FA-18071 / Time representation / Open access
Hybrid logical component overflows or saturates instead of carrying · case 01
The decoded time state disagrees with the explicit regression oracle for normalized_l.
ROOT CAUSE
Hybrid logical component overflows or saturates instead of carrying.
VERIFIED REPAIR
Preserve the declared coordinate and state contract at normalized_l: normalized_l = logical % 256.
Unsuccessful approach: The partial correction still substitutes min(logical,255) at the same fault site.
Case contract
A bounded hybrid logical timestamp has physical integer p and logical integer l, cap 255. On receive, p=max(local p,remote p,wall). Increment max logical when both timestamps share p, increment owning side when only one shares p, otherwise reset logical to zero. Carry logical overflow into physical. Return canonical pair, physical source mask, ordering versus inputs and wall-advance flag.
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):
physical = max(r['local_p'],r['remote_p'],r['wall'])
local_owns = physical == r['local_p']
remote_owns = physical == r['remote_p']
logical = max(r['local_l'],r['remote_l']) + 1 if local_owns and remote_owns else (r['local_l'] + 1 if local_owns else (r['remote_l'] + 1 if remote_owns else 0))
carry = logical // 256
normalized_p = physical + carry
normalized_l = logical
mask = int(local_owns) + 2 * int(remote_owns) + 4 * int(physical == r['wall'])
after_local = (normalized_p,normalized_l) > (r['local_p'],r['local_l'])
after_remote = (normalized_p,normalized_l) > (r['remote_p'],r['remote_l'])
return [[normalized_p,normalized_l],mask,after_local,after_remote,normalized_p > r['wall']]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 4, 'wall': 9}), [[10, 5], 3, True, True, True])
check('fixture 2', solve({'local_p': 10, 'local_l': 5, 'remote_p': 9, 'remote_l': 8, 'wall': 8}), [[10, 6], 1, True, True, True])
check('fixture 3', solve({'local_p': 9, 'local_l': 7, 'remote_p': 10, 'remote_l': 2, 'wall': 8}), [[10, 3], 2, True, True, True])
check('fixture 4', solve({'local_p': 10, 'local_l': 5, 'remote_p': 10, 'remote_l': 7, 'wall': 11}), [[11, 0], 4, True, True, False])
check('fixture 5', solve({'local_p': 10, 'local_l': 255, 'remote_p': 10, 'remote_l': 2, 'wall': 10}), [[11, 0], 7, True, True, True])
check('fixture 6', solve({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 255, 'wall': 9}), [[11, 0], 3, True, True, True])
check('fixture 7', solve({'local_p': 10, 'local_l': 0, 'remote_p': 10, 'remote_l': 0, 'wall': 10}), [[10, 1], 7, True, True, False])
check('fixture 8', solve({'local_p': 1, 'local_l': 200, 'remote_p': 2, 'remote_l': 0, 'wall': 1}), [[2, 1], 2, True, True, True])
check('fixture 9', solve({'local_p': 2, 'local_l': 0, 'remote_p': 1, 'remote_l': 200, 'wall': 1}), [[2, 1], 1, True, True, True])
check('fixture 10', solve({'local_p': 0, 'local_l': 0, 'remote_p': 0, 'remote_l': 0, 'wall': 1}), [[1, 0], 4, True, True, False])
check('fixture 11', solve({'local_p': 10, 'local_l': 254, 'remote_p': 10, 'remote_l': 0, 'wall': 9}), [[10, 255], 3, True, True, True])
variant = [({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 4, 'wall': 10}, [[10, 5], 7, True, True, False]), ({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 4, 'wall': 11}, [[11, 0], 4, True, True, False]), ({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 4, 'wall': 12}, [[12, 0], 4, True, True, False]), ({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 4, 'wall': 13}, [[13, 0], 4, True, True, False]), ({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 4, 'wall': 14}, [[14, 0], 4, True, True, False])]
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, 5], 3, True, True, True] | [[10, 5], 3, True, True, True] | Passed |
| fixture 2 | [[10, 6], 1, True, True, True] | [[10, 6], 1, True, True, True] | Passed |
| fixture 3 | [[10, 3], 2, True, True, True] | [[10, 3], 2, True, True, True] | Passed |
| fixture 4 | [[11, 0], 4, True, True, False] | [[11, 0], 4, True, True, False] | Passed |
| fixture 5 | [[11, 256], 7, True, True, True] | [[11, 0], 7, True, True, True] | Failed |
| fixture 6 | [[11, 256], 3, True, True, True] | [[11, 0], 3, True, True, True] | Failed |
| fixture 7 | [[10, 1], 7, True, True, False] | [[10, 1], 7, True, True, False] | Passed |
| fixture 8 | [[2, 1], 2, True, True, True] | [[2, 1], 2, True, True, True] | Passed |
| fixture 9 | [[2, 1], 1, True, True, True] | [[2, 1], 1, True, True, True] | Passed |
| fixture 10 | [[1, 0], 4, True, True, False] | [[1, 0], 4, True, True, False] | Passed |
| fixture 11 | [[10, 255], 3, True, True, True] | [[10, 255], 3, True, True, True] | Passed |
| variant capture | [[10, 5], 7, True, True, False] | [[10, 5], 7, True, True, False] | Passed |
SHA-256 / 6e3a8c5b5e57817a20c12ecf3ec0371635bc99ea65fb9fd70dc89bfc7abbf7f1
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):
physical = max(r['local_p'],r['remote_p'],r['wall'])
local_owns = physical == r['local_p']
remote_owns = physical == r['remote_p']
logical = max(r['local_l'],r['remote_l']) + 1 if local_owns and remote_owns else (r['local_l'] + 1 if local_owns else (r['remote_l'] + 1 if remote_owns else 0))
carry = logical // 256
normalized_p = physical + carry
normalized_l = min(logical,255)
mask = int(local_owns) + 2 * int(remote_owns) + 4 * int(physical == r['wall'])
after_local = (normalized_p,normalized_l) > (r['local_p'],r['local_l'])
after_remote = (normalized_p,normalized_l) > (r['remote_p'],r['remote_l'])
return [[normalized_p,normalized_l],mask,after_local,after_remote,normalized_p > r['wall']]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 4, 'wall': 9}), [[10, 5], 3, True, True, True])
check('fixture 2', solve({'local_p': 10, 'local_l': 5, 'remote_p': 9, 'remote_l': 8, 'wall': 8}), [[10, 6], 1, True, True, True])
check('fixture 3', solve({'local_p': 9, 'local_l': 7, 'remote_p': 10, 'remote_l': 2, 'wall': 8}), [[10, 3], 2, True, True, True])
check('fixture 4', solve({'local_p': 10, 'local_l': 5, 'remote_p': 10, 'remote_l': 7, 'wall': 11}), [[11, 0], 4, True, True, False])
check('fixture 5', solve({'local_p': 10, 'local_l': 255, 'remote_p': 10, 'remote_l': 2, 'wall': 10}), [[11, 0], 7, True, True, True])
check('fixture 6', solve({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 255, 'wall': 9}), [[11, 0], 3, True, True, True])
check('fixture 7', solve({'local_p': 10, 'local_l': 0, 'remote_p': 10, 'remote_l': 0, 'wall': 10}), [[10, 1], 7, True, True, False])
check('fixture 8', solve({'local_p': 1, 'local_l': 200, 'remote_p': 2, 'remote_l': 0, 'wall': 1}), [[2, 1], 2, True, True, True])
check('fixture 9', solve({'local_p': 2, 'local_l': 0, 'remote_p': 1, 'remote_l': 200, 'wall': 1}), [[2, 1], 1, True, True, True])
check('fixture 10', solve({'local_p': 0, 'local_l': 0, 'remote_p': 0, 'remote_l': 0, 'wall': 1}), [[1, 0], 4, True, True, False])
check('fixture 11', solve({'local_p': 10, 'local_l': 254, 'remote_p': 10, 'remote_l': 0, 'wall': 9}), [[10, 255], 3, True, True, True])
variant = [({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 4, 'wall': 10}, [[10, 5], 7, True, True, False]), ({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 4, 'wall': 11}, [[11, 0], 4, True, True, False]), ({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 4, 'wall': 12}, [[12, 0], 4, True, True, False]), ({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 4, 'wall': 13}, [[13, 0], 4, True, True, False]), ({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 4, 'wall': 14}, [[14, 0], 4, True, True, False])]
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, 5], 3, True, True, True] | [[10, 5], 3, True, True, True] | Passed |
| fixture 2 | [[10, 6], 1, True, True, True] | [[10, 6], 1, True, True, True] | Passed |
| fixture 3 | [[10, 3], 2, True, True, True] | [[10, 3], 2, True, True, True] | Passed |
| fixture 4 | [[11, 0], 4, True, True, False] | [[11, 0], 4, True, True, False] | Passed |
| fixture 5 | [[11, 255], 7, True, True, True] | [[11, 0], 7, True, True, True] | Failed |
| fixture 6 | [[11, 255], 3, True, True, True] | [[11, 0], 3, True, True, True] | Failed |
| fixture 7 | [[10, 1], 7, True, True, False] | [[10, 1], 7, True, True, False] | Passed |
| fixture 8 | [[2, 1], 2, True, True, True] | [[2, 1], 2, True, True, True] | Passed |
| fixture 9 | [[2, 1], 1, True, True, True] | [[2, 1], 1, True, True, True] | Passed |
| fixture 10 | [[1, 0], 4, True, True, False] | [[1, 0], 4, True, True, False] | Passed |
| fixture 11 | [[10, 255], 3, True, True, True] | [[10, 255], 3, True, True, True] | Passed |
| variant capture | [[10, 5], 7, True, True, False] | [[10, 5], 7, True, True, False] | Passed |
SHA-256 / 395271b4eeb0057ec3e8224f58384741934f8fed10a76ea10c5c2cf3927e63fd
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):
physical = max(r['local_p'],r['remote_p'],r['wall'])
local_owns = physical == r['local_p']
remote_owns = physical == r['remote_p']
logical = max(r['local_l'],r['remote_l']) + 1 if local_owns and remote_owns else (r['local_l'] + 1 if local_owns else (r['remote_l'] + 1 if remote_owns else 0))
carry = logical // 256
normalized_p = physical + carry
normalized_l = logical % 256
mask = int(local_owns) + 2 * int(remote_owns) + 4 * int(physical == r['wall'])
after_local = (normalized_p,normalized_l) > (r['local_p'],r['local_l'])
after_remote = (normalized_p,normalized_l) > (r['remote_p'],r['remote_l'])
return [[normalized_p,normalized_l],mask,after_local,after_remote,normalized_p > r['wall']]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 4, 'wall': 9}), [[10, 5], 3, True, True, True])
check('fixture 2', solve({'local_p': 10, 'local_l': 5, 'remote_p': 9, 'remote_l': 8, 'wall': 8}), [[10, 6], 1, True, True, True])
check('fixture 3', solve({'local_p': 9, 'local_l': 7, 'remote_p': 10, 'remote_l': 2, 'wall': 8}), [[10, 3], 2, True, True, True])
check('fixture 4', solve({'local_p': 10, 'local_l': 5, 'remote_p': 10, 'remote_l': 7, 'wall': 11}), [[11, 0], 4, True, True, False])
check('fixture 5', solve({'local_p': 10, 'local_l': 255, 'remote_p': 10, 'remote_l': 2, 'wall': 10}), [[11, 0], 7, True, True, True])
check('fixture 6', solve({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 255, 'wall': 9}), [[11, 0], 3, True, True, True])
check('fixture 7', solve({'local_p': 10, 'local_l': 0, 'remote_p': 10, 'remote_l': 0, 'wall': 10}), [[10, 1], 7, True, True, False])
check('fixture 8', solve({'local_p': 1, 'local_l': 200, 'remote_p': 2, 'remote_l': 0, 'wall': 1}), [[2, 1], 2, True, True, True])
check('fixture 9', solve({'local_p': 2, 'local_l': 0, 'remote_p': 1, 'remote_l': 200, 'wall': 1}), [[2, 1], 1, True, True, True])
check('fixture 10', solve({'local_p': 0, 'local_l': 0, 'remote_p': 0, 'remote_l': 0, 'wall': 1}), [[1, 0], 4, True, True, False])
check('fixture 11', solve({'local_p': 10, 'local_l': 254, 'remote_p': 10, 'remote_l': 0, 'wall': 9}), [[10, 255], 3, True, True, True])
variant = [({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 4, 'wall': 10}, [[10, 5], 7, True, True, False]), ({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 4, 'wall': 11}, [[11, 0], 4, True, True, False]), ({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 4, 'wall': 12}, [[12, 0], 4, True, True, False]), ({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 4, 'wall': 13}, [[13, 0], 4, True, True, False]), ({'local_p': 10, 'local_l': 2, 'remote_p': 10, 'remote_l': 4, 'wall': 14}, [[14, 0], 4, True, True, False])]
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, 5], 3, True, True, True] | [[10, 5], 3, True, True, True] | Passed |
| fixture 2 | [[10, 6], 1, True, True, True] | [[10, 6], 1, True, True, True] | Passed |
| fixture 3 | [[10, 3], 2, True, True, True] | [[10, 3], 2, True, True, True] | Passed |
| fixture 4 | [[11, 0], 4, True, True, False] | [[11, 0], 4, True, True, False] | Passed |
| fixture 5 | [[11, 0], 7, True, True, True] | [[11, 0], 7, True, True, True] | Passed |
| fixture 6 | [[11, 0], 3, True, True, True] | [[11, 0], 3, True, True, True] | Passed |
| fixture 7 | [[10, 1], 7, True, True, False] | [[10, 1], 7, True, True, False] | Passed |
| fixture 8 | [[2, 1], 2, True, True, True] | [[2, 1], 2, True, True, True] | Passed |
| fixture 9 | [[2, 1], 1, True, True, True] | [[2, 1], 1, True, True, True] | Passed |
| fixture 10 | [[1, 0], 4, True, True, False] | [[1, 0], 4, True, True, False] | Passed |
| fixture 11 | [[10, 255], 3, True, True, True] | [[10, 255], 3, True, True, True] | Passed |
| variant capture | [[10, 5], 7, True, True, False] | [[10, 5], 7, True, True, False] | Passed |
SHA-256 / cd4d4744632e99dd36ab227866c5362b6e92d6517fb14b53867ac83003e5f4a1
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 2026-09-29T14:39:53.970985+00:00.
Case digest / 702bc2f2f491e607485c869e009fa0013ab7dcb0c7e97842059a5f86d5d70b23