FA-18476 / Time representation / Open access
Piecewise clock discards continuity anchor or active rate · case 01
The decoded time state disagrees with the explicit regression oracle for coordinate.
ROOT CAUSE
Piecewise clock discards continuity anchor or active rate.
VERIFIED REPAIR
Preserve the declared coordinate and state contract at coordinate: coordinate = (join if second else r['anchor']) + delta * active.
Unsuccessful approach: The partial correction still substitutes (join if second else r['anchor']) + delta at the same fault site.
Case contract
Virtual clock has anchor A at monotonic M0, rate p0/q0 until switch S, then p1/q1 thereafter. Readings may precede M0 and use first rate. The switch is continuous. Report exact coordinate, active rate, continuity anchor, next target delta and inverse monotonic coordinate for a target at or after switch. All rates positive.
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):
first_span = r['switch'] - r['mono_origin']
first_rate = Fraction(r['p0'],r['q0'])
second_rate = Fraction(r['p1'],r['q1'])
join = r['anchor'] + first_span * first_rate
second = r['reading'] >= r['switch']
delta = r['reading'] - (r['switch'] if second else r['mono_origin'])
active = second_rate if second else first_rate
coordinate = r['anchor'] + delta * active
until = r['target'] - coordinate
inverse = r['switch'] + (r['target'] - join) / second_rate
return [str(coordinate),str(active),str(join),str(until),str(inverse)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 5, 'target': 130}), ['185/2', '3/2', '115', '75/2', '85/2'])
check('fixture 2', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 10, 'target': 130}), ['100', '3/2', '115', '30', '85/2'])
check('fixture 3', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 19, 'target': 130}), ['227/2', '3/2', '115', '33/2', '85/2'])
check('fixture 4', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 20, 'target': 130}), ['115', '2/3', '115', '15', '85/2'])
check('fixture 5', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 21, 'target': 130}), ['347/3', '2/3', '115', '43/3', '85/2'])
check('fixture 6', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 30, 'target': 130}), ['365/3', '2/3', '115', '25/3', '85/2'])
check('fixture 7', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 50, 'target': 120}), ['135', '2/3', '115', '-15', '55/2'])
check('fixture 8', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 25, 'target': 115}), ['355/3', '2/3', '115', '-10/3', '20'])
check('fixture 9', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 15, 'target': 116}), ['215/2', '3/2', '115', '17/2', '43/2'])
check('fixture 10', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 100, 'target': 130}), ['505/3', '2/3', '115', '-115/3', '85/2'])
variant = [({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 6, 'target': 130}, ['94', '3/2', '115', '36', '85/2']), ({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 7, 'target': 130}, ['191/2', '3/2', '115', '69/2', '85/2']), ({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 8, 'target': 130}, ['97', '3/2', '115', '33', '85/2']), ({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 9, 'target': 130}, ['197/2', '3/2', '115', '63/2', '85/2']), ({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 10, 'target': 130}, ['100', '3/2', '115', '30', '85/2'])]
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 | ['185/2', '3/2', '115', '75/2', '85/2'] | ['185/2', '3/2', '115', '75/2', '85/2'] | Passed |
| fixture 2 | ['100', '3/2', '115', '30', '85/2'] | ['100', '3/2', '115', '30', '85/2'] | Passed |
| fixture 3 | ['227/2', '3/2', '115', '33/2', '85/2'] | ['227/2', '3/2', '115', '33/2', '85/2'] | Passed |
| fixture 4 | ['100', '2/3', '115', '30', '85/2'] | ['115', '2/3', '115', '15', '85/2'] | Failed |
| fixture 5 | ['302/3', '2/3', '115', '88/3', '85/2'] | ['347/3', '2/3', '115', '43/3', '85/2'] | Failed |
| fixture 6 | ['320/3', '2/3', '115', '70/3', '85/2'] | ['365/3', '2/3', '115', '25/3', '85/2'] | Failed |
| fixture 7 | ['120', '2/3', '115', '0', '55/2'] | ['135', '2/3', '115', '-15', '55/2'] | Failed |
| fixture 8 | ['310/3', '2/3', '115', '35/3', '20'] | ['355/3', '2/3', '115', '-10/3', '20'] | Failed |
| fixture 9 | ['215/2', '3/2', '115', '17/2', '43/2'] | ['215/2', '3/2', '115', '17/2', '43/2'] | Passed |
| fixture 10 | ['460/3', '2/3', '115', '-70/3', '85/2'] | ['505/3', '2/3', '115', '-115/3', '85/2'] | Failed |
| variant capture | ['94', '3/2', '115', '36', '85/2'] | ['94', '3/2', '115', '36', '85/2'] | Passed |
SHA-256 / 6139901bc776e785eebe5561023d8aa76f233ad86ae70097f70cb95a1c120e11
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):
first_span = r['switch'] - r['mono_origin']
first_rate = Fraction(r['p0'],r['q0'])
second_rate = Fraction(r['p1'],r['q1'])
join = r['anchor'] + first_span * first_rate
second = r['reading'] >= r['switch']
delta = r['reading'] - (r['switch'] if second else r['mono_origin'])
active = second_rate if second else first_rate
coordinate = (join if second else r['anchor']) + delta
until = r['target'] - coordinate
inverse = r['switch'] + (r['target'] - join) / second_rate
return [str(coordinate),str(active),str(join),str(until),str(inverse)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 5, 'target': 130}), ['185/2', '3/2', '115', '75/2', '85/2'])
check('fixture 2', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 10, 'target': 130}), ['100', '3/2', '115', '30', '85/2'])
check('fixture 3', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 19, 'target': 130}), ['227/2', '3/2', '115', '33/2', '85/2'])
check('fixture 4', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 20, 'target': 130}), ['115', '2/3', '115', '15', '85/2'])
check('fixture 5', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 21, 'target': 130}), ['347/3', '2/3', '115', '43/3', '85/2'])
check('fixture 6', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 30, 'target': 130}), ['365/3', '2/3', '115', '25/3', '85/2'])
check('fixture 7', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 50, 'target': 120}), ['135', '2/3', '115', '-15', '55/2'])
check('fixture 8', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 25, 'target': 115}), ['355/3', '2/3', '115', '-10/3', '20'])
check('fixture 9', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 15, 'target': 116}), ['215/2', '3/2', '115', '17/2', '43/2'])
check('fixture 10', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 100, 'target': 130}), ['505/3', '2/3', '115', '-115/3', '85/2'])
variant = [({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 6, 'target': 130}, ['94', '3/2', '115', '36', '85/2']), ({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 7, 'target': 130}, ['191/2', '3/2', '115', '69/2', '85/2']), ({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 8, 'target': 130}, ['97', '3/2', '115', '33', '85/2']), ({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 9, 'target': 130}, ['197/2', '3/2', '115', '63/2', '85/2']), ({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 10, 'target': 130}, ['100', '3/2', '115', '30', '85/2'])]
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 | ['95', '3/2', '115', '35', '85/2'] | ['185/2', '3/2', '115', '75/2', '85/2'] | Failed |
| fixture 2 | ['100', '3/2', '115', '30', '85/2'] | ['100', '3/2', '115', '30', '85/2'] | Passed |
| fixture 3 | ['109', '3/2', '115', '21', '85/2'] | ['227/2', '3/2', '115', '33/2', '85/2'] | Failed |
| fixture 4 | ['115', '2/3', '115', '15', '85/2'] | ['115', '2/3', '115', '15', '85/2'] | Passed |
| fixture 5 | ['116', '2/3', '115', '14', '85/2'] | ['347/3', '2/3', '115', '43/3', '85/2'] | Failed |
| fixture 6 | ['125', '2/3', '115', '5', '85/2'] | ['365/3', '2/3', '115', '25/3', '85/2'] | Failed |
| fixture 7 | ['145', '2/3', '115', '-25', '55/2'] | ['135', '2/3', '115', '-15', '55/2'] | Failed |
| fixture 8 | ['120', '2/3', '115', '-5', '20'] | ['355/3', '2/3', '115', '-10/3', '20'] | Failed |
| fixture 9 | ['105', '3/2', '115', '11', '43/2'] | ['215/2', '3/2', '115', '17/2', '43/2'] | Failed |
| fixture 10 | ['195', '2/3', '115', '-65', '85/2'] | ['505/3', '2/3', '115', '-115/3', '85/2'] | Failed |
| variant capture | ['96', '3/2', '115', '34', '85/2'] | ['94', '3/2', '115', '36', '85/2'] | Failed |
SHA-256 / 0f6744b3366c8ef7b0d68fc1c434c452a2ad6e90607c40e9ed11151f9291c511
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):
first_span = r['switch'] - r['mono_origin']
first_rate = Fraction(r['p0'],r['q0'])
second_rate = Fraction(r['p1'],r['q1'])
join = r['anchor'] + first_span * first_rate
second = r['reading'] >= r['switch']
delta = r['reading'] - (r['switch'] if second else r['mono_origin'])
active = second_rate if second else first_rate
coordinate = (join if second else r['anchor']) + delta * active
until = r['target'] - coordinate
inverse = r['switch'] + (r['target'] - join) / second_rate
return [str(coordinate),str(active),str(join),str(until),str(inverse)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 5, 'target': 130}), ['185/2', '3/2', '115', '75/2', '85/2'])
check('fixture 2', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 10, 'target': 130}), ['100', '3/2', '115', '30', '85/2'])
check('fixture 3', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 19, 'target': 130}), ['227/2', '3/2', '115', '33/2', '85/2'])
check('fixture 4', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 20, 'target': 130}), ['115', '2/3', '115', '15', '85/2'])
check('fixture 5', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 21, 'target': 130}), ['347/3', '2/3', '115', '43/3', '85/2'])
check('fixture 6', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 30, 'target': 130}), ['365/3', '2/3', '115', '25/3', '85/2'])
check('fixture 7', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 50, 'target': 120}), ['135', '2/3', '115', '-15', '55/2'])
check('fixture 8', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 25, 'target': 115}), ['355/3', '2/3', '115', '-10/3', '20'])
check('fixture 9', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 15, 'target': 116}), ['215/2', '3/2', '115', '17/2', '43/2'])
check('fixture 10', solve({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 100, 'target': 130}), ['505/3', '2/3', '115', '-115/3', '85/2'])
variant = [({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 6, 'target': 130}, ['94', '3/2', '115', '36', '85/2']), ({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 7, 'target': 130}, ['191/2', '3/2', '115', '69/2', '85/2']), ({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 8, 'target': 130}, ['97', '3/2', '115', '33', '85/2']), ({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 9, 'target': 130}, ['197/2', '3/2', '115', '63/2', '85/2']), ({'mono_origin': 10, 'anchor': 100, 'switch': 20, 'p0': 3, 'q0': 2, 'p1': 2, 'q1': 3, 'reading': 10, 'target': 130}, ['100', '3/2', '115', '30', '85/2'])]
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 | ['185/2', '3/2', '115', '75/2', '85/2'] | ['185/2', '3/2', '115', '75/2', '85/2'] | Passed |
| fixture 2 | ['100', '3/2', '115', '30', '85/2'] | ['100', '3/2', '115', '30', '85/2'] | Passed |
| fixture 3 | ['227/2', '3/2', '115', '33/2', '85/2'] | ['227/2', '3/2', '115', '33/2', '85/2'] | Passed |
| fixture 4 | ['115', '2/3', '115', '15', '85/2'] | ['115', '2/3', '115', '15', '85/2'] | Passed |
| fixture 5 | ['347/3', '2/3', '115', '43/3', '85/2'] | ['347/3', '2/3', '115', '43/3', '85/2'] | Passed |
| fixture 6 | ['365/3', '2/3', '115', '25/3', '85/2'] | ['365/3', '2/3', '115', '25/3', '85/2'] | Passed |
| fixture 7 | ['135', '2/3', '115', '-15', '55/2'] | ['135', '2/3', '115', '-15', '55/2'] | Passed |
| fixture 8 | ['355/3', '2/3', '115', '-10/3', '20'] | ['355/3', '2/3', '115', '-10/3', '20'] | Passed |
| fixture 9 | ['215/2', '3/2', '115', '17/2', '43/2'] | ['215/2', '3/2', '115', '17/2', '43/2'] | Passed |
| fixture 10 | ['505/3', '2/3', '115', '-115/3', '85/2'] | ['505/3', '2/3', '115', '-115/3', '85/2'] | Passed |
| variant capture | ['94', '3/2', '115', '36', '85/2'] | ['94', '3/2', '115', '36', '85/2'] | Passed |
SHA-256 / 8fdcdffbb20c91deb17e8de8625c7ba422be0170c4d12248e7529db60f2b6fc4
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 2026-09-29T14:39:58.057550+00:00.
Case digest / 1e2839093a8f9fb315e7b666d4fe9d5a12fb43c7dccc103c8a2487c0c6fc4b29