FAILURE MAP
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FA-17526 / Time representation / Open access

Epoch containment excludes endpoint or accepts every interval · case 01

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

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

ROOT CAUSE

Epoch containment excludes endpoint or accepts every interval.

VERIFIED REPAIR

Preserve the declared coordinate and state contract at contains_zero: contains_zero = low <= 0 <= high.

Unsuccessful approach: The partial correction still substitutes low <= 0 or high >= 0 at the same fault site.

Case contract

Project a center with asymmetric early/late error through signed elapsed ticks. Error growth uses elapsed magnitude and independent parts-per-thousand bounds rounded outward. Return projected [low,high], full width, zero containment, earliest/latest signed query duration and strict certainty of preceding query.

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):
    age = abs(r['elapsed'])
    early_growth = (age * r['early_rate'] + 999) // 1000
    late_growth = (age * r['late_rate'] + 999) // 1000
    center = r['anchor'] + r['elapsed']
    low = center - r['early'] - early_growth
    high = center + r['late'] + late_growth
    width = high - low
    contains_zero = low < 0 < high
    earliest = r['query'] - high
    latest = r['query'] - low
    return [[low,high],width,contains_zero,[earliest,latest],high < r['query']]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 20}), [[8, 15], 7, False, [5, 12], True])
check('fixture 2', solve({'anchor': 0, 'elapsed': -5, 'early': 0, 'late': 1, 'early_rate': 200, 'late_rate': 1, 'query': 0}), [[-6, -3], 3, False, [3, 6], True])
check('fixture 3', solve({'anchor': -1, 'elapsed': 1, 'early': 0, 'late': 0, 'early_rate': 0, 'late_rate': 0, 'query': -3}), [[0, 0], 0, True, [-3, -3], False])
check('fixture 4', solve({'anchor': 20, 'elapsed': 1000, 'early': 3, 'late': 5, 'early_rate': 2, 'late_rate': 7, 'query': 100}), [[1015, 1032], 17, False, [-932, -915], False])
check('fixture 5', solve({'anchor': -10, 'elapsed': 0, 'early': 2, 'late': 3, 'early_rate': 0, 'late_rate': 0, 'query': -20}), [[-12, -7], 5, False, [-13, -8], False])
check('fixture 6', solve({'anchor': 0, 'elapsed': 2, 'early': 5, 'late': 0, 'early_rate': 1, 'late_rate': 2000, 'query': 0}), [[-4, 6], 10, True, [-6, 4], False])
check('fixture 7', solve({'anchor': 10, 'elapsed': -1001, 'early': 0, 'late': 1, 'early_rate': 2, 'late_rate': 1, 'query': 8}), [[-994, -988], 6, False, [996, 1002], True])
check('fixture 8', solve({'anchor': 0, 'elapsed': 0, 'early': 0, 'late': 0, 'early_rate': 0, 'late_rate': 0, 'query': 0}), [[0, 0], 0, True, [0, 0], False])
check('fixture 9', solve({'anchor': 2, 'elapsed': -1, 'early': 0, 'late': 0, 'early_rate': 1000, 'late_rate': 1000, 'query': 2}), [[0, 2], 2, True, [0, 2], False])
check('fixture 10', solve({'anchor': 0, 'elapsed': 10, 'early': 1, 'late': 10, 'early_rate': 90, 'late_rate': 150, 'query': 20}), [[8, 22], 14, False, [-2, 12], False])
variant = [({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 21}, [[8, 15], 7, False, [6, 13], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 22}, [[8, 15], 7, False, [7, 14], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 23}, [[8, 15], 7, False, [8, 15], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 24}, [[8, 15], 7, False, [9, 16], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 25}, [[8, 15], 7, False, [10, 17], True])]
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[[8, 15], 7, False, [5, 12], True][[8, 15], 7, False, [5, 12], True]Passed
fixture 2[[-6, -3], 3, False, [3, 6], True][[-6, -3], 3, False, [3, 6], True]Passed
fixture 3[[0, 0], 0, False, [-3, -3], False][[0, 0], 0, True, [-3, -3], False]Failed
fixture 4[[1015, 1032], 17, False, [-932, -915], False][[1015, 1032], 17, False, [-932, -915], False]Passed
fixture 5[[-12, -7], 5, False, [-13, -8], False][[-12, -7], 5, False, [-13, -8], False]Passed
fixture 6[[-4, 6], 10, True, [-6, 4], False][[-4, 6], 10, True, [-6, 4], False]Passed
fixture 7[[-994, -988], 6, False, [996, 1002], True][[-994, -988], 6, False, [996, 1002], True]Passed
fixture 8[[0, 0], 0, False, [0, 0], False][[0, 0], 0, True, [0, 0], False]Failed
fixture 9[[0, 2], 2, False, [0, 2], False][[0, 2], 2, True, [0, 2], False]Failed
fixture 10[[8, 22], 14, False, [-2, 12], False][[8, 22], 14, False, [-2, 12], False]Passed
variant capture[[8, 15], 7, False, [6, 13], True][[8, 15], 7, False, [6, 13], True]Passed

SHA-256 / aae3a55bf57c08d2ca4529f716767be4a831fc0bdeb9800ee852bd698a89202a

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):
    age = abs(r['elapsed'])
    early_growth = (age * r['early_rate'] + 999) // 1000
    late_growth = (age * r['late_rate'] + 999) // 1000
    center = r['anchor'] + r['elapsed']
    low = center - r['early'] - early_growth
    high = center + r['late'] + late_growth
    width = high - low
    contains_zero = low <= 0 or high >= 0
    earliest = r['query'] - high
    latest = r['query'] - low
    return [[low,high],width,contains_zero,[earliest,latest],high < r['query']]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 20}), [[8, 15], 7, False, [5, 12], True])
check('fixture 2', solve({'anchor': 0, 'elapsed': -5, 'early': 0, 'late': 1, 'early_rate': 200, 'late_rate': 1, 'query': 0}), [[-6, -3], 3, False, [3, 6], True])
check('fixture 3', solve({'anchor': -1, 'elapsed': 1, 'early': 0, 'late': 0, 'early_rate': 0, 'late_rate': 0, 'query': -3}), [[0, 0], 0, True, [-3, -3], False])
check('fixture 4', solve({'anchor': 20, 'elapsed': 1000, 'early': 3, 'late': 5, 'early_rate': 2, 'late_rate': 7, 'query': 100}), [[1015, 1032], 17, False, [-932, -915], False])
check('fixture 5', solve({'anchor': -10, 'elapsed': 0, 'early': 2, 'late': 3, 'early_rate': 0, 'late_rate': 0, 'query': -20}), [[-12, -7], 5, False, [-13, -8], False])
check('fixture 6', solve({'anchor': 0, 'elapsed': 2, 'early': 5, 'late': 0, 'early_rate': 1, 'late_rate': 2000, 'query': 0}), [[-4, 6], 10, True, [-6, 4], False])
check('fixture 7', solve({'anchor': 10, 'elapsed': -1001, 'early': 0, 'late': 1, 'early_rate': 2, 'late_rate': 1, 'query': 8}), [[-994, -988], 6, False, [996, 1002], True])
check('fixture 8', solve({'anchor': 0, 'elapsed': 0, 'early': 0, 'late': 0, 'early_rate': 0, 'late_rate': 0, 'query': 0}), [[0, 0], 0, True, [0, 0], False])
check('fixture 9', solve({'anchor': 2, 'elapsed': -1, 'early': 0, 'late': 0, 'early_rate': 1000, 'late_rate': 1000, 'query': 2}), [[0, 2], 2, True, [0, 2], False])
check('fixture 10', solve({'anchor': 0, 'elapsed': 10, 'early': 1, 'late': 10, 'early_rate': 90, 'late_rate': 150, 'query': 20}), [[8, 22], 14, False, [-2, 12], False])
variant = [({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 21}, [[8, 15], 7, False, [6, 13], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 22}, [[8, 15], 7, False, [7, 14], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 23}, [[8, 15], 7, False, [8, 15], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 24}, [[8, 15], 7, False, [9, 16], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 25}, [[8, 15], 7, False, [10, 17], True])]
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[[8, 15], 7, True, [5, 12], True][[8, 15], 7, False, [5, 12], True]Failed
fixture 2[[-6, -3], 3, True, [3, 6], True][[-6, -3], 3, False, [3, 6], True]Failed
fixture 3[[0, 0], 0, True, [-3, -3], False][[0, 0], 0, True, [-3, -3], False]Passed
fixture 4[[1015, 1032], 17, True, [-932, -915], False][[1015, 1032], 17, False, [-932, -915], False]Failed
fixture 5[[-12, -7], 5, True, [-13, -8], False][[-12, -7], 5, False, [-13, -8], False]Failed
fixture 6[[-4, 6], 10, True, [-6, 4], False][[-4, 6], 10, True, [-6, 4], False]Passed
fixture 7[[-994, -988], 6, True, [996, 1002], True][[-994, -988], 6, False, [996, 1002], True]Failed
fixture 8[[0, 0], 0, True, [0, 0], False][[0, 0], 0, True, [0, 0], False]Passed
fixture 9[[0, 2], 2, True, [0, 2], False][[0, 2], 2, True, [0, 2], False]Passed
fixture 10[[8, 22], 14, True, [-2, 12], False][[8, 22], 14, False, [-2, 12], False]Failed
variant capture[[8, 15], 7, True, [6, 13], True][[8, 15], 7, False, [6, 13], True]Failed

SHA-256 / d76015047870102b9ca33becbdc0605e79ef9b0758a6dbe125d0b56bf2184b0e

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):
    age = abs(r['elapsed'])
    early_growth = (age * r['early_rate'] + 999) // 1000
    late_growth = (age * r['late_rate'] + 999) // 1000
    center = r['anchor'] + r['elapsed']
    low = center - r['early'] - early_growth
    high = center + r['late'] + late_growth
    width = high - low
    contains_zero = low <= 0 <= high
    earliest = r['query'] - high
    latest = r['query'] - low
    return [[low,high],width,contains_zero,[earliest,latest],high < r['query']]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 20}), [[8, 15], 7, False, [5, 12], True])
check('fixture 2', solve({'anchor': 0, 'elapsed': -5, 'early': 0, 'late': 1, 'early_rate': 200, 'late_rate': 1, 'query': 0}), [[-6, -3], 3, False, [3, 6], True])
check('fixture 3', solve({'anchor': -1, 'elapsed': 1, 'early': 0, 'late': 0, 'early_rate': 0, 'late_rate': 0, 'query': -3}), [[0, 0], 0, True, [-3, -3], False])
check('fixture 4', solve({'anchor': 20, 'elapsed': 1000, 'early': 3, 'late': 5, 'early_rate': 2, 'late_rate': 7, 'query': 100}), [[1015, 1032], 17, False, [-932, -915], False])
check('fixture 5', solve({'anchor': -10, 'elapsed': 0, 'early': 2, 'late': 3, 'early_rate': 0, 'late_rate': 0, 'query': -20}), [[-12, -7], 5, False, [-13, -8], False])
check('fixture 6', solve({'anchor': 0, 'elapsed': 2, 'early': 5, 'late': 0, 'early_rate': 1, 'late_rate': 2000, 'query': 0}), [[-4, 6], 10, True, [-6, 4], False])
check('fixture 7', solve({'anchor': 10, 'elapsed': -1001, 'early': 0, 'late': 1, 'early_rate': 2, 'late_rate': 1, 'query': 8}), [[-994, -988], 6, False, [996, 1002], True])
check('fixture 8', solve({'anchor': 0, 'elapsed': 0, 'early': 0, 'late': 0, 'early_rate': 0, 'late_rate': 0, 'query': 0}), [[0, 0], 0, True, [0, 0], False])
check('fixture 9', solve({'anchor': 2, 'elapsed': -1, 'early': 0, 'late': 0, 'early_rate': 1000, 'late_rate': 1000, 'query': 2}), [[0, 2], 2, True, [0, 2], False])
check('fixture 10', solve({'anchor': 0, 'elapsed': 10, 'early': 1, 'late': 10, 'early_rate': 90, 'late_rate': 150, 'query': 20}), [[8, 22], 14, False, [-2, 12], False])
variant = [({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 21}, [[8, 15], 7, False, [6, 13], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 22}, [[8, 15], 7, False, [7, 14], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 23}, [[8, 15], 7, False, [8, 15], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 24}, [[8, 15], 7, False, [9, 16], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 25}, [[8, 15], 7, False, [10, 17], True])]
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[[8, 15], 7, False, [5, 12], True][[8, 15], 7, False, [5, 12], True]Passed
fixture 2[[-6, -3], 3, False, [3, 6], True][[-6, -3], 3, False, [3, 6], True]Passed
fixture 3[[0, 0], 0, True, [-3, -3], False][[0, 0], 0, True, [-3, -3], False]Passed
fixture 4[[1015, 1032], 17, False, [-932, -915], False][[1015, 1032], 17, False, [-932, -915], False]Passed
fixture 5[[-12, -7], 5, False, [-13, -8], False][[-12, -7], 5, False, [-13, -8], False]Passed
fixture 6[[-4, 6], 10, True, [-6, 4], False][[-4, 6], 10, True, [-6, 4], False]Passed
fixture 7[[-994, -988], 6, False, [996, 1002], True][[-994, -988], 6, False, [996, 1002], True]Passed
fixture 8[[0, 0], 0, True, [0, 0], False][[0, 0], 0, True, [0, 0], False]Passed
fixture 9[[0, 2], 2, True, [0, 2], False][[0, 2], 2, True, [0, 2], False]Passed
fixture 10[[8, 22], 14, False, [-2, 12], False][[8, 22], 14, False, [-2, 12], False]Passed
variant capture[[8, 15], 7, False, [6, 13], True][[8, 15], 7, False, [6, 13], True]Passed

SHA-256 / aa55e7e33da430a76e8337d1d7d40432f808c718d350c76125d59a129f4a6015

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 2026-09-29T14:39:47.435611+00:00.

Case digest / ebea259ff9d8773227b22aa2e6092bf75c8384158593fe554706add23106c201