FA-97011 / Recipe scaling and nutrition / Open access
Percent daily value formatter: micronutrient 10 percent band · case 01
7% calcium prints 5% instead of 8%.
ROOT CAUSE
Calcium and vitamin D values at or below 10% skip the 2% increment.
VERIFIED REPAIR
Use 2%, 5% and 10% increments in their bands.
Unsuccessful approach: Dropping the 10% increment above 50% prints 65% instead of 70%.
Case contract
DVs: sodium 2300 mg, fat 78 g, fiber 28 g, calcium 1300 mg, vitamin d 20 mcg, added sugars 50 g, protein 50 g. Names are trimmed, case-insensitive; unknown -> "error: no daily value". Units g, mg, mcg convert exactly; "iu" is allowed only for vitamin d (40 IU = 1 mcg), else "error: unit". pct = amount/DV*100. Zero -> "0%". Calcium and vitamin d: <2 -> "<2%", <=10 -> nearest 2, <=50 -> nearest 5, else nearest 10. Others: <1 -> "<1%", else nearest 1. Half-up.
Why this case matters
Label software prints %DV with different increments for micronutrients and macronutrients.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(nutrient, amount, unit):
DV = {'sodium': (2300, 'mg'), 'fat': (78, 'g'), 'fiber': (28, 'g'), 'calcium': (1300, 'mg'),
'vitamin d': (20, 'mcg'), 'added sugars': (50, 'g'), 'protein': (50, 'g')}
SCALE = {'g': 1000000, 'mg': 1000, 'mcg': 1}
key = nutrient.strip().lower()
if key not in DV:
return 'error: no daily value'
amt = Fraction(str(amount))
if unit == 'iu':
if key != 'vitamin d':
return 'error: unit'
amt, unit = amt / 40, 'mcg'
if unit not in SCALE:
return 'error: unit'
dv, dvu = DV[key]
p = amt * SCALE[unit] / (dv * SCALE[dvu]) * 100
def near(v, s):
return math.floor(v / s + Fraction(1, 2)) * s
if p == 0:
return '0%'
if key in ('calcium', 'vitamin d'):
if p < 2:
return '<2%'
v = near(p, 5) if p <= 50 else near(p, 10)
else:
if p < 1:
return '<1%'
v = near(p, 1)
return '%d%%' % v
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['sodium control', ['sodium', 460, 'mg'], '20%'],
['calcium exactly two percent', ['calcium', 26, 'mg'], '2%'],
['vitamin d in IU', ['vitamin d', 400, 'iu'], '50%'],
['repair check: micronutrient 10 percent band', ['CALCIUM', 2300, 'g'], '176920%'],
['generated control 1', ['vitamin d', 0.2, 'mcg'], '<2%'],
['generated control 2', ['fiber', 0.2, 'g'], '<1%'], ['generated control 3', ['sodium', 5, 'g'], '217%'],
['generated control 4', ['protein', 3, 'mcg'], '<1%']],
[['calcium exactly two percent', ['calcium', 26, 'mg'], '2%'],
['vitamin d in IU', ['vitamin d', 400, 'iu'], '50%'], ['fat in grams', ['fat', 3, 'g'], '4%'],
['regression: micronutrient 10 percent band', ['CALCIUM', 26, 'mg'], '2%'],
['repair check: micronutrient 10 percent band', ['calcium', 40, 'g'], '3080%'],
['generated control 1', ['fiber', 10, 'iu'], 'error: unit'],
['generated control 2', ['fiber', 0.39, 'g'], '1%'],
['generated control 3', ['protein', 300, 'mcg'], '<1%']],
[['vitamin d in IU', ['vitamin d', 400, 'iu'], '50%'], ['fat in grams', ['fat', 3, 'g'], '4%'],
['zero calcium', ['calcium', 0, 'mg'], '0%'],
['regression: micronutrient 10 percent band', ['vitamin d', 0.5, 'mcg'], '2%'],
['repair check: micronutrient 10 percent band', ['calcium', 300, 'g'], '23080%'],
['generated control 1', ['sodium', 1500, 'mcg'], '<1%'],
['generated control 2', ['protein', 260, 'mcg'], '<1%'],
['generated control 3', ['iron', 0.2, 'mg'], 'error: no daily value']],
[['fat in grams', ['fat', 3, 'g'], '4%'], ['zero calcium', ['calcium', 0, 'mg'], '0%'],
['iu for sodium rejected', ['sodium', 10, 'iu'], 'error: unit'],
['regression: micronutrient 10 percent band', ['CALCIUM', 40, 'mg'], '4%'],
['repair check: micronutrient 10 percent band', ['CALCIUM', 2, 'g'], '150%'],
['generated control 1', ['sodium', 5, 'mg'], '<1%'],
['generated control 2', ['iron', 40, 'g'], 'error: no daily value'],
['generated control 3', ['calcium', 12, 'mcg'], '<2%']],
[['zero calcium', ['calcium', 0, 'mg'], '0%'],
['iu for sodium rejected', ['sodium', 10, 'iu'], 'error: unit'],
['sodium control', ['sodium', 460, 'mg'], '20%'],
['regression: micronutrient 10 percent band', ['calcium', 26, 'mg'], '2%'],
['repair check: micronutrient 10 percent band', ['CALCIUM', 1500, 'mg'], '120%'],
['generated control 1', ['sodium', 300, 'mg'], '13%'], ['generated control 2', ['fat', 0.5, 'g'], '<1%'],
['generated control 3', ['calcium', 0.2, 'mcg'], '<2%']]]
for label, args, expected in fixtures[N - 1]:
check(label, 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 |
|---|---|---|---|
| sodium control | 20% | 20% | Passed |
| calcium exactly two percent | 0% | 2% | Failed |
| vitamin d in IU | 50% | 50% | Passed |
| repair check: micronutrient 10 percent band | 176920% | 176920% | Passed |
| generated control 1 | <2% | <2% | Passed |
| generated control 2 | <1% | <1% | Passed |
| generated control 3 | 217% | 217% | Passed |
| generated control 4 | <1% | <1% | Passed |
SHA-256 / bc7ebf207b6e77859bf2e8b25ff1050b23b2434a00c191aba2cf12cbf6bccc3d
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(nutrient, amount, unit):
DV = {'sodium': (2300, 'mg'), 'fat': (78, 'g'), 'fiber': (28, 'g'), 'calcium': (1300, 'mg'),
'vitamin d': (20, 'mcg'), 'added sugars': (50, 'g'), 'protein': (50, 'g')}
SCALE = {'g': 1000000, 'mg': 1000, 'mcg': 1}
key = nutrient.strip().lower()
if key not in DV:
return 'error: no daily value'
amt = Fraction(str(amount))
if unit == 'iu':
if key != 'vitamin d':
return 'error: unit'
amt, unit = amt / 40, 'mcg'
if unit not in SCALE:
return 'error: unit'
dv, dvu = DV[key]
p = amt * SCALE[unit] / (dv * SCALE[dvu]) * 100
def near(v, s):
return math.floor(v / s + Fraction(1, 2)) * s
if p == 0:
return '0%'
if key in ('calcium', 'vitamin d'):
if p < 2:
return '<2%'
v = near(p, 2) if p <= 10 else near(p, 5)
else:
if p < 1:
return '<1%'
v = near(p, 1)
return '%d%%' % v
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['sodium control', ['sodium', 460, 'mg'], '20%'],
['calcium exactly two percent', ['calcium', 26, 'mg'], '2%'],
['vitamin d in IU', ['vitamin d', 400, 'iu'], '50%'],
['repair check: micronutrient 10 percent band', ['CALCIUM', 2300, 'g'], '176920%'],
['generated control 1', ['vitamin d', 0.2, 'mcg'], '<2%'],
['generated control 2', ['fiber', 0.2, 'g'], '<1%'], ['generated control 3', ['sodium', 5, 'g'], '217%'],
['generated control 4', ['protein', 3, 'mcg'], '<1%']],
[['calcium exactly two percent', ['calcium', 26, 'mg'], '2%'],
['vitamin d in IU', ['vitamin d', 400, 'iu'], '50%'], ['fat in grams', ['fat', 3, 'g'], '4%'],
['regression: micronutrient 10 percent band', ['CALCIUM', 26, 'mg'], '2%'],
['repair check: micronutrient 10 percent band', ['calcium', 40, 'g'], '3080%'],
['generated control 1', ['fiber', 10, 'iu'], 'error: unit'],
['generated control 2', ['fiber', 0.39, 'g'], '1%'],
['generated control 3', ['protein', 300, 'mcg'], '<1%']],
[['vitamin d in IU', ['vitamin d', 400, 'iu'], '50%'], ['fat in grams', ['fat', 3, 'g'], '4%'],
['zero calcium', ['calcium', 0, 'mg'], '0%'],
['regression: micronutrient 10 percent band', ['vitamin d', 0.5, 'mcg'], '2%'],
['repair check: micronutrient 10 percent band', ['calcium', 300, 'g'], '23080%'],
['generated control 1', ['sodium', 1500, 'mcg'], '<1%'],
['generated control 2', ['protein', 260, 'mcg'], '<1%'],
['generated control 3', ['iron', 0.2, 'mg'], 'error: no daily value']],
[['fat in grams', ['fat', 3, 'g'], '4%'], ['zero calcium', ['calcium', 0, 'mg'], '0%'],
['iu for sodium rejected', ['sodium', 10, 'iu'], 'error: unit'],
['regression: micronutrient 10 percent band', ['CALCIUM', 40, 'mg'], '4%'],
['repair check: micronutrient 10 percent band', ['CALCIUM', 2, 'g'], '150%'],
['generated control 1', ['sodium', 5, 'mg'], '<1%'],
['generated control 2', ['iron', 40, 'g'], 'error: no daily value'],
['generated control 3', ['calcium', 12, 'mcg'], '<2%']],
[['zero calcium', ['calcium', 0, 'mg'], '0%'],
['iu for sodium rejected', ['sodium', 10, 'iu'], 'error: unit'],
['sodium control', ['sodium', 460, 'mg'], '20%'],
['regression: micronutrient 10 percent band', ['calcium', 26, 'mg'], '2%'],
['repair check: micronutrient 10 percent band', ['CALCIUM', 1500, 'mg'], '120%'],
['generated control 1', ['sodium', 300, 'mg'], '13%'], ['generated control 2', ['fat', 0.5, 'g'], '<1%'],
['generated control 3', ['calcium', 0.2, 'mcg'], '<2%']]]
for label, args, expected in fixtures[N - 1]:
check(label, 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 |
|---|---|---|---|
| sodium control | 20% | 20% | Passed |
| calcium exactly two percent | 2% | 2% | Passed |
| vitamin d in IU | 50% | 50% | Passed |
| repair check: micronutrient 10 percent band | 176925% | 176920% | Failed |
| generated control 1 | <2% | <2% | Passed |
| generated control 2 | <1% | <1% | Passed |
| generated control 3 | 217% | 217% | Passed |
| generated control 4 | <1% | <1% | Passed |
SHA-256 / 3c6bd20baf5921fee157e80ccb5f0958c7721bd5334b3575880fbc3bda5ef3d8
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(nutrient, amount, unit):
DV = {'sodium': (2300, 'mg'), 'fat': (78, 'g'), 'fiber': (28, 'g'), 'calcium': (1300, 'mg'),
'vitamin d': (20, 'mcg'), 'added sugars': (50, 'g'), 'protein': (50, 'g')}
SCALE = {'g': 1000000, 'mg': 1000, 'mcg': 1}
key = nutrient.strip().lower()
if key not in DV:
return 'error: no daily value'
amt = Fraction(str(amount))
if unit == 'iu':
if key != 'vitamin d':
return 'error: unit'
amt, unit = amt / 40, 'mcg'
if unit not in SCALE:
return 'error: unit'
dv, dvu = DV[key]
p = amt * SCALE[unit] / (dv * SCALE[dvu]) * 100
def near(v, s):
return math.floor(v / s + Fraction(1, 2)) * s
if p == 0:
return '0%'
if key in ('calcium', 'vitamin d'):
if p < 2:
return '<2%'
v = near(p, 2) if p <= 10 else near(p, 5) if p <= 50 else near(p, 10)
else:
if p < 1:
return '<1%'
v = near(p, 1)
return '%d%%' % v
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['sodium control', ['sodium', 460, 'mg'], '20%'],
['calcium exactly two percent', ['calcium', 26, 'mg'], '2%'],
['vitamin d in IU', ['vitamin d', 400, 'iu'], '50%'],
['repair check: micronutrient 10 percent band', ['CALCIUM', 2300, 'g'], '176920%'],
['generated control 1', ['vitamin d', 0.2, 'mcg'], '<2%'],
['generated control 2', ['fiber', 0.2, 'g'], '<1%'], ['generated control 3', ['sodium', 5, 'g'], '217%'],
['generated control 4', ['protein', 3, 'mcg'], '<1%']],
[['calcium exactly two percent', ['calcium', 26, 'mg'], '2%'],
['vitamin d in IU', ['vitamin d', 400, 'iu'], '50%'], ['fat in grams', ['fat', 3, 'g'], '4%'],
['regression: micronutrient 10 percent band', ['CALCIUM', 26, 'mg'], '2%'],
['repair check: micronutrient 10 percent band', ['calcium', 40, 'g'], '3080%'],
['generated control 1', ['fiber', 10, 'iu'], 'error: unit'],
['generated control 2', ['fiber', 0.39, 'g'], '1%'],
['generated control 3', ['protein', 300, 'mcg'], '<1%']],
[['vitamin d in IU', ['vitamin d', 400, 'iu'], '50%'], ['fat in grams', ['fat', 3, 'g'], '4%'],
['zero calcium', ['calcium', 0, 'mg'], '0%'],
['regression: micronutrient 10 percent band', ['vitamin d', 0.5, 'mcg'], '2%'],
['repair check: micronutrient 10 percent band', ['calcium', 300, 'g'], '23080%'],
['generated control 1', ['sodium', 1500, 'mcg'], '<1%'],
['generated control 2', ['protein', 260, 'mcg'], '<1%'],
['generated control 3', ['iron', 0.2, 'mg'], 'error: no daily value']],
[['fat in grams', ['fat', 3, 'g'], '4%'], ['zero calcium', ['calcium', 0, 'mg'], '0%'],
['iu for sodium rejected', ['sodium', 10, 'iu'], 'error: unit'],
['regression: micronutrient 10 percent band', ['CALCIUM', 40, 'mg'], '4%'],
['repair check: micronutrient 10 percent band', ['CALCIUM', 2, 'g'], '150%'],
['generated control 1', ['sodium', 5, 'mg'], '<1%'],
['generated control 2', ['iron', 40, 'g'], 'error: no daily value'],
['generated control 3', ['calcium', 12, 'mcg'], '<2%']],
[['zero calcium', ['calcium', 0, 'mg'], '0%'],
['iu for sodium rejected', ['sodium', 10, 'iu'], 'error: unit'],
['sodium control', ['sodium', 460, 'mg'], '20%'],
['regression: micronutrient 10 percent band', ['calcium', 26, 'mg'], '2%'],
['repair check: micronutrient 10 percent band', ['CALCIUM', 1500, 'mg'], '120%'],
['generated control 1', ['sodium', 300, 'mg'], '13%'], ['generated control 2', ['fat', 0.5, 'g'], '<1%'],
['generated control 3', ['calcium', 0.2, 'mcg'], '<2%']]]
for label, args, expected in fixtures[N - 1]:
check(label, 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 |
|---|---|---|---|
| sodium control | 20% | 20% | Passed |
| calcium exactly two percent | 2% | 2% | Passed |
| vitamin d in IU | 50% | 50% | Passed |
| repair check: micronutrient 10 percent band | 176920% | 176920% | Passed |
| generated control 1 | <2% | <2% | Passed |
| generated control 2 | <1% | <1% | Passed |
| generated control 3 | 217% | 217% | Passed |
| generated control 4 | <1% | <1% | Passed |
SHA-256 / 5c812030af0f412d478274e0b5a67fca04cfac8ed476a57ae45cceeeed9e9bf1
Verification & scope
A deterministic toy contract stated in full here; it is a bounded teaching model, not an authoritative reference or standards implementation. 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 2026-09-29T14:52:28.008157+00:00.
Case digest / c7cbbc06d77fc23485ce1e3ccf3f050e3bab970d9517a16ea9c0a15de7cffbdf