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FA-18486 / Time representation / Open access

Inverse switched clock uses old origin or multiplies instead of divides rate · case 01

The decoded time state disagrees with the explicit regression oracle for inverse.

Verified by executionVariant 1 · 11 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Inverse switched clock uses old origin or multiplies instead of divides rate.

THE FAILURE

Inverse switched clock uses old origin or multiplies instead of divides rate.

Unsuccessful approach: The partial correction still substitutes r['switch'] + (r['target'] - join) * second_rate 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 = (join if second else r['anchor']) + delta * active
    until = r['target'] - coordinate
    inverse = r['mono_origin'] + (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 fixtureActualExpectedOutcome
fixture 1['185/2', '3/2', '115', '75/2', '65/2']['185/2', '3/2', '115', '75/2', '85/2']Failed
fixture 2['100', '3/2', '115', '30', '65/2']['100', '3/2', '115', '30', '85/2']Failed
fixture 3['227/2', '3/2', '115', '33/2', '65/2']['227/2', '3/2', '115', '33/2', '85/2']Failed
fixture 4['115', '2/3', '115', '15', '65/2']['115', '2/3', '115', '15', '85/2']Failed
fixture 5['347/3', '2/3', '115', '43/3', '65/2']['347/3', '2/3', '115', '43/3', '85/2']Failed
fixture 6['365/3', '2/3', '115', '25/3', '65/2']['365/3', '2/3', '115', '25/3', '85/2']Failed
fixture 7['135', '2/3', '115', '-15', '35/2']['135', '2/3', '115', '-15', '55/2']Failed
fixture 8['355/3', '2/3', '115', '-10/3', '10']['355/3', '2/3', '115', '-10/3', '20']Failed
fixture 9['215/2', '3/2', '115', '17/2', '23/2']['215/2', '3/2', '115', '17/2', '43/2']Failed
fixture 10['505/3', '2/3', '115', '-115/3', '65/2']['505/3', '2/3', '115', '-115/3', '85/2']Failed
variant capture['94', '3/2', '115', '36', '65/2']['94', '3/2', '115', '36', '85/2']Failed

SHA-256 / 20546f3da125c7021d7f318c67d55f9f557e36c2438c232df5572b418ee739bf

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 * 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 fixtureActualExpectedOutcome
fixture 1['185/2', '3/2', '115', '75/2', '30']['185/2', '3/2', '115', '75/2', '85/2']Failed
fixture 2['100', '3/2', '115', '30', '30']['100', '3/2', '115', '30', '85/2']Failed
fixture 3['227/2', '3/2', '115', '33/2', '30']['227/2', '3/2', '115', '33/2', '85/2']Failed
fixture 4['115', '2/3', '115', '15', '30']['115', '2/3', '115', '15', '85/2']Failed
fixture 5['347/3', '2/3', '115', '43/3', '30']['347/3', '2/3', '115', '43/3', '85/2']Failed
fixture 6['365/3', '2/3', '115', '25/3', '30']['365/3', '2/3', '115', '25/3', '85/2']Failed
fixture 7['135', '2/3', '115', '-15', '70/3']['135', '2/3', '115', '-15', '55/2']Failed
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', '62/3']['215/2', '3/2', '115', '17/2', '43/2']Failed
fixture 10['505/3', '2/3', '115', '-115/3', '30']['505/3', '2/3', '115', '-115/3', '85/2']Failed
variant capture['94', '3/2', '115', '36', '30']['94', '3/2', '115', '36', '85/2']Failed

SHA-256 / 3d3ee836fdc22ac3200b6140732a03611edf51a6757ac021ea251d6be1a45030

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 11 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:39:58.104406+00:00.

Case digest / 8c882143a80f6d0cd3b04ad40098422529075d573ce1a4609ec8bb6030d7e995