500': 5}} | {'net': 1925, 'receivable': 2103, 'tax': {'0': 0, '2100': 173, '500': 5}} | Failed |
SHA-256 / 81551676eb4de552ca94ddc63fec1390cb50bdbfc842d1ddf3e275def14e843a
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
def rnd(n, d):
q, r = divmod(n, d)
return q + (1 if 2 * r >= d else 0)
incl = x['mode'] == 'inclusive'
groups = {}
tax = {}
for amount, bp, acct in x['lines']:
denom = 10000 + bp if incl else 10000
key = str(bp)
if x['rounding'] == 'line':
tax[key] = tax.get(key, 0) + rnd(amount * bp, denom)
groups[key] = groups.get(key, 0) + amount
if x['rounding'] == 'invoice':
for key, total in groups.items():
bp = int(key)
tax[key] = rnd(total * bp, 10000 + bp if incl else 10000)
gross_in = sum(groups.values())
total_tax = sum(tax.values())
if incl:
receivable = gross_in
net = gross_in - total_tax
else:
receivable = gross_in + total_tax
net = gross_in
return {'receivable': receivable, 'net': net, 'tax': tax}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: half-cent tie', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[15, 1900, 'services'], [15, 2000, 'services'], [15, 0, 'sales'], [1000, 2100, 'services'], [15, 500, 'sales']]}, {'receivable': 1060, 'net': 880, 'tax': {'1900': 2, '2000': 3, '0': 0, '2100': 174, '500': 1}}], ['control 1', {'mode': 'exclusive', 'rounding': 'line', 'lines': [[2500, 1900, 'sales'], [15, 700, 'sales']]}, {'receivable': 2991, 'net': 2515, 'tax': {'1900': 475, '700': 1}}], ['control 2', {'mode': 'exclusive', 'rounding': 'line', 'lines': [[105, 700, 'services'], [5, 700, 'sales'], [5, 500, 'services'], [105, 1900, 'services'], [15, 500, 'services']]}, {'receivable': 263, 'net': 235, 'tax': {'700': 7, '500': 1, '1900': 20}}], ['control 3', {'mode': 'exclusive', 'rounding': 'line', 'lines': [[1999, 700, 'services'], [999, 0, 'sales']]}, {'receivable': 3138, 'net': 2998, 'tax': {'700': 140, '0': 0}}], ['control 4', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[1999, 2100, 'services'], [12345, 2100, 'sales'], [2500, 500, 'services'], [105, 2100, 'services']]}, {'receivable': 16949, 'net': 14322, 'tax': {'2100': 2508, '500': 119}}], ['control 5', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[1000, 2100, 'services'], [999, 2000, 'sales'], [999, 0, 'sales'], [1999, 2100, 'services'], [1000, 2000, 'services']]}, {'receivable': 7027, 'net': 5997, 'tax': {'2100': 630, '2000': 400, '0': 0}}], ['control 6', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[999, 2100, 'sales'], [105, 500, 'services'], [999, 0, 'services']]}, {'receivable': 2103, 'net': 1925, 'tax': {'2100': 173, '500': 5, '0': 0}}]], [['regression: half-cent tie', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[15, 2100, 'services'], [5, 2000, 'sales'], [12345, 2000, 'sales']]}, {'receivable': 12365, 'net': 10303, 'tax': {'2100': 3, '2000': 2059}}], ['regression: half-cent tie, partial-repair probe', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[2500, 500, 'services'], [105, 500, 'sales']]}, {'receivable': 2605, 'net': 2481, 'tax': {'500': 124}}], ['control 1', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[999, 500, 'services'], [15, 700, 'sales']]}, {'receivable': 1014, 'net': 965, 'tax': {'500': 48, '700': 1}}], ['control 2', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[15, 1900, 'services']]}, {'receivable': 18, 'net': 15, 'tax': {'1900': 3}}], ['control 3', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[12345, 700, 'sales'], [15, 2100, 'sales'], [1000, 700, 'sales'], [2500, 0, 'services']]}, {'receivable': 16797, 'net': 15860, 'tax': {'700': 934, '2100': 3, '0': 0}}], ['control 4', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[1999, 0, 'sales']]}, {'receivable': 1999, 'net': 1999, 'tax': {'0': 0}}], ['control 5', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[15, 700, 'services'], [12345, 700, 'services'], [999, 1900, 'sales'], [1999, 2000, 'sales']]}, {'receivable': 15358, 'net': 14056, 'tax': {'700': 809, '1900': 160, '2000': 333}}]], [['regression: half-cent tie', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[1999, 2100, 'sales'], [105, 2000, 'sales'], [2500, 0, 'services']]}, {'receivable': 4604, 'net': 4239, 'tax': {'2100': 347, '2000': 18, '0': 0}}], ['regression: half-cent tie, partial-repair probe', {'mode': 'exclusive', 'rounding': 'line', 'lines': [[1999, 2100, 'sales'], [5, 2100, 'sales'], [12345, 0, 'services'], [2500, 2000, 'sales']]}, {'receivable': 17770, 'net': 16849, 'tax': {'2100': 421, '0': 0, '2000': 500}}], ['control 1', {'mode': 'exclusive', 'rounding': 'line', 'lines': [[5, 700, 'sales'], [1000, 1900, 'sales'], [15, 2000, 'services'], [1999, 700, 'services'], [15, 0, 'services']]}, {'receivable': 3367, 'net': 3034, 'tax': {'700': 140, '1900': 190, '2000': 3, '0': 0}}], ['control 2', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[1999, 2000, 'sales'], [1999, 1900, 'sales']]}, {'receivable': 4778, 'net': 3998, 'tax': {'2000': 400, '1900': 380}}], ['control 3', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[999, 0, 'sales']]}, {'receivable': 999, 'net': 999, 'tax': {'0': 0}}], ['control 4', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[12345, 700, 'sales'], [105, 700, 'sales']]}, {'receivable': 12450, 'net': 11636, 'tax': {'700': 814}}], ['control 5', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[12345, 2100, 'sales'], [1000, 2100, 'services']]}, {'receivable': 16147, 'net': 13345, 'tax': {'2100': 2802}}]], [['regression: half-cent tie', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[105, 2100, 'sales'], [999, 2000, 'sales'], [105, 2000, 'sales']]}, {'receivable': 1209, 'net': 1006, 'tax': {'2100': 18, '2000': 185}}], ['control 1', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[15, 1900, 'sales'], [2500, 1900, 'services'], [15, 700, 'sales']]}, {'receivable': 3009, 'net': 2530, 'tax': {'1900': 478, '700': 1}}], ['control 2', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[15, 2100, 'sales'], [15, 2100, 'sales'], [105, 0, 'sales'], [1999, 1900, 'sales']]}, {'receivable': 2134, 'net': 1810, 'tax': {'2100': 5, '0': 0, '1900': 319}}], ['control 3', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[5, 0, 'services'], [105, 500, 'sales'], [1000, 700, 'sales'], [5, 2100, 'services'], [5, 0, 'services']]}, {'receivable': 1120, 'net': 1049, 'tax': {'0': 0, '500': 5, '700': 65, '2100': 1}}], ['control 4', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[1999, 700, 'sales']]}, {'receivable': 1999, 'net': 1868, 'tax': {'700': 131}}], ['control 5', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[105, 700, 'services'], [1000, 700, 'sales'], [5, 2100, 'services'], [105, 700, 'services'], [105, 2000, 'services']]}, {'receivable': 1427, 'net': 1320, 'tax': {'700': 85, '2100': 1, '2000': 21}}], ['control 6', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[105, 700, 'services'], [15, 0, 'services'], [1999, 0, 'sales'], [1999, 700, 'services'], [15, 1900, 'sales']]}, {'receivable': 4283, 'net': 4133, 'tax': {'700': 147, '0': 0, '1900': 3}}]], [['regression: half-cent tie', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[105, 2100, 'sales'], [1000, 2000, 'sales'], [1999, 500, 'sales'], [12345, 2000, 'services'], [1000, 500, 'sales']]}, {'receivable': 16449, 'net': 14063, 'tax': {'2100': 18, '2000': 2225, '500': 143}}], ['control 1', {'mode': 'inclusive', 'rounding': 'line', 'lines': [[15, 0, 'sales'], [1999, 0, 'services'], [999, 700, 'services'], [15, 500, 'sales'], [999, 2100, 'sales']]}, {'receivable': 4027, 'net': 3788, 'tax': {'0': 0, '700': 65, '500': 1, '2100': 173}}], ['control 2', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[5, 700, 'services'], [2500, 1900, 'sales'], [1999, 1900, 'services'], [5, 500, 'sales'], [999, 2100, 'sales']]}, {'receivable': 5508, 'net': 4617, 'tax': {'700': 0, '1900': 718, '500': 0, '2100': 173}}], ['control 3', {'mode': 'inclusive', 'rounding': 'invoice', 'lines': [[1999, 2100, 'services'], [15, 500, 'sales'], [1999, 700, 'sales'], [2500, 2100, 'sales'], [12345, 700, 'services']]}, {'receivable': 18858, 'net': 17138, 'tax': {'2100': 781, '500': 1, '700': 938}}], ['control 4', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[15, 500, 'sales']]}, {'receivable': 16, 'net': 15, 'tax': {'500': 1}}], ['control 5', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[999, 700, 'services']]}, {'receivable': 1069, 'net': 999, 'tax': {'700': 70}}], ['control 6', {'mode': 'exclusive', 'rounding': 'invoice', 'lines': [[105, 1900, 'sales'], [12345, 500, 'sales'], [1000, 2000, 'sales'], [999, 700, 'services']]}, {'receivable': 15356, 'net': 14449, 'tax': {'1900': 20, '500': 617, '2000': 200, '700': 70}}]]]
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: half-cent tie | {'net': 880, 'receivable': 1060, 'tax': {'0': 0, '1900': 2, '2000': 3, '2100': 174, '500': 1}} | {'net': 880, 'receivable': 1060, 'tax': {'0': 0, '1900': 2, '2000': 3, '2100': 174, '500': 1}} | Passed |
| control 1 | {'net': 2515, 'receivable': 2991, 'tax': {'1900': 475, '700': 1}} | {'net': 2515, 'receivable': 2991, 'tax': {'1900': 475, '700': 1}} | Passed |
| control 2 | {'net': 235, 'receivable': 263, 'tax': {'1900': 20, '500': 1, '700': 7}} | {'net': 235, 'receivable': 263, 'tax': {'1900': 20, '500': 1, '700': 7}} | Passed |
| control 3 | {'net': 2998, 'receivable': 3138, 'tax': {'0': 0, '700': 140}} | {'net': 2998, 'receivable': 3138, 'tax': {'0': 0, '700': 140}} | Passed |
| control 4 | {'net': 14322, 'receivable': 16949, 'tax': {'2100': 2508, '500': 119}} | {'net': 14322, 'receivable': 16949, 'tax': {'2100': 2508, '500': 119}} | Passed |
| control 5 | {'net': 5997, 'receivable': 7027, 'tax': {'0': 0, '2000': 400, '2100': 630}} | {'net': 5997, 'receivable': 7027, 'tax': {'0': 0, '2000': 400, '2100': 630}} | Passed |
| control 6 | {'net': 1925, 'receivable': 2103, 'tax': {'0': 0, '2100': 173, '500': 5}} | {'net': 1925, 'receivable': 2103, 'tax': {'0': 0, '2100': 173, '500': 5}} | Passed |
SHA-256 / a135f790652e40506c279e0ebef6c2d4c86e17bc43af1e0beee3c0f0959c3e30
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 2026-09-29T14:46:24.197458+00:00.
Case digest / 9a548c01c1b8e1ed71a7fc9dfb4b719e90415287944a1ee49d9622538341d260