FA-59256 / Payroll withholding rules / Open access
Daily, weekly and seventh-day overtime split: seventh-day trigger · case 01
Anyone working the last day of the week gets seventh-day premium pay.
ROOT CAUSE
The seventh-day rule checks only the last day instead of all seven consecutive days.
VERIFIED REPAIR
Restore the contract rule at the seventh-day trigger step: use `worked_all = all(h > 0 for h in hours)`.
Unsuccessful approach: The attempt accepts six worked days, still paying the premium without a full seven-day streak.
Case contract
Input seven daily hour counts (workweek order). If all seven days are worked, day 7 hours are 1.5x up to 8 and double beyond 8. Other days: first 8 regular, 8-12 at 1.5x, over 12 double; regular hours beyond a weekly total of 40 regular hours become 1.5x. Return [regular, overtime, double].
Why this case matters
Stacked daily and weekly overtime rules must not double count hours or miss the seventh consecutive day.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
hours = x
reg = ot = dt = 0
worked_all = hours[6] > 0
for i, h in enumerate(hours):
if i == 6 and worked_all:
ot += min(h, 8)
dt += max(0, h - 8)
continue
d_reg = min(h, 8)
d_ot = max(0, min(h, 12) - 8)
d_dt = max(0, h - 12)
room = max(0, 40 - reg)
if d_reg > room:
d_ot += d_reg - room
d_reg = room
reg += d_reg
ot += d_ot
dt += d_dt
return [reg, ot, dt]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', [6, 8, 9, 0, 8, 3, 8], [40, 2, 0]), ('regression (boundary)', [0, 0, 0, 0, 0, 0, 13], [8, 4, 1]), ('partial-repair probe', [12, 8, 3, 0, 12, 4, 12], [39, 12, 0]), ('partial-repair probe', [8, 2, 8, 0, 12, 9, 7], [40, 6, 0]), ('boundary control', [8, 8, 8, 8, 8, 8, 8], [40, 16, 0]), ('boundary control', [10, 10, 10, 10, 10, 0, 0], [40, 10, 0]), ('normal control', [12, 12, 8, 7, 0, 8, 0], [39, 8, 0]), ('normal control', [0, 12, 10, 8, 8, 12, 0], [40, 10, 0]), ('normal control', [10, 8, 6, 12, 9, 10, 0], [40, 15, 0]), ('normal control', [14, 9, 8, 7, 0, 12, 0], [39, 9, 2])], [('regression', [12, 8, 3, 0, 12, 4, 12], [39, 12, 0]), ('regression', [6, 8, 9, 0, 8, 3, 8], [40, 2, 0]), ('partial-repair probe', [8, 2, 8, 0, 12, 9, 7], [40, 6, 0]), ('partial-repair probe', [9, 8, 8, 0, 12, 8, 12], [40, 17, 0]), ('boundary control', [8, 8, 8, 8, 8, 8, 8], [40, 16, 0]), ('boundary control', [10, 10, 10, 10, 10, 0, 0], [40, 10, 0]), ('normal control', [0, 0, 0, 7, 10, 8, 0], [23, 2, 0]), ('normal control', [8, 8, 5, 0, 0, 10, 0], [29, 2, 0]), ('normal control', [0, 7, 12, 8, 0, 7, 0], [30, 4, 0]), ('normal control', [0, 4, 4, 9, 8, 8, 0], [32, 1, 0])], [('regression', [8, 2, 8, 0, 12, 9, 7], [40, 6, 0]), ('regression', [8, 7, 14, 0, 12, 0, 8], [39, 8, 2]), ('partial-repair probe', [0, 10, 12, 8, 10, 12, 9], [40, 21, 0]), ('partial-repair probe', [9, 12, 8, 0, 1, 8, 8], [40, 6, 0]), ('boundary control', [8, 8, 8, 8, 8, 8, 8], [40, 16, 0]), ('boundary control', [10, 10, 10, 10, 10, 0, 0], [40, 10, 0]), ('normal control', [0, 12, 0, 0, 10, 8, 0], [24, 6, 0]), ('normal control', [12, 7, 12, 0, 8, 8, 0], [39, 8, 0]), ('normal control', [8, 8, 10, 8, 8, 8, 6], [40, 16, 0]), ('normal control', [14, 10, 12, 6, 12, 0, 0], [38, 14, 2])], [('regression', [9, 8, 8, 0, 12, 8, 12], [40, 17, 0]), ('regression', [12, 8, 3, 0, 12, 4, 12], [39, 12, 0]), ('partial-repair probe', [8, 8, 7, 8, 0, 14, 6], [40, 9, 2]), ('partial-repair probe', [7, 8, 8, 0, 9, 8, 8], [40, 8, 0]), ('boundary control', [8, 8, 8, 8, 8, 8, 8], [40, 16, 0]), ('boundary control', [10, 10, 10, 10, 10, 0, 0], [40, 10, 0]), ('normal control', [0, 2, 8, 8, 12, 12, 0], [34, 8, 0]), ('normal control', [8, 8, 0, 12, 12, 0, 0], [32, 8, 0]), ('normal control', [7, 0, 8, 0, 8, 12, 0], [31, 4, 0]), ('normal control', [12, 4, 12, 12, 2, 9, 14], [38, 21, 6])], [('regression', [0, 10, 12, 8, 10, 12, 9], [40, 21, 0]), ('regression', [0, 0, 0, 8, 0, 0, 8], [16, 0, 0]), ('partial-repair probe', [8, 8, 0, 12, 8, 12, 12], [40, 20, 0]), ('partial-repair probe', [8, 12, 0, 12, 9, 8, 10], [40, 19, 0]), ('boundary control', [8, 8, 8, 8, 8, 8, 8], [40, 16, 0]), ('boundary control', [10, 10, 10, 10, 10, 0, 0], [40, 10, 0]), ('normal control', [9, 9, 6, 8, 0, 12, 0], [38, 6, 0]), ('normal control', [0, 12, 3, 6, 12, 12, 0], [33, 12, 0]), ('normal control', [0, 0, 0, 9, 0, 8, 0], [16, 1, 0]), ('normal control', [0, 8, 6, 8, 6, 12, 0], [36, 4, 0])]]
for i, (label, args, expected) in enumerate(fixtures[N-1]):
check("%s %d" % (label, i), solve(args), 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 0 | [33, 9, 0] | [40, 2, 0] | Failed |
| regression (boundary) 1 | [0, 8, 5] | [8, 4, 1] | Failed |
| partial-repair probe 2 | [31, 16, 4] | [39, 12, 0] | Failed |
| partial-repair probe 3 | [34, 12, 0] | [40, 6, 0] | Failed |
| boundary control 4 | [40, 16, 0] | [40, 16, 0] | Passed |
| boundary control 5 | [40, 10, 0] | [40, 10, 0] | Passed |
| normal control 6 | [39, 8, 0] | [39, 8, 0] | Passed |
| normal control 7 | [40, 10, 0] | [40, 10, 0] | Passed |
| normal control 8 | [40, 15, 0] | [40, 15, 0] | Passed |
| normal control 9 | [39, 9, 2] | [39, 9, 2] | Passed |
SHA-256 / 5ec97c7f7ddbf1fbbeb346fa42a55664f50d69ca8ad1daa995b423f9cb715401
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
hours = x
reg = ot = dt = 0
worked_all = sum(1 for h in hours if h > 0) >= 6
for i, h in enumerate(hours):
if i == 6 and worked_all:
ot += min(h, 8)
dt += max(0, h - 8)
continue
d_reg = min(h, 8)
d_ot = max(0, min(h, 12) - 8)
d_dt = max(0, h - 12)
room = max(0, 40 - reg)
if d_reg > room:
d_ot += d_reg - room
d_reg = room
reg += d_reg
ot += d_ot
dt += d_dt
return [reg, ot, dt]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', [6, 8, 9, 0, 8, 3, 8], [40, 2, 0]), ('regression (boundary)', [0, 0, 0, 0, 0, 0, 13], [8, 4, 1]), ('partial-repair probe', [12, 8, 3, 0, 12, 4, 12], [39, 12, 0]), ('partial-repair probe', [8, 2, 8, 0, 12, 9, 7], [40, 6, 0]), ('boundary control', [8, 8, 8, 8, 8, 8, 8], [40, 16, 0]), ('boundary control', [10, 10, 10, 10, 10, 0, 0], [40, 10, 0]), ('normal control', [12, 12, 8, 7, 0, 8, 0], [39, 8, 0]), ('normal control', [0, 12, 10, 8, 8, 12, 0], [40, 10, 0]), ('normal control', [10, 8, 6, 12, 9, 10, 0], [40, 15, 0]), ('normal control', [14, 9, 8, 7, 0, 12, 0], [39, 9, 2])], [('regression', [12, 8, 3, 0, 12, 4, 12], [39, 12, 0]), ('regression', [6, 8, 9, 0, 8, 3, 8], [40, 2, 0]), ('partial-repair probe', [8, 2, 8, 0, 12, 9, 7], [40, 6, 0]), ('partial-repair probe', [9, 8, 8, 0, 12, 8, 12], [40, 17, 0]), ('boundary control', [8, 8, 8, 8, 8, 8, 8], [40, 16, 0]), ('boundary control', [10, 10, 10, 10, 10, 0, 0], [40, 10, 0]), ('normal control', [0, 0, 0, 7, 10, 8, 0], [23, 2, 0]), ('normal control', [8, 8, 5, 0, 0, 10, 0], [29, 2, 0]), ('normal control', [0, 7, 12, 8, 0, 7, 0], [30, 4, 0]), ('normal control', [0, 4, 4, 9, 8, 8, 0], [32, 1, 0])], [('regression', [8, 2, 8, 0, 12, 9, 7], [40, 6, 0]), ('regression', [8, 7, 14, 0, 12, 0, 8], [39, 8, 2]), ('partial-repair probe', [0, 10, 12, 8, 10, 12, 9], [40, 21, 0]), ('partial-repair probe', [9, 12, 8, 0, 1, 8, 8], [40, 6, 0]), ('boundary control', [8, 8, 8, 8, 8, 8, 8], [40, 16, 0]), ('boundary control', [10, 10, 10, 10, 10, 0, 0], [40, 10, 0]), ('normal control', [0, 12, 0, 0, 10, 8, 0], [24, 6, 0]), ('normal control', [12, 7, 12, 0, 8, 8, 0], [39, 8, 0]), ('normal control', [8, 8, 10, 8, 8, 8, 6], [40, 16, 0]), ('normal control', [14, 10, 12, 6, 12, 0, 0], [38, 14, 2])], [('regression', [9, 8, 8, 0, 12, 8, 12], [40, 17, 0]), ('regression', [12, 8, 3, 0, 12, 4, 12], [39, 12, 0]), ('partial-repair probe', [8, 8, 7, 8, 0, 14, 6], [40, 9, 2]), ('partial-repair probe', [7, 8, 8, 0, 9, 8, 8], [40, 8, 0]), ('boundary control', [8, 8, 8, 8, 8, 8, 8], [40, 16, 0]), ('boundary control', [10, 10, 10, 10, 10, 0, 0], [40, 10, 0]), ('normal control', [0, 2, 8, 8, 12, 12, 0], [34, 8, 0]), ('normal control', [8, 8, 0, 12, 12, 0, 0], [32, 8, 0]), ('normal control', [7, 0, 8, 0, 8, 12, 0], [31, 4, 0]), ('normal control', [12, 4, 12, 12, 2, 9, 14], [38, 21, 6])], [('regression', [0, 10, 12, 8, 10, 12, 9], [40, 21, 0]), ('regression', [0, 0, 0, 8, 0, 0, 8], [16, 0, 0]), ('partial-repair probe', [8, 8, 0, 12, 8, 12, 12], [40, 20, 0]), ('partial-repair probe', [8, 12, 0, 12, 9, 8, 10], [40, 19, 0]), ('boundary control', [8, 8, 8, 8, 8, 8, 8], [40, 16, 0]), ('boundary control', [10, 10, 10, 10, 10, 0, 0], [40, 10, 0]), ('normal control', [9, 9, 6, 8, 0, 12, 0], [38, 6, 0]), ('normal control', [0, 12, 3, 6, 12, 12, 0], [33, 12, 0]), ('normal control', [0, 0, 0, 9, 0, 8, 0], [16, 1, 0]), ('normal control', [0, 8, 6, 8, 6, 12, 0], [36, 4, 0])]]
for i, (label, args, expected) in enumerate(fixtures[N-1]):
check("%s %d" % (label, i), solve(args), 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 0 | [33, 9, 0] | [40, 2, 0] | Failed |
| regression (boundary) 1 | [8, 4, 1] | [8, 4, 1] | Passed |
| partial-repair probe 2 | [31, 16, 4] | [39, 12, 0] | Failed |
| partial-repair probe 3 | [34, 12, 0] | [40, 6, 0] | Failed |
| boundary control 4 | [40, 16, 0] | [40, 16, 0] | Passed |
| boundary control 5 | [40, 10, 0] | [40, 10, 0] | Passed |
| normal control 6 | [39, 8, 0] | [39, 8, 0] | Passed |
| normal control 7 | [40, 10, 0] | [40, 10, 0] | Passed |
| normal control 8 | [40, 15, 0] | [40, 15, 0] | Passed |
| normal control 9 | [39, 9, 2] | [39, 9, 2] | Passed |
SHA-256 / 21d88e680fa505f24487b6c6ba3e0abcb226a4d42cc076b2992a2cab76a4c976
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
hours = x
reg = ot = dt = 0
worked_all = all(h > 0 for h in hours)
for i, h in enumerate(hours):
if i == 6 and worked_all:
ot += min(h, 8)
dt += max(0, h - 8)
continue
d_reg = min(h, 8)
d_ot = max(0, min(h, 12) - 8)
d_dt = max(0, h - 12)
room = max(0, 40 - reg)
if d_reg > room:
d_ot += d_reg - room
d_reg = room
reg += d_reg
ot += d_ot
dt += d_dt
return [reg, ot, dt]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', [6, 8, 9, 0, 8, 3, 8], [40, 2, 0]), ('regression (boundary)', [0, 0, 0, 0, 0, 0, 13], [8, 4, 1]), ('partial-repair probe', [12, 8, 3, 0, 12, 4, 12], [39, 12, 0]), ('partial-repair probe', [8, 2, 8, 0, 12, 9, 7], [40, 6, 0]), ('boundary control', [8, 8, 8, 8, 8, 8, 8], [40, 16, 0]), ('boundary control', [10, 10, 10, 10, 10, 0, 0], [40, 10, 0]), ('normal control', [12, 12, 8, 7, 0, 8, 0], [39, 8, 0]), ('normal control', [0, 12, 10, 8, 8, 12, 0], [40, 10, 0]), ('normal control', [10, 8, 6, 12, 9, 10, 0], [40, 15, 0]), ('normal control', [14, 9, 8, 7, 0, 12, 0], [39, 9, 2])], [('regression', [12, 8, 3, 0, 12, 4, 12], [39, 12, 0]), ('regression', [6, 8, 9, 0, 8, 3, 8], [40, 2, 0]), ('partial-repair probe', [8, 2, 8, 0, 12, 9, 7], [40, 6, 0]), ('partial-repair probe', [9, 8, 8, 0, 12, 8, 12], [40, 17, 0]), ('boundary control', [8, 8, 8, 8, 8, 8, 8], [40, 16, 0]), ('boundary control', [10, 10, 10, 10, 10, 0, 0], [40, 10, 0]), ('normal control', [0, 0, 0, 7, 10, 8, 0], [23, 2, 0]), ('normal control', [8, 8, 5, 0, 0, 10, 0], [29, 2, 0]), ('normal control', [0, 7, 12, 8, 0, 7, 0], [30, 4, 0]), ('normal control', [0, 4, 4, 9, 8, 8, 0], [32, 1, 0])], [('regression', [8, 2, 8, 0, 12, 9, 7], [40, 6, 0]), ('regression', [8, 7, 14, 0, 12, 0, 8], [39, 8, 2]), ('partial-repair probe', [0, 10, 12, 8, 10, 12, 9], [40, 21, 0]), ('partial-repair probe', [9, 12, 8, 0, 1, 8, 8], [40, 6, 0]), ('boundary control', [8, 8, 8, 8, 8, 8, 8], [40, 16, 0]), ('boundary control', [10, 10, 10, 10, 10, 0, 0], [40, 10, 0]), ('normal control', [0, 12, 0, 0, 10, 8, 0], [24, 6, 0]), ('normal control', [12, 7, 12, 0, 8, 8, 0], [39, 8, 0]), ('normal control', [8, 8, 10, 8, 8, 8, 6], [40, 16, 0]), ('normal control', [14, 10, 12, 6, 12, 0, 0], [38, 14, 2])], [('regression', [9, 8, 8, 0, 12, 8, 12], [40, 17, 0]), ('regression', [12, 8, 3, 0, 12, 4, 12], [39, 12, 0]), ('partial-repair probe', [8, 8, 7, 8, 0, 14, 6], [40, 9, 2]), ('partial-repair probe', [7, 8, 8, 0, 9, 8, 8], [40, 8, 0]), ('boundary control', [8, 8, 8, 8, 8, 8, 8], [40, 16, 0]), ('boundary control', [10, 10, 10, 10, 10, 0, 0], [40, 10, 0]), ('normal control', [0, 2, 8, 8, 12, 12, 0], [34, 8, 0]), ('normal control', [8, 8, 0, 12, 12, 0, 0], [32, 8, 0]), ('normal control', [7, 0, 8, 0, 8, 12, 0], [31, 4, 0]), ('normal control', [12, 4, 12, 12, 2, 9, 14], [38, 21, 6])], [('regression', [0, 10, 12, 8, 10, 12, 9], [40, 21, 0]), ('regression', [0, 0, 0, 8, 0, 0, 8], [16, 0, 0]), ('partial-repair probe', [8, 8, 0, 12, 8, 12, 12], [40, 20, 0]), ('partial-repair probe', [8, 12, 0, 12, 9, 8, 10], [40, 19, 0]), ('boundary control', [8, 8, 8, 8, 8, 8, 8], [40, 16, 0]), ('boundary control', [10, 10, 10, 10, 10, 0, 0], [40, 10, 0]), ('normal control', [9, 9, 6, 8, 0, 12, 0], [38, 6, 0]), ('normal control', [0, 12, 3, 6, 12, 12, 0], [33, 12, 0]), ('normal control', [0, 0, 0, 9, 0, 8, 0], [16, 1, 0]), ('normal control', [0, 8, 6, 8, 6, 12, 0], [36, 4, 0])]]
for i, (label, args, expected) in enumerate(fixtures[N-1]):
check("%s %d" % (label, i), solve(args), 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 0 | [40, 2, 0] | [40, 2, 0] | Passed |
| regression (boundary) 1 | [8, 4, 1] | [8, 4, 1] | Passed |
| partial-repair probe 2 | [39, 12, 0] | [39, 12, 0] | Passed |
| partial-repair probe 3 | [40, 6, 0] | [40, 6, 0] | Passed |
| boundary control 4 | [40, 16, 0] | [40, 16, 0] | Passed |
| boundary control 5 | [40, 10, 0] | [40, 10, 0] | Passed |
| normal control 6 | [39, 8, 0] | [39, 8, 0] | Passed |
| normal control 7 | [40, 10, 0] | [40, 10, 0] | Passed |
| normal control 8 | [40, 15, 0] | [40, 15, 0] | Passed |
| normal control 9 | [39, 9, 2] | [39, 9, 2] | Passed |
SHA-256 / b0d6a07017775345a5d5137691054ef330a453db32e215516e220414c4a747e0
Verification & scope
A deterministic teaching model of a stipulated payroll rule with toy thresholds and rates. It makes no claim of conformance to any tax authority, statute or jurisdiction and is not payroll software. 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 2026-09-29T14:46:34.505379+00:00.
Case digest / ee81574f4b4d5cbfe9a04c8b8d7a2e84c5dfd90325be8dbcbbfcd50173446131