FA-67106 / Railway interlocking logic / Open access

Two-out-of-three occupancy voting: tie resolution · case 01

Two healthy channels that disagree produce a clear vote.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

A tie between occupied and clear is resolved towards clear.

VERIFIED REPAIR

Resolve ties towards occupied.

Unsuccessful approach: Forcing occupied whenever exactly two channels are healthy overrides two agreeing clear reports.

Case contract

Three channels report occupancy (True/False) or None when failed. A channel isolated earlier counts as None. With fewer than two healthy channels the vote is occupied. Otherwise the vote is occupied when occupied reports are at least as many as clear ones (ties are occupied). A healthy channel that disagrees with the vote increments its discrepancy count, otherwise (agreeing or None) the count resets; a channel is isolated for good when its count reaches isolate_after. Return all votes and isolated channel indices.

Why this case matters

Interlocking logic decides whether trains may be given authority; a wrong decision at this point either grants unsafe movements or strands traffic.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    k = x['isolate_after']
    bad = [0, 0, 0]
    iso = [False, False, False]
    votes = []
    for cyc in x['cycles']:
        vals = [None if iso[i] else cyc[i] for i in range(3)]
        healthy = [v for v in vals if v is not None]
        if len(healthy) < 2:
            vote = True
        else:
            t = sum(1 for v in healthy if v)
            f = len(healthy) - t
            vote = t > f
        votes.append(vote)
        for i in range(3):
            if vals[i] is not None and vals[i] != vote:
                bad[i] += 1
                if bad[i] >= k:
                    iso[i] = True
            else:
                bad[i] = 0
    return {'votes': votes, 'isolated': [i for i in range(3) if iso[i]]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: two healthy channels disagree', {'isolate_after': 3, 'cycles': [[True, False, None]]}, {'votes': [True], 'isolated': []}), ('boundary: two healthy channels agree clear', {'isolate_after': 3, 'cycles': [[False, False, None]]}, {'votes': [False], 'isolated': []}), ('sampled regression 2', {'isolate_after': 2, 'cycles': [[True, False, True], [None, True, False], [None, False, False], [False, None, False], [True, False, False], [True, False, True]]}, {'votes': [True, True, False, False, False, True], 'isolated': []}), ('boundary: persistent dissenter', {'isolate_after': 2, 'cycles': [[True, False, False], [True, False, False], [False, False, False]]}, {'votes': [False, False, False], 'isolated': [0]}), ('boundary: single healthy channel says clear', {'isolate_after': 3, 'cycles': [[False, None, None]]}, {'votes': [True], 'isolated': []}), ('control 1', {'isolate_after': 2, 'cycles': [[False, False, False], [True, None, True], [True, True, True], [None, False, False]]}, {'votes': [False, True, True, False], 'isolated': []}), ('control 4', {'isolate_after': 2, 'cycles': [[False, True, True], [False, False, False], [False, False, False], [True, True, False], [True, True, True], [True, False, True], [False, False, False], [False, False, None], [True, True, True]]}, {'votes': [True, False, False, True, True, True, False, False, True], 'isolated': []}), ('control 7', {'isolate_after': 3, 'cycles': [[False, False, True], [False, False, False], [True, True, True], [False, True, True], [True, True, None], [False, False, False], [True, True, True], [False, False, False]]}, {'votes': [False, False, True, True, True, False, True, False], 'isolated': []})], [('regression: two dissenters in turn', {'isolate_after': 2, 'cycles': [[True, False, False], [True, False, False], [False, True, False], [False, True, False], [False, False, False]]}, {'votes': [False, False, True, True, True], 'isolated': [0, 2]}), ('boundary: persistent dissenter', {'isolate_after': 2, 'cycles': [[True, False, False], [True, False, False], [False, False, False]]}, {'votes': [False, False, False], 'isolated': [0]}), ('sampled regression 18', {'isolate_after': 2, 'cycles': [[False, False, False], [None, False, True], [False, False, True], [True, False, False], [True, False, True], [False, False, False], [False, True, None], [False, False, False], [False, False, False]]}, {'votes': [False, True, False, False, True, False, True, False, False], 'isolated': []}), ('control 4', {'isolate_after': 2, 'cycles': [[False, True, True], [False, False, False], [False, False, False], [True, True, False], [True, True, True], [True, False, True], [False, False, False], [False, False, None], [True, True, True]]}, {'votes': [True, False, False, True, True, True, False, False, True], 'isolated': []}), ('boundary: single healthy channel says clear', {'isolate_after': 3, 'cycles': [[False, None, None]]}, {'votes': [True], 'isolated': []}), ('sampled regression 12', {'isolate_after': 3, 'cycles': [[False, False, False], [False, True, False], [True, False, True], [True, False, True], [False, False, True], [False, False, False], [True, False, True], [True, True, True]]}, {'votes': [False, False, True, True, True, False, True, True], 'isolated': [1]}), ('sampled regression 15', {'isolate_after': 3, 'cycles': [[False, False, False], [False, None, False], [True, False, False], [True, None, False]]}, {'votes': [False, False, False, True], 'isolated': []}), ('control 21', {'isolate_after': 3, 'cycles': [[True, True, True], [False, True, False], [True, True, True], [True, True, False], [None, False, False], [False, False, False], [False, False, False]]}, {'votes': [True, False, True, True, False, False, False], 'isolated': []})], [('regression: isolated channel keeps reporting', {'isolate_after': 1, 'cycles': [[True, False, False], [True, True, False]]}, {'votes': [False, True], 'isolated': [0, 2]}), ('boundary: dissent interrupted by failure', {'isolate_after': 2, 'cycles': [[True, False, False], [None, False, False], [True, False, False]]}, {'votes': [False, False, False], 'isolated': []}), ('sampled regression 42', {'isolate_after': 3, 'cycles': [[False, False, False], [True, False, False], [False, False, False], [False, False, True], [False, True, False], [False, False, True], [None, False, False], [True, None, False], [False, True, True]]}, {'votes': [False, False, False, False, False, False, False, True, True], 'isolated': []}), ('control 13', {'isolate_after': 3, 'cycles': [[False, False, False], [True, None, True], [True, True, True], [False, None, False], [False, False, True]]}, {'votes': [False, True, True, False, False], 'isolated': []}), ('regression: two dissenters in turn', {'isolate_after': 2, 'cycles': [[True, False, False], [True, False, False], [False, True, False], [False, True, False], [False, False, False]]}, {'votes': [False, False, True, True, True], 'isolated': [0, 2]}), ('control 23', {'isolate_after': 2, 'cycles': [[True, False, True], [None, False, False], [False, False, False], [False, False, False], [False, False, None], [False, False, False], [True, None, True]]}, {'votes': [True, False, False, False, False, False, True], 'isolated': []}), ('control 26', {'isolate_after': 2, 'cycles': [[True, True, True], [False, False, False], [False, False, True], [False, False, None]]}, {'votes': [True, False, False, False], 'isolated': []}), ('control 29', {'isolate_after': 2, 'cycles': [[False, False, True], [False, False, False], [False, False, True], [False, True, False], [False, True, True]]}, {'votes': [False, False, False, False, True], 'isolated': []})], [('regression: two healthy channels disagree', {'isolate_after': 3, 'cycles': [[True, False, None]]}, {'votes': [True], 'isolated': []}), ('boundary: two healthy channels agree clear', {'isolate_after': 3, 'cycles': [[False, False, None]]}, {'votes': [False], 'isolated': []}), ('sampled regression 56', {'isolate_after': 2, 'cycles': [[False, True, None], [False, True, None], [False, False, False], [True, False, False], [False, False, True]]}, {'votes': [True, True, False, False, True], 'isolated': [0]}), ('control 21', {'isolate_after': 3, 'cycles': [[True, True, True], [False, True, False], [True, True, True], [True, True, False], [None, False, False], [False, False, False], [False, False, False]]}, {'votes': [True, False, True, True, False, False, False], 'isolated': []}), ('regression: isolated channel keeps reporting', {'isolate_after': 1, 'cycles': [[True, False, False], [True, True, False]]}, {'votes': [False, True], 'isolated': [0, 2]}), ('control 34', {'isolate_after': 2, 'cycles': [[True, True, False], [False, True, False], [True, True, True], [True, True, True], [True, False, True], [False, False, False], [True, False, True]]}, {'votes': [True, False, True, True, True, False, True], 'isolated': []}), ('control 37', {'isolate_after': 3, 'cycles': [[True, True, True], [False, False, False], [False, False, False], [False, True, False], [True, False, False], [False, False, False]]}, {'votes': [True, False, False, False, False, False], 'isolated': []}), ('sampled regression 40', {'isolate_after': 2, 'cycles': [[True, None, True], [False, False, None], [False, True, False], [False, True, False], [True, True, True], [True, None, False], [None, False, False], [True, True, True]]}, {'votes': [True, False, False, False, True, True, True, True], 'isolated': [1, 2]})], [('regression: two dissenters in turn', {'isolate_after': 2, 'cycles': [[True, False, False], [True, False, False], [False, True, False], [False, True, False], [False, False, False]]}, {'votes': [False, False, True, True, True], 'isolated': [0, 2]}), ('boundary: persistent dissenter', {'isolate_after': 2, 'cycles': [[True, False, False], [True, False, False], [False, False, False]]}, {'votes': [False, False, False], 'isolated': [0]}), ('sampled regression 69', {'isolate_after': 3, 'cycles': [[False, True, True], [True, True, False], [False, False, False], [False, None, True]]}, {'votes': [True, True, False, True], 'isolated': []}), ('control 32', {'isolate_after': 3, 'cycles': [[False, True, True], [False, False, False], [False, False, None], [True, True, None], [False, False, False], [True, True, False], [True, None, True]]}, {'votes': [True, False, False, True, False, True, True], 'isolated': []}), ('boundary: two healthy channels agree clear', {'isolate_after': 3, 'cycles': [[False, False, None]]}, {'votes': [False], 'isolated': []}), ('sampled regression 45', {'isolate_after': 2, 'cycles': [[True, True, True], [False, False, False], [False, False, False], [False, True, False], [None, True, False], [None, True, False], [True, False, False]]}, {'votes': [True, False, False, False, True, True, True], 'isolated': [2]}), ('control 48', {'isolate_after': 2, 'cycles': [[False, False, False], [False, False, False], [False, True, True], [True, True, None], [False, True, False], [True, True, True], [False, False, False], [False, False, False], [False, True, False]]}, {'votes': [False, False, True, True, False, True, False, False, False], 'isolated': []}), ('control 51', {'isolate_after': 3, 'cycles': [[False, False, False], [True, False, False], [True, True, True], [True, True, True], [True, True, True], [True, True, True], [True, False, True], [True, False, False], [True, True, True]]}, {'votes': [False, False, True, True, True, True, True, False, True], 'isolated': []})]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
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
regression: two healthy channels disagree	`{'isolated': [], 'votes': [False]}`	`{'isolated': [], 'votes': [True]}`	Failed
boundary: two healthy channels agree clear	`{'isolated': [], 'votes': [False]}`	`{'isolated': [], 'votes': [False]}`	Passed
sampled regression 2	`{'isolated': [1], 'votes': [True, False, True, False, False, True]}`	`{'isolated': [], 'votes': [True, True, False, False, False, True]}`	Failed
boundary: persistent dissenter	`{'isolated': [0], 'votes': [False, False, False]}`	`{'isolated': [0], 'votes': [False, False, False]}`	Passed
boundary: single healthy channel says clear	`{'isolated': [], 'votes': [True]}`	`{'isolated': [], 'votes': [True]}`	Passed
control 1	`{'isolated': [], 'votes': [False, True, True, False]}`	`{'isolated': [], 'votes': [False, True, True, False]}`	Passed
control 4	`{'isolated': [], 'votes': [True, False, False, True, True, True, False, False, True]}`	`{'isolated': [], 'votes': [True, False, False, True, True, True, False, False, True]}`	Passed
control 7	`{'isolated': [], 'votes': [False, False, True, True, True, False, True, False]}`	`{'isolated': [], 'votes': [False, False, True, True, True, False, True, False]}`	Passed

SHA-256 / 9972e3971d1df23d5055deb221de6d3ad2e7b166a1dc05285e19ba841aadb85e

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    k = x['isolate_after']
    bad = [0, 0, 0]
    iso = [False, False, False]
    votes = []
    for cyc in x['cycles']:
        vals = [None if iso[i] else cyc[i] for i in range(3)]
        healthy = [v for v in vals if v is not None]
        if len(healthy) < 2:
            vote = True
        else:
            t = sum(1 for v in healthy if v)
            f = len(healthy) - t
            vote = t > f or len(healthy) == 2
        votes.append(vote)
        for i in range(3):
            if vals[i] is not None and vals[i] != vote:
                bad[i] += 1
                if bad[i] >= k:
                    iso[i] = True
            else:
                bad[i] = 0
    return {'votes': votes, 'isolated': [i for i in range(3) if iso[i]]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: two healthy channels disagree', {'isolate_after': 3, 'cycles': [[True, False, None]]}, {'votes': [True], 'isolated': []}), ('boundary: two healthy channels agree clear', {'isolate_after': 3, 'cycles': [[False, False, None]]}, {'votes': [False], 'isolated': []}), ('sampled regression 2', {'isolate_after': 2, 'cycles': [[True, False, True], [None, True, False], [None, False, False], [False, None, False], [True, False, False], [True, False, True]]}, {'votes': [True, True, False, False, False, True], 'isolated': []}), ('boundary: persistent dissenter', {'isolate_after': 2, 'cycles': [[True, False, False], [True, False, False], [False, False, False]]}, {'votes': [False, False, False], 'isolated': [0]}), ('boundary: single healthy channel says clear', {'isolate_after': 3, 'cycles': [[False, None, None]]}, {'votes': [True], 'isolated': []}), ('control 1', {'isolate_after': 2, 'cycles': [[False, False, False], [True, None, True], [True, True, True], [None, False, False]]}, {'votes': [False, True, True, False], 'isolated': []}), ('control 4', {'isolate_after': 2, 'cycles': [[False, True, True], [False, False, False], [False, False, False], [True, True, False], [True, True, True], [True, False, True], [False, False, False], [False, False, None], [True, True, True]]}, {'votes': [True, False, False, True, True, True, False, False, True], 'isolated': []}), ('control 7', {'isolate_after': 3, 'cycles': [[False, False, True], [False, False, False], [True, True, True], [False, True, True], [True, True, None], [False, False, False], [True, True, True], [False, False, False]]}, {'votes': [False, False, True, True, True, False, True, False], 'isolated': []})], [('regression: two dissenters in turn', {'isolate_after': 2, 'cycles': [[True, False, False], [True, False, False], [False, True, False], [False, True, False], [False, False, False]]}, {'votes': [False, False, True, True, True], 'isolated': [0, 2]}), ('boundary: persistent dissenter', {'isolate_after': 2, 'cycles': [[True, False, False], [True, False, False], [False, False, False]]}, {'votes': [False, False, False], 'isolated': [0]}), ('sampled regression 18', {'isolate_after': 2, 'cycles': [[False, False, False], [None, False, True], [False, False, True], [True, False, False], [True, False, True], [False, False, False], [False, True, None], [False, False, False], [False, False, False]]}, {'votes': [False, True, False, False, True, False, True, False, False], 'isolated': []}), ('control 4', {'isolate_after': 2, 'cycles': [[False, True, True], [False, False, False], [False, False, False], [True, True, False], [True, True, True], [True, False, True], [False, False, False], [False, False, None], [True, True, True]]}, {'votes': [True, False, False, True, True, True, False, False, True], 'isolated': []}), ('boundary: single healthy channel says clear', {'isolate_after': 3, 'cycles': [[False, None, None]]}, {'votes': [True], 'isolated': []}), ('sampled regression 12', {'isolate_after': 3, 'cycles': [[False, False, False], [False, True, False], [True, False, True], [True, False, True], [False, False, True], [False, False, False], [True, False, True], [True, True, True]]}, {'votes': [False, False, True, True, True, False, True, True], 'isolated': [1]}), ('sampled regression 15', {'isolate_after': 3, 'cycles': [[False, False, False], [False, None, False], [True, False, False], [True, None, False]]}, {'votes': [False, False, False, True], 'isolated': []}), ('control 21', {'isolate_after': 3, 'cycles': [[True, True, True], [False, True, False], [True, True, True], [True, True, False], [None, False, False], [False, False, False], [False, False, False]]}, {'votes': [True, False, True, True, False, False, False], 'isolated': []})], [('regression: isolated channel keeps reporting', {'isolate_after': 1, 'cycles': [[True, False, False], [True, True, False]]}, {'votes': [False, True], 'isolated': [0, 2]}), ('boundary: dissent interrupted by failure', {'isolate_after': 2, 'cycles': [[True, False, False], [None, False, False], [True, False, False]]}, {'votes': [False, False, False], 'isolated': []}), ('sampled regression 42', {'isolate_after': 3, 'cycles': [[False, False, False], [True, False, False], [False, False, False], [False, False, True], [False, True, False], [False, False, True], [None, False, False], [True, None, False], [False, True, True]]}, {'votes': [False, False, False, False, False, False, False, True, True], 'isolated': []}), ('control 13', {'isolate_after': 3, 'cycles': [[False, False, False], [True, None, True], [True, True, True], [False, None, False], [False, False, True]]}, {'votes': [False, True, True, False, False], 'isolated': []}), ('regression: two dissenters in turn', {'isolate_after': 2, 'cycles': [[True, False, False], [True, False, False], [False, True, False], [False, True, False], [False, False, False]]}, {'votes': [False, False, True, True, True], 'isolated': [0, 2]}), ('control 23', {'isolate_after': 2, 'cycles': [[True, False, True], [None, False, False], [False, False, False], [False, False, False], [False, False, None], [False, False, False], [True, None, True]]}, {'votes': [True, False, False, False, False, False, True], 'isolated': []}), ('control 26', {'isolate_after': 2, 'cycles': [[True, True, True], [False, False, False], [False, False, True], [False, False, None]]}, {'votes': [True, False, False, False], 'isolated': []}), ('control 29', {'isolate_after': 2, 'cycles': [[False, False, True], [False, False, False], [False, False, True], [False, True, False], [False, True, True]]}, {'votes': [False, False, False, False, True], 'isolated': []})], [('regression: two healthy channels disagree', {'isolate_after': 3, 'cycles': [[True, False, None]]}, {'votes': [True], 'isolated': []}), ('boundary: two healthy channels agree clear', {'isolate_after': 3, 'cycles': [[False, False, None]]}, {'votes': [False], 'isolated': []}), ('sampled regression 56', {'isolate_after': 2, 'cycles': [[False, True, None], [False, True, None], [False, False, False], [True, False, False], [False, False, True]]}, {'votes': [True, True, False, False, True], 'isolated': [0]}), ('control 21', {'isolate_after': 3, 'cycles': [[True, True, True], [False, True, False], [True, True, True], [True, True, False], [None, False, False], [False, False, False], [False, False, False]]}, {'votes': [True, False, True, True, False, False, False], 'isolated': []}), ('regression: isolated channel keeps reporting', {'isolate_after': 1, 'cycles': [[True, False, False], [True, True, False]]}, {'votes': [False, True], 'isolated': [0, 2]}), ('control 34', {'isolate_after': 2, 'cycles': [[True, True, False], [False, True, False], [True, True, True], [True, True, True], [True, False, True], [False, False, False], [True, False, True]]}, {'votes': [True, False, True, True, True, False, True], 'isolated': []}), ('control 37', {'isolate_after': 3, 'cycles': [[True, True, True], [False, False, False], [False, False, False], [False, True, False], [True, False, False], [False, False, False]]}, {'votes': [True, False, False, False, False, False], 'isolated': []}), ('sampled regression 40', {'isolate_after': 2, 'cycles': [[True, None, True], [False, False, None], [False, True, False], [False, True, False], [True, True, True], [True, None, False], [None, False, False], [True, True, True]]}, {'votes': [True, False, False, False, True, True, True, True], 'isolated': [1, 2]})], [('regression: two dissenters in turn', {'isolate_after': 2, 'cycles': [[True, False, False], [True, False, False], [False, True, False], [False, True, False], [False, False, False]]}, {'votes': [False, False, True, True, True], 'isolated': [0, 2]}), ('boundary: persistent dissenter', {'isolate_after': 2, 'cycles': [[True, False, False], [True, False, False], [False, False, False]]}, {'votes': [False, False, False], 'isolated': [0]}), ('sampled regression 69', {'isolate_after': 3, 'cycles': [[False, True, True], [True, True, False], [False, False, False], [False, None, True]]}, {'votes': [True, True, False, True], 'isolated': []}), ('control 32', {'isolate_after': 3, 'cycles': [[False, True, True], [False, False, False], [False, False, None], [True, True, None], [False, False, False], [True, True, False], [True, None, True]]}, {'votes': [True, False, False, True, False, True, True], 'isolated': []}), ('boundary: two healthy channels agree clear', {'isolate_after': 3, 'cycles': [[False, False, None]]}, {'votes': [False], 'isolated': []}), ('sampled regression 45', {'isolate_after': 2, 'cycles': [[True, True, True], [False, False, False], [False, False, False], [False, True, False], [None, True, False], [None, True, False], [True, False, False]]}, {'votes': [True, False, False, False, True, True, True], 'isolated': [2]}), ('control 48', {'isolate_after': 2, 'cycles': [[False, False, False], [False, False, False], [False, True, True], [True, True, None], [False, True, False], [True, True, True], [False, False, False], [False, False, False], [False, True, False]]}, {'votes': [False, False, True, True, False, True, False, False, False], 'isolated': []}), ('control 51', {'isolate_after': 3, 'cycles': [[False, False, False], [True, False, False], [True, True, True], [True, True, True], [True, True, True], [True, True, True], [True, False, True], [True, False, False], [True, True, True]]}, {'votes': [False, False, True, True, True, True, True, False, True], 'isolated': []})]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
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
regression: two healthy channels disagree	`{'isolated': [], 'votes': [True]}`	`{'isolated': [], 'votes': [True]}`	Passed
boundary: two healthy channels agree clear	`{'isolated': [], 'votes': [True]}`	`{'isolated': [], 'votes': [False]}`	Failed
sampled regression 2	`{'isolated': [1, 2], 'votes': [True, True, True, True, True, True]}`	`{'isolated': [], 'votes': [True, True, False, False, False, True]}`	Failed
boundary: persistent dissenter	`{'isolated': [0], 'votes': [False, False, True]}`	`{'isolated': [0], 'votes': [False, False, False]}`	Failed
boundary: single healthy channel says clear	`{'isolated': [], 'votes': [True]}`	`{'isolated': [], 'votes': [True]}`	Passed
control 1	`{'isolated': [], 'votes': [False, True, True, True]}`	`{'isolated': [], 'votes': [False, True, True, False]}`	Failed
control 4	`{'isolated': [], 'votes': [True, False, False, True, True, True, False, True, True]}`	`{'isolated': [], 'votes': [True, False, False, True, True, True, False, False, True]}`	Failed
control 7	`{'isolated': [], 'votes': [False, False, True, True, True, False, True, False]}`	`{'isolated': [], 'votes': [False, False, True, True, True, False, True, False]}`	Passed

SHA-256 / fd01a19b02caff0fcf0c5e40d73bde38bf77583e5e759905362638134184f92b

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    k = x['isolate_after']
    bad = [0, 0, 0]
    iso = [False, False, False]
    votes = []
    for cyc in x['cycles']:
        vals = [None if iso[i] else cyc[i] for i in range(3)]
        healthy = [v for v in vals if v is not None]
        if len(healthy) < 2:
            vote = True
        else:
            t = sum(1 for v in healthy if v)
            f = len(healthy) - t
            vote = t >= f
        votes.append(vote)
        for i in range(3):
            if vals[i] is not None and vals[i] != vote:
                bad[i] += 1
                if bad[i] >= k:
                    iso[i] = True
            else:
                bad[i] = 0
    return {'votes': votes, 'isolated': [i for i in range(3) if iso[i]]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: two healthy channels disagree', {'isolate_after': 3, 'cycles': [[True, False, None]]}, {'votes': [True], 'isolated': []}), ('boundary: two healthy channels agree clear', {'isolate_after': 3, 'cycles': [[False, False, None]]}, {'votes': [False], 'isolated': []}), ('sampled regression 2', {'isolate_after': 2, 'cycles': [[True, False, True], [None, True, False], [None, False, False], [False, None, False], [True, False, False], [True, False, True]]}, {'votes': [True, True, False, False, False, True], 'isolated': []}), ('boundary: persistent dissenter', {'isolate_after': 2, 'cycles': [[True, False, False], [True, False, False], [False, False, False]]}, {'votes': [False, False, False], 'isolated': [0]}), ('boundary: single healthy channel says clear', {'isolate_after': 3, 'cycles': [[False, None, None]]}, {'votes': [True], 'isolated': []}), ('control 1', {'isolate_after': 2, 'cycles': [[False, False, False], [True, None, True], [True, True, True], [None, False, False]]}, {'votes': [False, True, True, False], 'isolated': []}), ('control 4', {'isolate_after': 2, 'cycles': [[False, True, True], [False, False, False], [False, False, False], [True, True, False], [True, True, True], [True, False, True], [False, False, False], [False, False, None], [True, True, True]]}, {'votes': [True, False, False, True, True, True, False, False, True], 'isolated': []}), ('control 7', {'isolate_after': 3, 'cycles': [[False, False, True], [False, False, False], [True, True, True], [False, True, True], [True, True, None], [False, False, False], [True, True, True], [False, False, False]]}, {'votes': [False, False, True, True, True, False, True, False], 'isolated': []})], [('regression: two dissenters in turn', {'isolate_after': 2, 'cycles': [[True, False, False], [True, False, False], [False, True, False], [False, True, False], [False, False, False]]}, {'votes': [False, False, True, True, True], 'isolated': [0, 2]}), ('boundary: persistent dissenter', {'isolate_after': 2, 'cycles': [[True, False, False], [True, False, False], [False, False, False]]}, {'votes': [False, False, False], 'isolated': [0]}), ('sampled regression 18', {'isolate_after': 2, 'cycles': [[False, False, False], [None, False, True], [False, False, True], [True, False, False], [True, False, True], [False, False, False], [False, True, None], [False, False, False], [False, False, False]]}, {'votes': [False, True, False, False, True, False, True, False, False], 'isolated': []}), ('control 4', {'isolate_after': 2, 'cycles': [[False, True, True], [False, False, False], [False, False, False], [True, True, False], [True, True, True], [True, False, True], [False, False, False], [False, False, None], [True, True, True]]}, {'votes': [True, False, False, True, True, True, False, False, True], 'isolated': []}), ('boundary: single healthy channel says clear', {'isolate_after': 3, 'cycles': [[False, None, None]]}, {'votes': [True], 'isolated': []}), ('sampled regression 12', {'isolate_after': 3, 'cycles': [[False, False, False], [False, True, False], [True, False, True], [True, False, True], [False, False, True], [False, False, False], [True, False, True], [True, True, True]]}, {'votes': [False, False, True, True, True, False, True, True], 'isolated': [1]}), ('sampled regression 15', {'isolate_after': 3, 'cycles': [[False, False, False], [False, None, False], [True, False, False], [True, None, False]]}, {'votes': [False, False, False, True], 'isolated': []}), ('control 21', {'isolate_after': 3, 'cycles': [[True, True, True], [False, True, False], [True, True, True], [True, True, False], [None, False, False], [False, False, False], [False, False, False]]}, {'votes': [True, False, True, True, False, False, False], 'isolated': []})], [('regression: isolated channel keeps reporting', {'isolate_after': 1, 'cycles': [[True, False, False], [True, True, False]]}, {'votes': [False, True], 'isolated': [0, 2]}), ('boundary: dissent interrupted by failure', {'isolate_after': 2, 'cycles': [[True, False, False], [None, False, False], [True, False, False]]}, {'votes': [False, False, False], 'isolated': []}), ('sampled regression 42', {'isolate_after': 3, 'cycles': [[False, False, False], [True, False, False], [False, False, False], [False, False, True], [False, True, False], [False, False, True], [None, False, False], [True, None, False], [False, True, True]]}, {'votes': [False, False, False, False, False, False, False, True, True], 'isolated': []}), ('control 13', {'isolate_after': 3, 'cycles': [[False, False, False], [True, None, True], [True, True, True], [False, None, False], [False, False, True]]}, {'votes': [False, True, True, False, False], 'isolated': []}), ('regression: two dissenters in turn', {'isolate_after': 2, 'cycles': [[True, False, False], [True, False, False], [False, True, False], [False, True, False], [False, False, False]]}, {'votes': [False, False, True, True, True], 'isolated': [0, 2]}), ('control 23', {'isolate_after': 2, 'cycles': [[True, False, True], [None, False, False], [False, False, False], [False, False, False], [False, False, None], [False, False, False], [True, None, True]]}, {'votes': [True, False, False, False, False, False, True], 'isolated': []}), ('control 26', {'isolate_after': 2, 'cycles': [[True, True, True], [False, False, False], [False, False, True], [False, False, None]]}, {'votes': [True, False, False, False], 'isolated': []}), ('control 29', {'isolate_after': 2, 'cycles': [[False, False, True], [False, False, False], [False, False, True], [False, True, False], [False, True, True]]}, {'votes': [False, False, False, False, True], 'isolated': []})], [('regression: two healthy channels disagree', {'isolate_after': 3, 'cycles': [[True, False, None]]}, {'votes': [True], 'isolated': []}), ('boundary: two healthy channels agree clear', {'isolate_after': 3, 'cycles': [[False, False, None]]}, {'votes': [False], 'isolated': []}), ('sampled regression 56', {'isolate_after': 2, 'cycles': [[False, True, None], [False, True, None], [False, False, False], [True, False, False], [False, False, True]]}, {'votes': [True, True, False, False, True], 'isolated': [0]}), ('control 21', {'isolate_after': 3, 'cycles': [[True, True, True], [False, True, False], [True, True, True], [True, True, False], [None, False, False], [False, False, False], [False, False, False]]}, {'votes': [True, False, True, True, False, False, False], 'isolated': []}), ('regression: isolated channel keeps reporting', {'isolate_after': 1, 'cycles': [[True, False, False], [True, True, False]]}, {'votes': [False, True], 'isolated': [0, 2]}), ('control 34', {'isolate_after': 2, 'cycles': [[True, True, False], [False, True, False], [True, True, True], [True, True, True], [True, False, True], [False, False, False], [True, False, True]]}, {'votes': [True, False, True, True, True, False, True], 'isolated': []}), ('control 37', {'isolate_after': 3, 'cycles': [[True, True, True], [False, False, False], [False, False, False], [False, True, False], [True, False, False], [False, False, False]]}, {'votes': [True, False, False, False, False, False], 'isolated': []}), ('sampled regression 40', {'isolate_after': 2, 'cycles': [[True, None, True], [False, False, None], [False, True, False], [False, True, False], [True, True, True], [True, None, False], [None, False, False], [True, True, True]]}, {'votes': [True, False, False, False, True, True, True, True], 'isolated': [1, 2]})], [('regression: two dissenters in turn', {'isolate_after': 2, 'cycles': [[True, False, False], [True, False, False], [False, True, False], [False, True, False], [False, False, False]]}, {'votes': [False, False, True, True, True], 'isolated': [0, 2]}), ('boundary: persistent dissenter', {'isolate_after': 2, 'cycles': [[True, False, False], [True, False, False], [False, False, False]]}, {'votes': [False, False, False], 'isolated': [0]}), ('sampled regression 69', {'isolate_after': 3, 'cycles': [[False, True, True], [True, True, False], [False, False, False], [False, None, True]]}, {'votes': [True, True, False, True], 'isolated': []}), ('control 32', {'isolate_after': 3, 'cycles': [[False, True, True], [False, False, False], [False, False, None], [True, True, None], [False, False, False], [True, True, False], [True, None, True]]}, {'votes': [True, False, False, True, False, True, True], 'isolated': []}), ('boundary: two healthy channels agree clear', {'isolate_after': 3, 'cycles': [[False, False, None]]}, {'votes': [False], 'isolated': []}), ('sampled regression 45', {'isolate_after': 2, 'cycles': [[True, True, True], [False, False, False], [False, False, False], [False, True, False], [None, True, False], [None, True, False], [True, False, False]]}, {'votes': [True, False, False, False, True, True, True], 'isolated': [2]}), ('control 48', {'isolate_after': 2, 'cycles': [[False, False, False], [False, False, False], [False, True, True], [True, True, None], [False, True, False], [True, True, True], [False, False, False], [False, False, False], [False, True, False]]}, {'votes': [False, False, True, True, False, True, False, False, False], 'isolated': []}), ('control 51', {'isolate_after': 3, 'cycles': [[False, False, False], [True, False, False], [True, True, True], [True, True, True], [True, True, True], [True, True, True], [True, False, True], [True, False, False], [True, True, True]]}, {'votes': [False, False, True, True, True, True, True, False, True], 'isolated': []})]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
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
regression: two healthy channels disagree	`{'isolated': [], 'votes': [True]}`	`{'isolated': [], 'votes': [True]}`	Passed
boundary: two healthy channels agree clear	`{'isolated': [], 'votes': [False]}`	`{'isolated': [], 'votes': [False]}`	Passed
sampled regression 2	`{'isolated': [], 'votes': [True, True, False, False, False, True]}`	`{'isolated': [], 'votes': [True, True, False, False, False, True]}`	Passed
boundary: persistent dissenter	`{'isolated': [0], 'votes': [False, False, False]}`	`{'isolated': [0], 'votes': [False, False, False]}`	Passed
boundary: single healthy channel says clear	`{'isolated': [], 'votes': [True]}`	`{'isolated': [], 'votes': [True]}`	Passed
control 1	`{'isolated': [], 'votes': [False, True, True, False]}`	`{'isolated': [], 'votes': [False, True, True, False]}`	Passed
control 4	`{'isolated': [], 'votes': [True, False, False, True, True, True, False, False, True]}`	`{'isolated': [], 'votes': [True, False, False, True, True, True, False, False, True]}`	Passed
control 7	`{'isolated': [], 'votes': [False, False, True, True, True, False, True, False]}`	`{'isolated': [], 'votes': [False, False, True, True, True, False, True, False]}`	Passed

SHA-256 / 6514bf02ab7ea36812de96e28c3ebd93c8c8a671e3cb994a76b314d1aa73da6a

Verification & scope

Stipulated toy interlocking contract for a bounded teaching model; it makes no claim of conformance to any railway signalling standard and omits real safety cases. 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 2026-09-29T14:47:49.828215+00:00.

Case digest / 564f497097c66ca59e3e0d1202bf12a5892a4a00a917182848a4bdd103adc2e0