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FA-17821 / Time representation / Open access

Smear residual loses the signed removed leap amount · case 01

The decoded time state disagrees with the explicit regression oracle for residual.

Verified by executionVariant 1 · 11 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Smear residual loses the signed removed leap amount.

THE FAILURE

Smear residual loses the signed removed leap amount.

Unsuccessful approach: The partial correction still substitutes abs(r['atomic'] - smeared) 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 = smeared - r['atomic']
    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 fixtureActualExpectedOutcome
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']Failed
fixture 3['19', '1', '-1', [10, 19], '0']['19', '1', '1', [10, 19], '0']Failed
fixture 4['24', '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['31/2', '11/10', '1/2', [10, 21], '-1/2']['31/2', '11/10', '-1/2', [10, 21], '-1/2']Failed
fixture 7['8/3', '2/3', '-1/3', [2, 6], '5/3']['8/3', '2/3', '1/3', [2, 6], '5/3']Failed
fixture 8['26/3', '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['5/3', '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 / cd7f4409a16647c7c4494427dcabd0cfab31a8126900e605ae7f424412b26582

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'] - correction
    active = r['start'] <= r['atomic'] < r['end']
    slope = 1 - Fraction(r['leap'],width) if active else Fraction(1)
    residual = abs(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 fixtureActualExpectedOutcome
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']Failed
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']Failed
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 / a2940adfaa51498ec0dfb39932163c4222ee9fbc3fbea11c31ce7c610e78325b

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 11 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:39:51.309787+00:00.

Case digest / f22ac00fbeff364786dfbb50ed147fe94561925e7f7c7a360a402c96c3f29057