FA-17981 / Time representation / Open access
Equal point labels conceal different represented precision intervals · case 01
The decoded time state disagrees with the explicit regression oracle for equal.
ROOT CAUSE
Equal point labels conceal different represented precision intervals.
VERIFIED REPAIR
Preserve the declared coordinate and state contract at equal: equal = compatible and r['a'] == r['b'] and r['qa'] == r['qb'].
Unsuccessful approach: The partial correction still substitutes compatible and r['qa'] == r['qb'] at the same fault site.
Case contract
A timestamp rounded down to resolution q represents half-open [stamp,stamp+q). Preserve domain tag; q positive. Comparing two buckets yields exact intersection and possible/definite-before relations, equality of represented sets and union envelope. Query membership is half-open. This model handles precision buckets, not point timestamps.
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):
a_end = r['a'] + r['qa']
b_end = r['b'] + r['qb']
compatible = r['domain_a'] == r['domain_b']
low = max(r['a'],r['b'])
high = min(a_end,b_end)
overlap = compatible and low < high
definite_before = compatible and a_end <= r['b']
possible_before = compatible and r['a'] < b_end
equal = compatible and r['a'] == r['b']
contains = r['a'] <= r['query'] < a_end
return [None if not overlap else [low,high],definite_before,possible_before,equal,contains, None if not compatible else [min(r['a'],r['b']),max(a_end,b_end)]]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'a': 10, 'qa': 10, 'b': 15, 'qb': 20, 'query': 10, 'domain_a': 'utc', 'domain_b': 'utc'}), [[15, 20], False, True, False, True, [10, 35]])
check('fixture 2', solve({'a': 10, 'qa': 10, 'b': 20, 'qb': 2, 'query': 20, 'domain_a': 'utc', 'domain_b': 'utc'}), [None, True, True, False, False, [10, 22]])
check('fixture 3', solve({'a': 10, 'qa': 10, 'b': 10, 'qb': 2, 'query': 15, 'domain_a': 'utc', 'domain_b': 'utc'}), [[10, 12], False, True, False, True, [10, 20]])
check('fixture 4', solve({'a': 20, 'qa': 2, 'b': 10, 'qb': 10, 'query': 21, 'domain_a': 'utc', 'domain_b': 'utc'}), [None, False, False, False, True, [10, 22]])
check('fixture 5', solve({'a': 0, 'qa': 1, 'b': 0, 'qb': 1, 'query': 0, 'domain_a': 'mono', 'domain_b': 'mono'}), [[0, 1], False, True, True, True, [0, 1]])
check('fixture 6', solve({'a': 0, 'qa': 10, 'b': 2, 'qb': 3, 'query': 2, 'domain_a': 'a', 'domain_b': 'b'}), [None, False, False, False, True, None])
check('fixture 7', solve({'a': -10, 'qa': 5, 'b': -8, 'qb': 1, 'query': -5, 'domain_a': 'utc', 'domain_b': 'utc'}), [[-8, -7], False, True, False, False, [-10, -5]])
check('fixture 8', solve({'a': 0, 'qa': 3, 'b': 2, 'qb': 1, 'query': 1, 'domain_a': 'utc', 'domain_b': 'utc'}), [[2, 3], False, True, False, True, [0, 3]])
check('fixture 9', solve({'a': 10, 'qa': 1, 'b': 20, 'qb': 1, 'query': 11, 'domain_a': 'utc', 'domain_b': 'utc'}), [None, True, True, False, False, [10, 21]])
check('fixture 10', solve({'a': 0, 'qa': 1, 'b': -1, 'qb': 1, 'query': 0, 'domain_a': 'utc', 'domain_b': 'utc'}), [None, False, False, False, True, [-1, 1]])
variant = [({'a': 10, 'qa': 10, 'b': 16, 'qb': 20, 'query': 10, 'domain_a': 'utc', 'domain_b': 'utc'}, [[16, 20], False, True, False, True, [10, 36]]), ({'a': 10, 'qa': 10, 'b': 17, 'qb': 20, 'query': 10, 'domain_a': 'utc', 'domain_b': 'utc'}, [[17, 20], False, True, False, True, [10, 37]]), ({'a': 10, 'qa': 10, 'b': 18, 'qb': 20, 'query': 10, 'domain_a': 'utc', 'domain_b': 'utc'}, [[18, 20], False, True, False, True, [10, 38]]), ({'a': 10, 'qa': 10, 'b': 19, 'qb': 20, 'query': 10, 'domain_a': 'utc', 'domain_b': 'utc'}, [[19, 20], False, True, False, True, [10, 39]]), ({'a': 10, 'qa': 10, 'b': 20, 'qb': 20, 'query': 10, 'domain_a': 'utc', 'domain_b': 'utc'}, [None, True, True, False, True, [10, 40]])]
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 | [[15, 20], False, True, False, True, [10, 35]] | [[15, 20], False, True, False, True, [10, 35]] | Passed |
| fixture 2 | [None, True, True, False, False, [10, 22]] | [None, True, True, False, False, [10, 22]] | Passed |
| fixture 3 | [[10, 12], False, True, True, True, [10, 20]] | [[10, 12], False, True, False, True, [10, 20]] | Failed |
| fixture 4 | [None, False, False, False, True, [10, 22]] | [None, False, False, False, True, [10, 22]] | Passed |
| fixture 5 | [[0, 1], False, True, True, True, [0, 1]] | [[0, 1], False, True, True, True, [0, 1]] | Passed |
| fixture 6 | [None, False, False, False, True, None] | [None, False, False, False, True, None] | Passed |
| fixture 7 | [[-8, -7], False, True, False, False, [-10, -5]] | [[-8, -7], False, True, False, False, [-10, -5]] | Passed |
| fixture 8 | [[2, 3], False, True, False, True, [0, 3]] | [[2, 3], False, True, False, True, [0, 3]] | Passed |
| fixture 9 | [None, True, True, False, False, [10, 21]] | [None, True, True, False, False, [10, 21]] | Passed |
| fixture 10 | [None, False, False, False, True, [-1, 1]] | [None, False, False, False, True, [-1, 1]] | Passed |
| variant capture | [[16, 20], False, True, False, True, [10, 36]] | [[16, 20], False, True, False, True, [10, 36]] | Passed |
SHA-256 / f17496d6c1dafd1bd10b88f0e3afe0413c1b18687c5e3cd58336b203f0711f6a
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):
a_end = r['a'] + r['qa']
b_end = r['b'] + r['qb']
compatible = r['domain_a'] == r['domain_b']
low = max(r['a'],r['b'])
high = min(a_end,b_end)
overlap = compatible and low < high
definite_before = compatible and a_end <= r['b']
possible_before = compatible and r['a'] < b_end
equal = compatible and r['qa'] == r['qb']
contains = r['a'] <= r['query'] < a_end
return [None if not overlap else [low,high],definite_before,possible_before,equal,contains, None if not compatible else [min(r['a'],r['b']),max(a_end,b_end)]]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'a': 10, 'qa': 10, 'b': 15, 'qb': 20, 'query': 10, 'domain_a': 'utc', 'domain_b': 'utc'}), [[15, 20], False, True, False, True, [10, 35]])
check('fixture 2', solve({'a': 10, 'qa': 10, 'b': 20, 'qb': 2, 'query': 20, 'domain_a': 'utc', 'domain_b': 'utc'}), [None, True, True, False, False, [10, 22]])
check('fixture 3', solve({'a': 10, 'qa': 10, 'b': 10, 'qb': 2, 'query': 15, 'domain_a': 'utc', 'domain_b': 'utc'}), [[10, 12], False, True, False, True, [10, 20]])
check('fixture 4', solve({'a': 20, 'qa': 2, 'b': 10, 'qb': 10, 'query': 21, 'domain_a': 'utc', 'domain_b': 'utc'}), [None, False, False, False, True, [10, 22]])
check('fixture 5', solve({'a': 0, 'qa': 1, 'b': 0, 'qb': 1, 'query': 0, 'domain_a': 'mono', 'domain_b': 'mono'}), [[0, 1], False, True, True, True, [0, 1]])
check('fixture 6', solve({'a': 0, 'qa': 10, 'b': 2, 'qb': 3, 'query': 2, 'domain_a': 'a', 'domain_b': 'b'}), [None, False, False, False, True, None])
check('fixture 7', solve({'a': -10, 'qa': 5, 'b': -8, 'qb': 1, 'query': -5, 'domain_a': 'utc', 'domain_b': 'utc'}), [[-8, -7], False, True, False, False, [-10, -5]])
check('fixture 8', solve({'a': 0, 'qa': 3, 'b': 2, 'qb': 1, 'query': 1, 'domain_a': 'utc', 'domain_b': 'utc'}), [[2, 3], False, True, False, True, [0, 3]])
check('fixture 9', solve({'a': 10, 'qa': 1, 'b': 20, 'qb': 1, 'query': 11, 'domain_a': 'utc', 'domain_b': 'utc'}), [None, True, True, False, False, [10, 21]])
check('fixture 10', solve({'a': 0, 'qa': 1, 'b': -1, 'qb': 1, 'query': 0, 'domain_a': 'utc', 'domain_b': 'utc'}), [None, False, False, False, True, [-1, 1]])
variant = [({'a': 10, 'qa': 10, 'b': 16, 'qb': 20, 'query': 10, 'domain_a': 'utc', 'domain_b': 'utc'}, [[16, 20], False, True, False, True, [10, 36]]), ({'a': 10, 'qa': 10, 'b': 17, 'qb': 20, 'query': 10, 'domain_a': 'utc', 'domain_b': 'utc'}, [[17, 20], False, True, False, True, [10, 37]]), ({'a': 10, 'qa': 10, 'b': 18, 'qb': 20, 'query': 10, 'domain_a': 'utc', 'domain_b': 'utc'}, [[18, 20], False, True, False, True, [10, 38]]), ({'a': 10, 'qa': 10, 'b': 19, 'qb': 20, 'query': 10, 'domain_a': 'utc', 'domain_b': 'utc'}, [[19, 20], False, True, False, True, [10, 39]]), ({'a': 10, 'qa': 10, 'b': 20, 'qb': 20, 'query': 10, 'domain_a': 'utc', 'domain_b': 'utc'}, [None, True, True, False, True, [10, 40]])]
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 | [[15, 20], False, True, False, True, [10, 35]] | [[15, 20], False, True, False, True, [10, 35]] | Passed |
| fixture 2 | [None, True, True, False, False, [10, 22]] | [None, True, True, False, False, [10, 22]] | Passed |
| fixture 3 | [[10, 12], False, True, False, True, [10, 20]] | [[10, 12], False, True, False, True, [10, 20]] | Passed |
| fixture 4 | [None, False, False, False, True, [10, 22]] | [None, False, False, False, True, [10, 22]] | Passed |
| fixture 5 | [[0, 1], False, True, True, True, [0, 1]] | [[0, 1], False, True, True, True, [0, 1]] | Passed |
| fixture 6 | [None, False, False, False, True, None] | [None, False, False, False, True, None] | Passed |
| fixture 7 | [[-8, -7], False, True, False, False, [-10, -5]] | [[-8, -7], False, True, False, False, [-10, -5]] | Passed |
| fixture 8 | [[2, 3], False, True, False, True, [0, 3]] | [[2, 3], False, True, False, True, [0, 3]] | Passed |
| fixture 9 | [None, True, True, True, False, [10, 21]] | [None, True, True, False, False, [10, 21]] | Failed |
| fixture 10 | [None, False, False, True, True, [-1, 1]] | [None, False, False, False, True, [-1, 1]] | Failed |
| variant capture | [[16, 20], False, True, False, True, [10, 36]] | [[16, 20], False, True, False, True, [10, 36]] | Passed |
SHA-256 / 4b8c610de0572a0aaf9e8c77e1fedec078a21af651aa93d29fadcfea44241c6f
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):
a_end = r['a'] + r['qa']
b_end = r['b'] + r['qb']
compatible = r['domain_a'] == r['domain_b']
low = max(r['a'],r['b'])
high = min(a_end,b_end)
overlap = compatible and low < high
definite_before = compatible and a_end <= r['b']
possible_before = compatible and r['a'] < b_end
equal = compatible and r['a'] == r['b'] and r['qa'] == r['qb']
contains = r['a'] <= r['query'] < a_end
return [None if not overlap else [low,high],definite_before,possible_before,equal,contains, None if not compatible else [min(r['a'],r['b']),max(a_end,b_end)]]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'a': 10, 'qa': 10, 'b': 15, 'qb': 20, 'query': 10, 'domain_a': 'utc', 'domain_b': 'utc'}), [[15, 20], False, True, False, True, [10, 35]])
check('fixture 2', solve({'a': 10, 'qa': 10, 'b': 20, 'qb': 2, 'query': 20, 'domain_a': 'utc', 'domain_b': 'utc'}), [None, True, True, False, False, [10, 22]])
check('fixture 3', solve({'a': 10, 'qa': 10, 'b': 10, 'qb': 2, 'query': 15, 'domain_a': 'utc', 'domain_b': 'utc'}), [[10, 12], False, True, False, True, [10, 20]])
check('fixture 4', solve({'a': 20, 'qa': 2, 'b': 10, 'qb': 10, 'query': 21, 'domain_a': 'utc', 'domain_b': 'utc'}), [None, False, False, False, True, [10, 22]])
check('fixture 5', solve({'a': 0, 'qa': 1, 'b': 0, 'qb': 1, 'query': 0, 'domain_a': 'mono', 'domain_b': 'mono'}), [[0, 1], False, True, True, True, [0, 1]])
check('fixture 6', solve({'a': 0, 'qa': 10, 'b': 2, 'qb': 3, 'query': 2, 'domain_a': 'a', 'domain_b': 'b'}), [None, False, False, False, True, None])
check('fixture 7', solve({'a': -10, 'qa': 5, 'b': -8, 'qb': 1, 'query': -5, 'domain_a': 'utc', 'domain_b': 'utc'}), [[-8, -7], False, True, False, False, [-10, -5]])
check('fixture 8', solve({'a': 0, 'qa': 3, 'b': 2, 'qb': 1, 'query': 1, 'domain_a': 'utc', 'domain_b': 'utc'}), [[2, 3], False, True, False, True, [0, 3]])
check('fixture 9', solve({'a': 10, 'qa': 1, 'b': 20, 'qb': 1, 'query': 11, 'domain_a': 'utc', 'domain_b': 'utc'}), [None, True, True, False, False, [10, 21]])
check('fixture 10', solve({'a': 0, 'qa': 1, 'b': -1, 'qb': 1, 'query': 0, 'domain_a': 'utc', 'domain_b': 'utc'}), [None, False, False, False, True, [-1, 1]])
variant = [({'a': 10, 'qa': 10, 'b': 16, 'qb': 20, 'query': 10, 'domain_a': 'utc', 'domain_b': 'utc'}, [[16, 20], False, True, False, True, [10, 36]]), ({'a': 10, 'qa': 10, 'b': 17, 'qb': 20, 'query': 10, 'domain_a': 'utc', 'domain_b': 'utc'}, [[17, 20], False, True, False, True, [10, 37]]), ({'a': 10, 'qa': 10, 'b': 18, 'qb': 20, 'query': 10, 'domain_a': 'utc', 'domain_b': 'utc'}, [[18, 20], False, True, False, True, [10, 38]]), ({'a': 10, 'qa': 10, 'b': 19, 'qb': 20, 'query': 10, 'domain_a': 'utc', 'domain_b': 'utc'}, [[19, 20], False, True, False, True, [10, 39]]), ({'a': 10, 'qa': 10, 'b': 20, 'qb': 20, 'query': 10, 'domain_a': 'utc', 'domain_b': 'utc'}, [None, True, True, False, True, [10, 40]])]
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 | [[15, 20], False, True, False, True, [10, 35]] | [[15, 20], False, True, False, True, [10, 35]] | Passed |
| fixture 2 | [None, True, True, False, False, [10, 22]] | [None, True, True, False, False, [10, 22]] | Passed |
| fixture 3 | [[10, 12], False, True, False, True, [10, 20]] | [[10, 12], False, True, False, True, [10, 20]] | Passed |
| fixture 4 | [None, False, False, False, True, [10, 22]] | [None, False, False, False, True, [10, 22]] | Passed |
| fixture 5 | [[0, 1], False, True, True, True, [0, 1]] | [[0, 1], False, True, True, True, [0, 1]] | Passed |
| fixture 6 | [None, False, False, False, True, None] | [None, False, False, False, True, None] | Passed |
| fixture 7 | [[-8, -7], False, True, False, False, [-10, -5]] | [[-8, -7], False, True, False, False, [-10, -5]] | Passed |
| fixture 8 | [[2, 3], False, True, False, True, [0, 3]] | [[2, 3], False, True, False, True, [0, 3]] | Passed |
| fixture 9 | [None, True, True, False, False, [10, 21]] | [None, True, True, False, False, [10, 21]] | Passed |
| fixture 10 | [None, False, False, False, True, [-1, 1]] | [None, False, False, False, True, [-1, 1]] | Passed |
| variant capture | [[16, 20], False, True, False, True, [10, 36]] | [[16, 20], False, True, False, True, [10, 36]] | Passed |
SHA-256 / 89c84c19b65aab734ab1e19512bb8eea405fa3173b8db1203db8750a5b0ddb7a
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 2026-09-29T14:39:52.918754+00:00.
Case digest / 6486308114b7efddb8c0ca40cb223a9658f22f2ab53c63dbc943dcc77d6c70c1