FA-18031 / Time representation / Open access
Exchange validity admits impossible negative propagation or rejects zero delay · case 01
The decoded time state disagrees with the explicit regression oracle for valid.
ROOT CAUSE
Exchange validity admits impossible negative propagation or rejects zero delay.
VERIFIED REPAIR
Preserve the declared coordinate and state contract at valid: valid = round_trip >= 0.
Unsuccessful approach: The partial correction still substitutes round_trip > 0 at the same fault site.
Case contract
Four timestamps are ordered by message path: client send c0, server receive s1, server send s2, client receive c3. Constant offset server-minus-client is estimated by symmetric path assumption. Preserve exact half-tick fractions; report network round trip, offset, projected server now, local send/receive server equivalents, one-way path estimate and delay bounds from nonnegative path delays.
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):
client_span = r['c3'] - r['c0']
server_span = r['s2'] - r['s1']
round_trip = client_span - server_span
offset_low = r['s2'] - r['c3']
offset_high = r['s1'] - r['c0']
offset = Fraction(offset_low + offset_high,2)
projected = r['now'] + offset
one_way = Fraction(round_trip,2)
valid = True
uncertainty = Fraction(offset_high - offset_low,2)
return [valid,str(offset),str(projected),str(one_way),[offset_low,offset_high],str(uncertainty),str(r['c0']+offset),str(r['c3']+offset)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'c0': 0, 's1': 7, 's2': 9, 'c3': 6, 'now': 10}), [True, '5', '15', '2', [3, 7], '2', '5', '11'])
check('fixture 2', solve({'c0': 10, 's1': 9, 's2': 12, 'c3': 18, 'now': 20}), [True, '-7/2', '33/2', '5/2', [-6, -1], '5/2', '13/2', '29/2'])
check('fixture 3', solve({'c0': 0, 's1': 5, 's2': 5, 'c3': 0, 'now': 2}), [True, '5', '7', '0', [5, 5], '0', '5', '5'])
check('fixture 4', solve({'c0': 10, 's1': 10, 's2': 20, 'c3': 15, 'now': 30}), [False, '5/2', '65/2', '-5/2', [5, 0], '-5/2', '25/2', '35/2'])
check('fixture 5', solve({'c0': 20, 's1': 10, 's2': 10, 'c3': 10, 'now': 30}), [False, '-5', '25', '-5', [0, -10], '-5', '15', '5'])
check('fixture 6', solve({'c0': 0, 's1': 1, 's2': 2, 'c3': 4, 'now': 5}), [True, '-1/2', '9/2', '3/2', [-2, 1], '3/2', '-1/2', '7/2'])
check('fixture 7', solve({'c0': -10, 's1': -5, 's2': -3, 'c3': -2, 'now': 0}), [True, '2', '2', '3', [-1, 5], '3', '-8', '0'])
check('fixture 8', solve({'c0': 100, 's1': 150, 's2': 170, 'c3': 140, 'now': 200}), [True, '40', '240', '10', [30, 50], '10', '140', '180'])
check('fixture 9', solve({'c0': 0, 's1': -5, 's2': -3, 'c3': 5, 'now': 10}), [True, '-13/2', '7/2', '3/2', [-8, -5], '3/2', '-13/2', '-3/2'])
check('fixture 10', solve({'c0': 2, 's1': 5, 's2': 5, 'c3': 8, 'now': 10}), [True, '0', '10', '3', [-3, 3], '3', '2', '8'])
variant = [({'c0': 0, 's1': 7, 's2': 9, 'c3': 6, 'now': 11}, [True, '5', '16', '2', [3, 7], '2', '5', '11']), ({'c0': 0, 's1': 7, 's2': 9, 'c3': 6, 'now': 12}, [True, '5', '17', '2', [3, 7], '2', '5', '11']), ({'c0': 0, 's1': 7, 's2': 9, 'c3': 6, 'now': 13}, [True, '5', '18', '2', [3, 7], '2', '5', '11']), ({'c0': 0, 's1': 7, 's2': 9, 'c3': 6, 'now': 14}, [True, '5', '19', '2', [3, 7], '2', '5', '11']), ({'c0': 0, 's1': 7, 's2': 9, 'c3': 6, 'now': 15}, [True, '5', '20', '2', [3, 7], '2', '5', '11'])]
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 | [True, '5', '15', '2', [3, 7], '2', '5', '11'] | [True, '5', '15', '2', [3, 7], '2', '5', '11'] | Passed |
| fixture 2 | [True, '-7/2', '33/2', '5/2', [-6, -1], '5/2', '13/2', '29/2'] | [True, '-7/2', '33/2', '5/2', [-6, -1], '5/2', '13/2', '29/2'] | Passed |
| fixture 3 | [True, '5', '7', '0', [5, 5], '0', '5', '5'] | [True, '5', '7', '0', [5, 5], '0', '5', '5'] | Passed |
| fixture 4 | [True, '5/2', '65/2', '-5/2', [5, 0], '-5/2', '25/2', '35/2'] | [False, '5/2', '65/2', '-5/2', [5, 0], '-5/2', '25/2', '35/2'] | Failed |
| fixture 5 | [True, '-5', '25', '-5', [0, -10], '-5', '15', '5'] | [False, '-5', '25', '-5', [0, -10], '-5', '15', '5'] | Failed |
| fixture 6 | [True, '-1/2', '9/2', '3/2', [-2, 1], '3/2', '-1/2', '7/2'] | [True, '-1/2', '9/2', '3/2', [-2, 1], '3/2', '-1/2', '7/2'] | Passed |
| fixture 7 | [True, '2', '2', '3', [-1, 5], '3', '-8', '0'] | [True, '2', '2', '3', [-1, 5], '3', '-8', '0'] | Passed |
| fixture 8 | [True, '40', '240', '10', [30, 50], '10', '140', '180'] | [True, '40', '240', '10', [30, 50], '10', '140', '180'] | Passed |
| fixture 9 | [True, '-13/2', '7/2', '3/2', [-8, -5], '3/2', '-13/2', '-3/2'] | [True, '-13/2', '7/2', '3/2', [-8, -5], '3/2', '-13/2', '-3/2'] | Passed |
| fixture 10 | [True, '0', '10', '3', [-3, 3], '3', '2', '8'] | [True, '0', '10', '3', [-3, 3], '3', '2', '8'] | Passed |
| variant capture | [True, '5', '16', '2', [3, 7], '2', '5', '11'] | [True, '5', '16', '2', [3, 7], '2', '5', '11'] | Passed |
SHA-256 / c03e266a3b910d6e1f423d9311cb09c70d0c1842c968d34439695f389c487a5c
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):
client_span = r['c3'] - r['c0']
server_span = r['s2'] - r['s1']
round_trip = client_span - server_span
offset_low = r['s2'] - r['c3']
offset_high = r['s1'] - r['c0']
offset = Fraction(offset_low + offset_high,2)
projected = r['now'] + offset
one_way = Fraction(round_trip,2)
valid = round_trip > 0
uncertainty = Fraction(offset_high - offset_low,2)
return [valid,str(offset),str(projected),str(one_way),[offset_low,offset_high],str(uncertainty),str(r['c0']+offset),str(r['c3']+offset)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'c0': 0, 's1': 7, 's2': 9, 'c3': 6, 'now': 10}), [True, '5', '15', '2', [3, 7], '2', '5', '11'])
check('fixture 2', solve({'c0': 10, 's1': 9, 's2': 12, 'c3': 18, 'now': 20}), [True, '-7/2', '33/2', '5/2', [-6, -1], '5/2', '13/2', '29/2'])
check('fixture 3', solve({'c0': 0, 's1': 5, 's2': 5, 'c3': 0, 'now': 2}), [True, '5', '7', '0', [5, 5], '0', '5', '5'])
check('fixture 4', solve({'c0': 10, 's1': 10, 's2': 20, 'c3': 15, 'now': 30}), [False, '5/2', '65/2', '-5/2', [5, 0], '-5/2', '25/2', '35/2'])
check('fixture 5', solve({'c0': 20, 's1': 10, 's2': 10, 'c3': 10, 'now': 30}), [False, '-5', '25', '-5', [0, -10], '-5', '15', '5'])
check('fixture 6', solve({'c0': 0, 's1': 1, 's2': 2, 'c3': 4, 'now': 5}), [True, '-1/2', '9/2', '3/2', [-2, 1], '3/2', '-1/2', '7/2'])
check('fixture 7', solve({'c0': -10, 's1': -5, 's2': -3, 'c3': -2, 'now': 0}), [True, '2', '2', '3', [-1, 5], '3', '-8', '0'])
check('fixture 8', solve({'c0': 100, 's1': 150, 's2': 170, 'c3': 140, 'now': 200}), [True, '40', '240', '10', [30, 50], '10', '140', '180'])
check('fixture 9', solve({'c0': 0, 's1': -5, 's2': -3, 'c3': 5, 'now': 10}), [True, '-13/2', '7/2', '3/2', [-8, -5], '3/2', '-13/2', '-3/2'])
check('fixture 10', solve({'c0': 2, 's1': 5, 's2': 5, 'c3': 8, 'now': 10}), [True, '0', '10', '3', [-3, 3], '3', '2', '8'])
variant = [({'c0': 0, 's1': 7, 's2': 9, 'c3': 6, 'now': 11}, [True, '5', '16', '2', [3, 7], '2', '5', '11']), ({'c0': 0, 's1': 7, 's2': 9, 'c3': 6, 'now': 12}, [True, '5', '17', '2', [3, 7], '2', '5', '11']), ({'c0': 0, 's1': 7, 's2': 9, 'c3': 6, 'now': 13}, [True, '5', '18', '2', [3, 7], '2', '5', '11']), ({'c0': 0, 's1': 7, 's2': 9, 'c3': 6, 'now': 14}, [True, '5', '19', '2', [3, 7], '2', '5', '11']), ({'c0': 0, 's1': 7, 's2': 9, 'c3': 6, 'now': 15}, [True, '5', '20', '2', [3, 7], '2', '5', '11'])]
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 | [True, '5', '15', '2', [3, 7], '2', '5', '11'] | [True, '5', '15', '2', [3, 7], '2', '5', '11'] | Passed |
| fixture 2 | [True, '-7/2', '33/2', '5/2', [-6, -1], '5/2', '13/2', '29/2'] | [True, '-7/2', '33/2', '5/2', [-6, -1], '5/2', '13/2', '29/2'] | Passed |
| fixture 3 | [False, '5', '7', '0', [5, 5], '0', '5', '5'] | [True, '5', '7', '0', [5, 5], '0', '5', '5'] | Failed |
| fixture 4 | [False, '5/2', '65/2', '-5/2', [5, 0], '-5/2', '25/2', '35/2'] | [False, '5/2', '65/2', '-5/2', [5, 0], '-5/2', '25/2', '35/2'] | Passed |
| fixture 5 | [False, '-5', '25', '-5', [0, -10], '-5', '15', '5'] | [False, '-5', '25', '-5', [0, -10], '-5', '15', '5'] | Passed |
| fixture 6 | [True, '-1/2', '9/2', '3/2', [-2, 1], '3/2', '-1/2', '7/2'] | [True, '-1/2', '9/2', '3/2', [-2, 1], '3/2', '-1/2', '7/2'] | Passed |
| fixture 7 | [True, '2', '2', '3', [-1, 5], '3', '-8', '0'] | [True, '2', '2', '3', [-1, 5], '3', '-8', '0'] | Passed |
| fixture 8 | [True, '40', '240', '10', [30, 50], '10', '140', '180'] | [True, '40', '240', '10', [30, 50], '10', '140', '180'] | Passed |
| fixture 9 | [True, '-13/2', '7/2', '3/2', [-8, -5], '3/2', '-13/2', '-3/2'] | [True, '-13/2', '7/2', '3/2', [-8, -5], '3/2', '-13/2', '-3/2'] | Passed |
| fixture 10 | [True, '0', '10', '3', [-3, 3], '3', '2', '8'] | [True, '0', '10', '3', [-3, 3], '3', '2', '8'] | Passed |
| variant capture | [True, '5', '16', '2', [3, 7], '2', '5', '11'] | [True, '5', '16', '2', [3, 7], '2', '5', '11'] | Passed |
SHA-256 / 6f43c40cc32ed5935c376ae518add807d67c63517a592ec997d356da3d1b4fc2
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):
client_span = r['c3'] - r['c0']
server_span = r['s2'] - r['s1']
round_trip = client_span - server_span
offset_low = r['s2'] - r['c3']
offset_high = r['s1'] - r['c0']
offset = Fraction(offset_low + offset_high,2)
projected = r['now'] + offset
one_way = Fraction(round_trip,2)
valid = round_trip >= 0
uncertainty = Fraction(offset_high - offset_low,2)
return [valid,str(offset),str(projected),str(one_way),[offset_low,offset_high],str(uncertainty),str(r['c0']+offset),str(r['c3']+offset)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'c0': 0, 's1': 7, 's2': 9, 'c3': 6, 'now': 10}), [True, '5', '15', '2', [3, 7], '2', '5', '11'])
check('fixture 2', solve({'c0': 10, 's1': 9, 's2': 12, 'c3': 18, 'now': 20}), [True, '-7/2', '33/2', '5/2', [-6, -1], '5/2', '13/2', '29/2'])
check('fixture 3', solve({'c0': 0, 's1': 5, 's2': 5, 'c3': 0, 'now': 2}), [True, '5', '7', '0', [5, 5], '0', '5', '5'])
check('fixture 4', solve({'c0': 10, 's1': 10, 's2': 20, 'c3': 15, 'now': 30}), [False, '5/2', '65/2', '-5/2', [5, 0], '-5/2', '25/2', '35/2'])
check('fixture 5', solve({'c0': 20, 's1': 10, 's2': 10, 'c3': 10, 'now': 30}), [False, '-5', '25', '-5', [0, -10], '-5', '15', '5'])
check('fixture 6', solve({'c0': 0, 's1': 1, 's2': 2, 'c3': 4, 'now': 5}), [True, '-1/2', '9/2', '3/2', [-2, 1], '3/2', '-1/2', '7/2'])
check('fixture 7', solve({'c0': -10, 's1': -5, 's2': -3, 'c3': -2, 'now': 0}), [True, '2', '2', '3', [-1, 5], '3', '-8', '0'])
check('fixture 8', solve({'c0': 100, 's1': 150, 's2': 170, 'c3': 140, 'now': 200}), [True, '40', '240', '10', [30, 50], '10', '140', '180'])
check('fixture 9', solve({'c0': 0, 's1': -5, 's2': -3, 'c3': 5, 'now': 10}), [True, '-13/2', '7/2', '3/2', [-8, -5], '3/2', '-13/2', '-3/2'])
check('fixture 10', solve({'c0': 2, 's1': 5, 's2': 5, 'c3': 8, 'now': 10}), [True, '0', '10', '3', [-3, 3], '3', '2', '8'])
variant = [({'c0': 0, 's1': 7, 's2': 9, 'c3': 6, 'now': 11}, [True, '5', '16', '2', [3, 7], '2', '5', '11']), ({'c0': 0, 's1': 7, 's2': 9, 'c3': 6, 'now': 12}, [True, '5', '17', '2', [3, 7], '2', '5', '11']), ({'c0': 0, 's1': 7, 's2': 9, 'c3': 6, 'now': 13}, [True, '5', '18', '2', [3, 7], '2', '5', '11']), ({'c0': 0, 's1': 7, 's2': 9, 'c3': 6, 'now': 14}, [True, '5', '19', '2', [3, 7], '2', '5', '11']), ({'c0': 0, 's1': 7, 's2': 9, 'c3': 6, 'now': 15}, [True, '5', '20', '2', [3, 7], '2', '5', '11'])]
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 | [True, '5', '15', '2', [3, 7], '2', '5', '11'] | [True, '5', '15', '2', [3, 7], '2', '5', '11'] | Passed |
| fixture 2 | [True, '-7/2', '33/2', '5/2', [-6, -1], '5/2', '13/2', '29/2'] | [True, '-7/2', '33/2', '5/2', [-6, -1], '5/2', '13/2', '29/2'] | Passed |
| fixture 3 | [True, '5', '7', '0', [5, 5], '0', '5', '5'] | [True, '5', '7', '0', [5, 5], '0', '5', '5'] | Passed |
| fixture 4 | [False, '5/2', '65/2', '-5/2', [5, 0], '-5/2', '25/2', '35/2'] | [False, '5/2', '65/2', '-5/2', [5, 0], '-5/2', '25/2', '35/2'] | Passed |
| fixture 5 | [False, '-5', '25', '-5', [0, -10], '-5', '15', '5'] | [False, '-5', '25', '-5', [0, -10], '-5', '15', '5'] | Passed |
| fixture 6 | [True, '-1/2', '9/2', '3/2', [-2, 1], '3/2', '-1/2', '7/2'] | [True, '-1/2', '9/2', '3/2', [-2, 1], '3/2', '-1/2', '7/2'] | Passed |
| fixture 7 | [True, '2', '2', '3', [-1, 5], '3', '-8', '0'] | [True, '2', '2', '3', [-1, 5], '3', '-8', '0'] | Passed |
| fixture 8 | [True, '40', '240', '10', [30, 50], '10', '140', '180'] | [True, '40', '240', '10', [30, 50], '10', '140', '180'] | Passed |
| fixture 9 | [True, '-13/2', '7/2', '3/2', [-8, -5], '3/2', '-13/2', '-3/2'] | [True, '-13/2', '7/2', '3/2', [-8, -5], '3/2', '-13/2', '-3/2'] | Passed |
| fixture 10 | [True, '0', '10', '3', [-3, 3], '3', '2', '8'] | [True, '0', '10', '3', [-3, 3], '3', '2', '8'] | Passed |
| variant capture | [True, '5', '16', '2', [3, 7], '2', '5', '11'] | [True, '5', '16', '2', [3, 7], '2', '5', '11'] | Passed |
SHA-256 / 99a166f1a681d535cda721910b25cbc07889b501d8dc68785ba50f74a4403813
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 2026-09-29T14:39:53.337529+00:00.
Case digest / 9a497540afaa752e5a461d2b7761032d2b712cf38673f58e50eef8e8dfee8b40