FA-17536 / Time representation / Open access
Latest possible duration loses signed direction · case 01
The decoded time state disagrees with the explicit regression oracle for latest.
ROOT CAUSE
Latest possible duration loses signed direction.
VERIFIED REPAIR
Preserve the declared coordinate and state contract at latest: latest = r['query'] - low.
Unsuccessful approach: The partial correction still substitutes abs(r['query'] - low) 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'] - high
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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| fixture 1 | [[8, 15], 7, False, [5, 5], True] | [[8, 15], 7, False, [5, 12], True] | Failed |
| fixture 2 | [[-6, -3], 3, False, [3, 3], 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, False, [-932, -932], False] | [[1015, 1032], 17, False, [-932, -915], False] | Failed |
| fixture 5 | [[-12, -7], 5, False, [-13, -13], False] | [[-12, -7], 5, False, [-13, -8], False] | Failed |
| fixture 6 | [[-4, 6], 10, True, [-6, -6], False] | [[-4, 6], 10, True, [-6, 4], False] | Failed |
| fixture 7 | [[-994, -988], 6, False, [996, 996], 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, 0], False] | [[0, 2], 2, True, [0, 2], False] | Failed |
| fixture 10 | [[8, 22], 14, False, [-2, -2], False] | [[8, 22], 14, False, [-2, 12], False] | Failed |
| variant capture | [[8, 15], 7, False, [6, 6], True] | [[8, 15], 7, False, [6, 13], True] | Failed |
SHA-256 / 8500d8578f09c115ee8449f98f502b68276678049d05347c5e6dda14cd60ad1e
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 <= high
earliest = r['query'] - high
latest = abs(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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| 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] | Failed |
| fixture 4 | [[1015, 1032], 17, False, [-932, 915], False] | [[1015, 1032], 17, False, [-932, -915], False] | Failed |
| fixture 5 | [[-12, -7], 5, False, [-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, 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 / 98f8ec1ea3db4a6a6167bb8fc209b8413b16e6a66140f6a094e7f71ff23eec5a
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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| 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 2026-09-29T14:39:47.485287+00:00.
Case digest / 199342353a4f627af8d0ac11d5cac6aa839efe79d68d9d80f87fe5ab1bba5162