FA-17806 / Time representation / Open access
Smear coordinate reverses phase correction or quantizes early · case 01
The decoded time state disagrees with the explicit regression oracle for smeared.
ROOT CAUSE
Smear coordinate reverses phase correction or quantizes early.
VERIFIED REPAIR
Preserve the declared coordinate and state contract at smeared: smeared = r['atomic'] - correction.
Unsuccessful approach: The partial correction still substitutes r['atomic'] - int(correction) at the same fault site.
Case contract
Stipulated smear removes signed leap L linearly over atomic [start,end], with positive width>|L| and clamped progress outside. Return exact rational smeared coordinate, effective slope (inside start-inclusive/end-exclusive window), signed removed correction, smeared endpoint coordinates and remaining signed correction. Fraction outputs use canonical strings.
Why this case matters
Clock transfer and timestamp consumers require preserved coordinate, phase, validity and elapsed-time semantics.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(r):
width = r['end'] - r['start']
progress = Fraction(min(width,max(0,r['atomic'] - r['start'])),width)
correction = progress * r['leap']
smeared = r['atomic'] + correction
active = r['start'] <= r['atomic'] < r['end']
slope = 1 - Fraction(r['leap'],width) if active else Fraction(1)
residual = r['atomic'] - smeared
start_coordinate = r['start']
end_coordinate = r['end'] - r['leap']
remaining = r['leap'] - correction
return [str(smeared),str(slope),str(residual),[start_coordinate,end_coordinate],str(remaining)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'start': 10, 'end': 20, 'atomic': 10, 'leap': 1}), ['10', '9/10', '0', [10, 19], '1'])
check('fixture 2', solve({'start': 10, 'end': 20, 'atomic': 15, 'leap': 1}), ['29/2', '9/10', '1/2', [10, 19], '1/2'])
check('fixture 3', solve({'start': 10, 'end': 20, 'atomic': 20, 'leap': 1}), ['19', '1', '1', [10, 19], '0'])
check('fixture 4', solve({'start': 10, 'end': 20, 'atomic': 25, 'leap': 1}), ['24', '1', '1', [10, 19], '0'])
check('fixture 5', solve({'start': 10, 'end': 20, 'atomic': 5, 'leap': 1}), ['5', '1', '0', [10, 19], '1'])
check('fixture 6', solve({'start': 10, 'end': 20, 'atomic': 15, 'leap': -1}), ['31/2', '11/10', '-1/2', [10, 21], '-1/2'])
check('fixture 7', solve({'start': 2, 'end': 8, 'atomic': 3, 'leap': 2}), ['8/3', '2/3', '1/3', [2, 6], '5/3'])
check('fixture 8', solve({'start': 2, 'end': 8, 'atomic': 7, 'leap': -2}), ['26/3', '4/3', '-5/3', [2, 10], '-1/3'])
check('fixture 9', solve({'start': 10, 'end': 20, 'atomic': 15, 'leap': 0}), ['15', '1', '0', [10, 20], '0'])
check('fixture 10', solve({'start': 1, 'end': 4, 'atomic': 2, 'leap': 1}), ['5/3', '2/3', '1/3', [1, 3], '2/3'])
variant = [({'start': 10, 'end': 20, 'atomic': 10, 'leap': 2}, ['10', '4/5', '0', [10, 18], '2']), ({'start': 10, 'end': 20, 'atomic': 10, 'leap': 3}, ['10', '7/10', '0', [10, 17], '3']), ({'start': 10, 'end': 20, 'atomic': 10, 'leap': 4}, ['10', '3/5', '0', [10, 16], '4']), ({'start': 10, 'end': 20, 'atomic': 10, 'leap': 5}, ['10', '1/2', '0', [10, 15], '5']), ({'start': 10, 'end': 20, 'atomic': 10, 'leap': 6}, ['10', '2/5', '0', [10, 14], '6'])]
check("variant capture", solve(variant[N-1][0]), variant[N-1][1])
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 |
|---|---|---|---|
| fixture 1 | ['10', '9/10', '0', [10, 19], '1'] | ['10', '9/10', '0', [10, 19], '1'] | Passed |
| fixture 2 | ['31/2', '9/10', '-1/2', [10, 19], '1/2'] | ['29/2', '9/10', '1/2', [10, 19], '1/2'] | Failed |
| fixture 3 | ['21', '1', '-1', [10, 19], '0'] | ['19', '1', '1', [10, 19], '0'] | Failed |
| fixture 4 | ['26', '1', '-1', [10, 19], '0'] | ['24', '1', '1', [10, 19], '0'] | Failed |
| fixture 5 | ['5', '1', '0', [10, 19], '1'] | ['5', '1', '0', [10, 19], '1'] | Passed |
| fixture 6 | ['29/2', '11/10', '1/2', [10, 21], '-1/2'] | ['31/2', '11/10', '-1/2', [10, 21], '-1/2'] | Failed |
| fixture 7 | ['10/3', '2/3', '-1/3', [2, 6], '5/3'] | ['8/3', '2/3', '1/3', [2, 6], '5/3'] | Failed |
| fixture 8 | ['16/3', '4/3', '5/3', [2, 10], '-1/3'] | ['26/3', '4/3', '-5/3', [2, 10], '-1/3'] | Failed |
| fixture 9 | ['15', '1', '0', [10, 20], '0'] | ['15', '1', '0', [10, 20], '0'] | Passed |
| fixture 10 | ['7/3', '2/3', '-1/3', [1, 3], '2/3'] | ['5/3', '2/3', '1/3', [1, 3], '2/3'] | Failed |
| variant capture | ['10', '4/5', '0', [10, 18], '2'] | ['10', '4/5', '0', [10, 18], '2'] | Passed |
SHA-256 / 0393ae310cb8f11ee2948e9c760daea59c8e95f93f07705268b27a17f6dbeff0
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(r):
width = r['end'] - r['start']
progress = Fraction(min(width,max(0,r['atomic'] - r['start'])),width)
correction = progress * r['leap']
smeared = r['atomic'] - int(correction)
active = r['start'] <= r['atomic'] < r['end']
slope = 1 - Fraction(r['leap'],width) if active else Fraction(1)
residual = r['atomic'] - smeared
start_coordinate = r['start']
end_coordinate = r['end'] - r['leap']
remaining = r['leap'] - correction
return [str(smeared),str(slope),str(residual),[start_coordinate,end_coordinate],str(remaining)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'start': 10, 'end': 20, 'atomic': 10, 'leap': 1}), ['10', '9/10', '0', [10, 19], '1'])
check('fixture 2', solve({'start': 10, 'end': 20, 'atomic': 15, 'leap': 1}), ['29/2', '9/10', '1/2', [10, 19], '1/2'])
check('fixture 3', solve({'start': 10, 'end': 20, 'atomic': 20, 'leap': 1}), ['19', '1', '1', [10, 19], '0'])
check('fixture 4', solve({'start': 10, 'end': 20, 'atomic': 25, 'leap': 1}), ['24', '1', '1', [10, 19], '0'])
check('fixture 5', solve({'start': 10, 'end': 20, 'atomic': 5, 'leap': 1}), ['5', '1', '0', [10, 19], '1'])
check('fixture 6', solve({'start': 10, 'end': 20, 'atomic': 15, 'leap': -1}), ['31/2', '11/10', '-1/2', [10, 21], '-1/2'])
check('fixture 7', solve({'start': 2, 'end': 8, 'atomic': 3, 'leap': 2}), ['8/3', '2/3', '1/3', [2, 6], '5/3'])
check('fixture 8', solve({'start': 2, 'end': 8, 'atomic': 7, 'leap': -2}), ['26/3', '4/3', '-5/3', [2, 10], '-1/3'])
check('fixture 9', solve({'start': 10, 'end': 20, 'atomic': 15, 'leap': 0}), ['15', '1', '0', [10, 20], '0'])
check('fixture 10', solve({'start': 1, 'end': 4, 'atomic': 2, 'leap': 1}), ['5/3', '2/3', '1/3', [1, 3], '2/3'])
variant = [({'start': 10, 'end': 20, 'atomic': 10, 'leap': 2}, ['10', '4/5', '0', [10, 18], '2']), ({'start': 10, 'end': 20, 'atomic': 10, 'leap': 3}, ['10', '7/10', '0', [10, 17], '3']), ({'start': 10, 'end': 20, 'atomic': 10, 'leap': 4}, ['10', '3/5', '0', [10, 16], '4']), ({'start': 10, 'end': 20, 'atomic': 10, 'leap': 5}, ['10', '1/2', '0', [10, 15], '5']), ({'start': 10, 'end': 20, 'atomic': 10, 'leap': 6}, ['10', '2/5', '0', [10, 14], '6'])]
check("variant capture", solve(variant[N-1][0]), variant[N-1][1])
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 |
|---|---|---|---|
| fixture 1 | ['10', '9/10', '0', [10, 19], '1'] | ['10', '9/10', '0', [10, 19], '1'] | Passed |
| fixture 2 | ['15', '9/10', '0', [10, 19], '1/2'] | ['29/2', '9/10', '1/2', [10, 19], '1/2'] | Failed |
| fixture 3 | ['19', '1', '1', [10, 19], '0'] | ['19', '1', '1', [10, 19], '0'] | Passed |
| fixture 4 | ['24', '1', '1', [10, 19], '0'] | ['24', '1', '1', [10, 19], '0'] | Passed |
| fixture 5 | ['5', '1', '0', [10, 19], '1'] | ['5', '1', '0', [10, 19], '1'] | Passed |
| fixture 6 | ['15', '11/10', '0', [10, 21], '-1/2'] | ['31/2', '11/10', '-1/2', [10, 21], '-1/2'] | Failed |
| fixture 7 | ['3', '2/3', '0', [2, 6], '5/3'] | ['8/3', '2/3', '1/3', [2, 6], '5/3'] | Failed |
| fixture 8 | ['8', '4/3', '-1', [2, 10], '-1/3'] | ['26/3', '4/3', '-5/3', [2, 10], '-1/3'] | Failed |
| fixture 9 | ['15', '1', '0', [10, 20], '0'] | ['15', '1', '0', [10, 20], '0'] | Passed |
| fixture 10 | ['2', '2/3', '0', [1, 3], '2/3'] | ['5/3', '2/3', '1/3', [1, 3], '2/3'] | Failed |
| variant capture | ['10', '4/5', '0', [10, 18], '2'] | ['10', '4/5', '0', [10, 18], '2'] | Passed |
SHA-256 / 71737ab96452333d5df5b42375d4740e8f5e6394189af7c315b3e89c681725a8
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(r):
width = r['end'] - r['start']
progress = Fraction(min(width,max(0,r['atomic'] - r['start'])),width)
correction = progress * r['leap']
smeared = r['atomic'] - correction
active = r['start'] <= r['atomic'] < r['end']
slope = 1 - Fraction(r['leap'],width) if active else Fraction(1)
residual = r['atomic'] - smeared
start_coordinate = r['start']
end_coordinate = r['end'] - r['leap']
remaining = r['leap'] - correction
return [str(smeared),str(slope),str(residual),[start_coordinate,end_coordinate],str(remaining)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'start': 10, 'end': 20, 'atomic': 10, 'leap': 1}), ['10', '9/10', '0', [10, 19], '1'])
check('fixture 2', solve({'start': 10, 'end': 20, 'atomic': 15, 'leap': 1}), ['29/2', '9/10', '1/2', [10, 19], '1/2'])
check('fixture 3', solve({'start': 10, 'end': 20, 'atomic': 20, 'leap': 1}), ['19', '1', '1', [10, 19], '0'])
check('fixture 4', solve({'start': 10, 'end': 20, 'atomic': 25, 'leap': 1}), ['24', '1', '1', [10, 19], '0'])
check('fixture 5', solve({'start': 10, 'end': 20, 'atomic': 5, 'leap': 1}), ['5', '1', '0', [10, 19], '1'])
check('fixture 6', solve({'start': 10, 'end': 20, 'atomic': 15, 'leap': -1}), ['31/2', '11/10', '-1/2', [10, 21], '-1/2'])
check('fixture 7', solve({'start': 2, 'end': 8, 'atomic': 3, 'leap': 2}), ['8/3', '2/3', '1/3', [2, 6], '5/3'])
check('fixture 8', solve({'start': 2, 'end': 8, 'atomic': 7, 'leap': -2}), ['26/3', '4/3', '-5/3', [2, 10], '-1/3'])
check('fixture 9', solve({'start': 10, 'end': 20, 'atomic': 15, 'leap': 0}), ['15', '1', '0', [10, 20], '0'])
check('fixture 10', solve({'start': 1, 'end': 4, 'atomic': 2, 'leap': 1}), ['5/3', '2/3', '1/3', [1, 3], '2/3'])
variant = [({'start': 10, 'end': 20, 'atomic': 10, 'leap': 2}, ['10', '4/5', '0', [10, 18], '2']), ({'start': 10, 'end': 20, 'atomic': 10, 'leap': 3}, ['10', '7/10', '0', [10, 17], '3']), ({'start': 10, 'end': 20, 'atomic': 10, 'leap': 4}, ['10', '3/5', '0', [10, 16], '4']), ({'start': 10, 'end': 20, 'atomic': 10, 'leap': 5}, ['10', '1/2', '0', [10, 15], '5']), ({'start': 10, 'end': 20, 'atomic': 10, 'leap': 6}, ['10', '2/5', '0', [10, 14], '6'])]
check("variant capture", solve(variant[N-1][0]), variant[N-1][1])
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 |
|---|---|---|---|
| fixture 1 | ['10', '9/10', '0', [10, 19], '1'] | ['10', '9/10', '0', [10, 19], '1'] | Passed |
| fixture 2 | ['29/2', '9/10', '1/2', [10, 19], '1/2'] | ['29/2', '9/10', '1/2', [10, 19], '1/2'] | Passed |
| fixture 3 | ['19', '1', '1', [10, 19], '0'] | ['19', '1', '1', [10, 19], '0'] | Passed |
| fixture 4 | ['24', '1', '1', [10, 19], '0'] | ['24', '1', '1', [10, 19], '0'] | Passed |
| fixture 5 | ['5', '1', '0', [10, 19], '1'] | ['5', '1', '0', [10, 19], '1'] | Passed |
| fixture 6 | ['31/2', '11/10', '-1/2', [10, 21], '-1/2'] | ['31/2', '11/10', '-1/2', [10, 21], '-1/2'] | Passed |
| fixture 7 | ['8/3', '2/3', '1/3', [2, 6], '5/3'] | ['8/3', '2/3', '1/3', [2, 6], '5/3'] | Passed |
| fixture 8 | ['26/3', '4/3', '-5/3', [2, 10], '-1/3'] | ['26/3', '4/3', '-5/3', [2, 10], '-1/3'] | Passed |
| fixture 9 | ['15', '1', '0', [10, 20], '0'] | ['15', '1', '0', [10, 20], '0'] | Passed |
| fixture 10 | ['5/3', '2/3', '1/3', [1, 3], '2/3'] | ['5/3', '2/3', '1/3', [1, 3], '2/3'] | Passed |
| variant capture | ['10', '4/5', '0', [10, 18], '2'] | ['10', '4/5', '0', [10, 18], '2'] | Passed |
SHA-256 / d861840361a4868d69e9b7ab1a454aac33d01ddadccae48c420745eb0fca9736
Verification & scope
Deterministic integer reference model with stipulated units and policies; not a complete clock, wire standard or platform 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 2026-09-29T14:39:50.969552+00:00.
Case digest / 06ff8aeff2a88e805e85a0a5ba7bc09d4cd5b3a843e16078556f3eb90e61360a