FA-75321 / CRDT convergence / Open access

Delete set normalization: touching ranges are not merged · case 01

Two ranges that meet end to start stay separate, so encodings differ between replicas.

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

ROOT CAUSE

The merge test requires the next range to start strictly inside the previous one.

VERIFIED REPAIR

Merge when the next range starts at or before the end of the previous one.

Unsuccessful approach: Also merging across a one-clock gap marks a live clock as deleted.

Case contract

A delete set is a list of [client, clock, length] ranges, possibly unsorted, overlapping or adjacent. Normalize per client in client order: sort by clock and merge ranges that overlap or touch. Queries [client, clock] report whether the clock lies in a merged range (end exclusive). Return merged ranges and query answers.

Why this case matters

Sequence CRDTs ship deletions as compact range sets that every replica must normalize identically.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(ranges, queries):
    by = {}
    for c, clk, ln in ranges:
        by.setdefault(c, []).append([clk, ln])
    out = []
    for c in sorted(by):
        rs = sorted(by[c])
        merged = [rs[0][:]]
        for clk, ln in rs[1:]:
            last = merged[-1]
            if clk < last[0] + last[1]:
                last[1] = max(last[1], clk + ln - last[0])
            else:
                merged.append([clk, ln])
        out.extend([c, a, b] for a, b in merged)
    hits = [any(c == q[0] and a <= q[1] < a + b for c, a, b in out) for q in queries]
    return {'ranges': out, 'hits': hits}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = {
    1: [('adjacent ranges merge', [[[1, 0, 2], [1, 2, 3]], [[1, 4], [1, 5]]], {'ranges': [[1, 0, 5]], 'hits': [True, False]}), ('one-clock gap stays split', [[[1, 0, 2], [1, 3, 1]], [[1, 2], [1, 3]]], {'ranges': [[1, 0, 2], [1, 3, 1]], 'hits': [False, True]}), ('contained range does not shrink', [[[2, 0, 10], [2, 3, 2]], [[2, 9], [2, 10]]], {'ranges': [[2, 0, 10]], 'hits': [True, False]}), ('overlap extends', [[[3, 5, 4], [3, 7, 4]], [[3, 9], [3, 10], [3, 4]]], {'ranges': [[3, 5, 6]], 'hits': [True, True, False]}), ('unsorted input', [[[4, 9, 2], [4, 0, 3], [4, 3, 6]], [[4, 10], [4, 11]]], {'ranges': [[4, 0, 11]], 'hits': [True, False]}), ('several clients', [[[6, 1, 1], [5, 0, 1], [6, 2, 2], [5, 1, 1]], [[5, 1], [6, 0], [6, 3]]], {'ranges': [[5, 0, 2], [6, 1, 3]], 'hits': [True, False, True]}), ('long range earlier start sorted after by end', [[[8, 0, 20], [8, 5, 1], [8, 21, 2]], [[8, 20], [8, 21]]], {'ranges': [[8, 0, 20], [8, 21, 2]], 'hits': [False, True]}), ('empty input', [[], [[1, 0]]], {'ranges': [], 'hits': [False]})],
    2: [('adjacent ranges merge', [[[1, 0, 2], [1, 2, 3]], [[1, 4], [1, 5]]], {'ranges': [[1, 0, 5]], 'hits': [True, False]}), ('one-clock gap stays split', [[[1, 0, 2], [1, 3, 1]], [[1, 2], [1, 3]]], {'ranges': [[1, 0, 2], [1, 3, 1]], 'hits': [False, True]}), ('contained range does not shrink', [[[2, 0, 10], [2, 3, 2]], [[2, 9], [2, 10]]], {'ranges': [[2, 0, 10]], 'hits': [True, False]}), ('overlap extends', [[[3, 5, 4], [3, 7, 5]], [[3, 10], [3, 11], [3, 4]]], {'ranges': [[3, 5, 7]], 'hits': [True, True, False]}), ('unsorted input', [[[4, 9, 2], [4, 0, 3], [4, 3, 6]], [[4, 10], [4, 11]]], {'ranges': [[4, 0, 11]], 'hits': [True, False]}), ('several clients', [[[6, 1, 1], [5, 0, 2], [6, 2, 2], [5, 2, 1]], [[5, 2], [6, 0], [6, 3]]], {'ranges': [[5, 0, 3], [6, 1, 3]], 'hits': [True, False, True]}), ('long range earlier start sorted after by end', [[[8, 0, 20], [8, 5, 1], [8, 21, 2]], [[8, 20], [8, 21]]], {'ranges': [[8, 0, 20], [8, 21, 2]], 'hits': [False, True]}), ('empty input', [[], [[1, 0]]], {'ranges': [], 'hits': [False]})],
    3: [('adjacent ranges merge', [[[1, 0, 2], [1, 2, 3]], [[1, 4], [1, 5]]], {'ranges': [[1, 0, 5]], 'hits': [True, False]}), ('one-clock gap stays split', [[[1, 0, 2], [1, 3, 1]], [[1, 2], [1, 3]]], {'ranges': [[1, 0, 2], [1, 3, 1]], 'hits': [False, True]}), ('contained range does not shrink', [[[2, 0, 10], [2, 3, 2]], [[2, 9], [2, 10]]], {'ranges': [[2, 0, 10]], 'hits': [True, False]}), ('overlap extends', [[[3, 5, 4], [3, 7, 6]], [[3, 11], [3, 12], [3, 4]]], {'ranges': [[3, 5, 8]], 'hits': [True, True, False]}), ('unsorted input', [[[4, 9, 2], [4, 0, 3], [4, 3, 6]], [[4, 10], [4, 11]]], {'ranges': [[4, 0, 11]], 'hits': [True, False]}), ('several clients', [[[6, 1, 1], [5, 0, 3], [6, 2, 2], [5, 3, 1]], [[5, 3], [6, 0], [6, 3]]], {'ranges': [[5, 0, 4], [6, 1, 3]], 'hits': [True, False, True]}), ('long range earlier start sorted after by end', [[[8, 0, 20], [8, 5, 1], [8, 21, 2]], [[8, 20], [8, 21]]], {'ranges': [[8, 0, 20], [8, 21, 2]], 'hits': [False, True]}), ('empty input', [[], [[1, 0]]], {'ranges': [], 'hits': [False]})],
    4: [('adjacent ranges merge', [[[1, 0, 2], [1, 2, 3]], [[1, 4], [1, 5]]], {'ranges': [[1, 0, 5]], 'hits': [True, False]}), ('one-clock gap stays split', [[[1, 0, 2], [1, 3, 1]], [[1, 2], [1, 3]]], {'ranges': [[1, 0, 2], [1, 3, 1]], 'hits': [False, True]}), ('contained range does not shrink', [[[2, 0, 10], [2, 3, 2]], [[2, 9], [2, 10]]], {'ranges': [[2, 0, 10]], 'hits': [True, False]}), ('overlap extends', [[[3, 5, 4], [3, 7, 7]], [[3, 12], [3, 13], [3, 4]]], {'ranges': [[3, 5, 9]], 'hits': [True, True, False]}), ('unsorted input', [[[4, 9, 2], [4, 0, 3], [4, 3, 6]], [[4, 10], [4, 11]]], {'ranges': [[4, 0, 11]], 'hits': [True, False]}), ('several clients', [[[6, 1, 1], [5, 0, 4], [6, 2, 2], [5, 4, 1]], [[5, 4], [6, 0], [6, 3]]], {'ranges': [[5, 0, 5], [6, 1, 3]], 'hits': [True, False, True]}), ('long range earlier start sorted after by end', [[[8, 0, 20], [8, 5, 1], [8, 21, 2]], [[8, 20], [8, 21]]], {'ranges': [[8, 0, 20], [8, 21, 2]], 'hits': [False, True]}), ('empty input', [[], [[1, 0]]], {'ranges': [], 'hits': [False]})],
    5: [('adjacent ranges merge', [[[1, 0, 2], [1, 2, 3]], [[1, 4], [1, 5]]], {'ranges': [[1, 0, 5]], 'hits': [True, False]}), ('one-clock gap stays split', [[[1, 0, 2], [1, 3, 1]], [[1, 2], [1, 3]]], {'ranges': [[1, 0, 2], [1, 3, 1]], 'hits': [False, True]}), ('contained range does not shrink', [[[2, 0, 10], [2, 3, 2]], [[2, 9], [2, 10]]], {'ranges': [[2, 0, 10]], 'hits': [True, False]}), ('overlap extends', [[[3, 5, 4], [3, 7, 8]], [[3, 13], [3, 14], [3, 4]]], {'ranges': [[3, 5, 10]], 'hits': [True, True, False]}), ('unsorted input', [[[4, 9, 2], [4, 0, 3], [4, 3, 6]], [[4, 10], [4, 11]]], {'ranges': [[4, 0, 11]], 'hits': [True, False]}), ('several clients', [[[6, 1, 1], [5, 0, 5], [6, 2, 2], [5, 5, 1]], [[5, 5], [6, 0], [6, 3]]], {'ranges': [[5, 0, 6], [6, 1, 3]], 'hits': [True, False, True]}), ('long range earlier start sorted after by end', [[[8, 0, 20], [8, 5, 1], [8, 21, 2]], [[8, 20], [8, 21]]], {'ranges': [[8, 0, 20], [8, 21, 2]], 'hits': [False, True]}), ('empty input', [[], [[1, 0]]], {'ranges': [], 'hits': [False]})],
}[N]
for label, args, expected in cases:
    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
adjacent ranges merge	`{'hits': [True, False], 'ranges': [[1, 0, 2], [1, 2, 3]]}`	`{'hits': [True, False], 'ranges': [[1, 0, 5]]}`	Failed
one-clock gap stays split	`{'hits': [False, True], 'ranges': [[1, 0, 2], [1, 3, 1]]}`	`{'hits': [False, True], 'ranges': [[1, 0, 2], [1, 3, 1]]}`	Passed
contained range does not shrink	`{'hits': [True, False], 'ranges': [[2, 0, 10]]}`	`{'hits': [True, False], 'ranges': [[2, 0, 10]]}`	Passed
overlap extends	`{'hits': [True, True, False], 'ranges': [[3, 5, 6]]}`	`{'hits': [True, True, False], 'ranges': [[3, 5, 6]]}`	Passed
unsorted input	`{'hits': [True, False], 'ranges': [[4, 0, 3], [4, 3, 6], [4, 9, 2]]}`	`{'hits': [True, False], 'ranges': [[4, 0, 11]]}`	Failed
several clients	`{'hits': [True, False, True], 'ranges': [[5, 0, 1], [5, 1, 1], [6, 1, 1], [6, 2, 2]]}`	`{'hits': [True, False, True], 'ranges': [[5, 0, 2], [6, 1, 3]]}`	Failed
long range earlier start sorted after by end	`{'hits': [False, True], 'ranges': [[8, 0, 20], [8, 21, 2]]}`	`{'hits': [False, True], 'ranges': [[8, 0, 20], [8, 21, 2]]}`	Passed
empty input	`{'hits': [False], 'ranges': []}`	`{'hits': [False], 'ranges': []}`	Passed

SHA-256 / 338cf9cf0e0166e58a96cde159b8ea58d23d0db94fef4c93735df369a0e84743

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(ranges, queries):
    by = {}
    for c, clk, ln in ranges:
        by.setdefault(c, []).append([clk, ln])
    out = []
    for c in sorted(by):
        rs = sorted(by[c])
        merged = [rs[0][:]]
        for clk, ln in rs[1:]:
            last = merged[-1]
            if clk <= last[0] + last[1] + 1:
                last[1] = max(last[1], clk + ln - last[0])
            else:
                merged.append([clk, ln])
        out.extend([c, a, b] for a, b in merged)
    hits = [any(c == q[0] and a <= q[1] < a + b for c, a, b in out) for q in queries]
    return {'ranges': out, 'hits': hits}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = {
    1: [('adjacent ranges merge', [[[1, 0, 2], [1, 2, 3]], [[1, 4], [1, 5]]], {'ranges': [[1, 0, 5]], 'hits': [True, False]}), ('one-clock gap stays split', [[[1, 0, 2], [1, 3, 1]], [[1, 2], [1, 3]]], {'ranges': [[1, 0, 2], [1, 3, 1]], 'hits': [False, True]}), ('contained range does not shrink', [[[2, 0, 10], [2, 3, 2]], [[2, 9], [2, 10]]], {'ranges': [[2, 0, 10]], 'hits': [True, False]}), ('overlap extends', [[[3, 5, 4], [3, 7, 4]], [[3, 9], [3, 10], [3, 4]]], {'ranges': [[3, 5, 6]], 'hits': [True, True, False]}), ('unsorted input', [[[4, 9, 2], [4, 0, 3], [4, 3, 6]], [[4, 10], [4, 11]]], {'ranges': [[4, 0, 11]], 'hits': [True, False]}), ('several clients', [[[6, 1, 1], [5, 0, 1], [6, 2, 2], [5, 1, 1]], [[5, 1], [6, 0], [6, 3]]], {'ranges': [[5, 0, 2], [6, 1, 3]], 'hits': [True, False, True]}), ('long range earlier start sorted after by end', [[[8, 0, 20], [8, 5, 1], [8, 21, 2]], [[8, 20], [8, 21]]], {'ranges': [[8, 0, 20], [8, 21, 2]], 'hits': [False, True]}), ('empty input', [[], [[1, 0]]], {'ranges': [], 'hits': [False]})],
    2: [('adjacent ranges merge', [[[1, 0, 2], [1, 2, 3]], [[1, 4], [1, 5]]], {'ranges': [[1, 0, 5]], 'hits': [True, False]}), ('one-clock gap stays split', [[[1, 0, 2], [1, 3, 1]], [[1, 2], [1, 3]]], {'ranges': [[1, 0, 2], [1, 3, 1]], 'hits': [False, True]}), ('contained range does not shrink', [[[2, 0, 10], [2, 3, 2]], [[2, 9], [2, 10]]], {'ranges': [[2, 0, 10]], 'hits': [True, False]}), ('overlap extends', [[[3, 5, 4], [3, 7, 5]], [[3, 10], [3, 11], [3, 4]]], {'ranges': [[3, 5, 7]], 'hits': [True, True, False]}), ('unsorted input', [[[4, 9, 2], [4, 0, 3], [4, 3, 6]], [[4, 10], [4, 11]]], {'ranges': [[4, 0, 11]], 'hits': [True, False]}), ('several clients', [[[6, 1, 1], [5, 0, 2], [6, 2, 2], [5, 2, 1]], [[5, 2], [6, 0], [6, 3]]], {'ranges': [[5, 0, 3], [6, 1, 3]], 'hits': [True, False, True]}), ('long range earlier start sorted after by end', [[[8, 0, 20], [8, 5, 1], [8, 21, 2]], [[8, 20], [8, 21]]], {'ranges': [[8, 0, 20], [8, 21, 2]], 'hits': [False, True]}), ('empty input', [[], [[1, 0]]], {'ranges': [], 'hits': [False]})],
    3: [('adjacent ranges merge', [[[1, 0, 2], [1, 2, 3]], [[1, 4], [1, 5]]], {'ranges': [[1, 0, 5]], 'hits': [True, False]}), ('one-clock gap stays split', [[[1, 0, 2], [1, 3, 1]], [[1, 2], [1, 3]]], {'ranges': [[1, 0, 2], [1, 3, 1]], 'hits': [False, True]}), ('contained range does not shrink', [[[2, 0, 10], [2, 3, 2]], [[2, 9], [2, 10]]], {'ranges': [[2, 0, 10]], 'hits': [True, False]}), ('overlap extends', [[[3, 5, 4], [3, 7, 6]], [[3, 11], [3, 12], [3, 4]]], {'ranges': [[3, 5, 8]], 'hits': [True, True, False]}), ('unsorted input', [[[4, 9, 2], [4, 0, 3], [4, 3, 6]], [[4, 10], [4, 11]]], {'ranges': [[4, 0, 11]], 'hits': [True, False]}), ('several clients', [[[6, 1, 1], [5, 0, 3], [6, 2, 2], [5, 3, 1]], [[5, 3], [6, 0], [6, 3]]], {'ranges': [[5, 0, 4], [6, 1, 3]], 'hits': [True, False, True]}), ('long range earlier start sorted after by end', [[[8, 0, 20], [8, 5, 1], [8, 21, 2]], [[8, 20], [8, 21]]], {'ranges': [[8, 0, 20], [8, 21, 2]], 'hits': [False, True]}), ('empty input', [[], [[1, 0]]], {'ranges': [], 'hits': [False]})],
    4: [('adjacent ranges merge', [[[1, 0, 2], [1, 2, 3]], [[1, 4], [1, 5]]], {'ranges': [[1, 0, 5]], 'hits': [True, False]}), ('one-clock gap stays split', [[[1, 0, 2], [1, 3, 1]], [[1, 2], [1, 3]]], {'ranges': [[1, 0, 2], [1, 3, 1]], 'hits': [False, True]}), ('contained range does not shrink', [[[2, 0, 10], [2, 3, 2]], [[2, 9], [2, 10]]], {'ranges': [[2, 0, 10]], 'hits': [True, False]}), ('overlap extends', [[[3, 5, 4], [3, 7, 7]], [[3, 12], [3, 13], [3, 4]]], {'ranges': [[3, 5, 9]], 'hits': [True, True, False]}), ('unsorted input', [[[4, 9, 2], [4, 0, 3], [4, 3, 6]], [[4, 10], [4, 11]]], {'ranges': [[4, 0, 11]], 'hits': [True, False]}), ('several clients', [[[6, 1, 1], [5, 0, 4], [6, 2, 2], [5, 4, 1]], [[5, 4], [6, 0], [6, 3]]], {'ranges': [[5, 0, 5], [6, 1, 3]], 'hits': [True, False, True]}), ('long range earlier start sorted after by end', [[[8, 0, 20], [8, 5, 1], [8, 21, 2]], [[8, 20], [8, 21]]], {'ranges': [[8, 0, 20], [8, 21, 2]], 'hits': [False, True]}), ('empty input', [[], [[1, 0]]], {'ranges': [], 'hits': [False]})],
    5: [('adjacent ranges merge', [[[1, 0, 2], [1, 2, 3]], [[1, 4], [1, 5]]], {'ranges': [[1, 0, 5]], 'hits': [True, False]}), ('one-clock gap stays split', [[[1, 0, 2], [1, 3, 1]], [[1, 2], [1, 3]]], {'ranges': [[1, 0, 2], [1, 3, 1]], 'hits': [False, True]}), ('contained range does not shrink', [[[2, 0, 10], [2, 3, 2]], [[2, 9], [2, 10]]], {'ranges': [[2, 0, 10]], 'hits': [True, False]}), ('overlap extends', [[[3, 5, 4], [3, 7, 8]], [[3, 13], [3, 14], [3, 4]]], {'ranges': [[3, 5, 10]], 'hits': [True, True, False]}), ('unsorted input', [[[4, 9, 2], [4, 0, 3], [4, 3, 6]], [[4, 10], [4, 11]]], {'ranges': [[4, 0, 11]], 'hits': [True, False]}), ('several clients', [[[6, 1, 1], [5, 0, 5], [6, 2, 2], [5, 5, 1]], [[5, 5], [6, 0], [6, 3]]], {'ranges': [[5, 0, 6], [6, 1, 3]], 'hits': [True, False, True]}), ('long range earlier start sorted after by end', [[[8, 0, 20], [8, 5, 1], [8, 21, 2]], [[8, 20], [8, 21]]], {'ranges': [[8, 0, 20], [8, 21, 2]], 'hits': [False, True]}), ('empty input', [[], [[1, 0]]], {'ranges': [], 'hits': [False]})],
}[N]
for label, args, expected in cases:
    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
adjacent ranges merge	`{'hits': [True, False], 'ranges': [[1, 0, 5]]}`	`{'hits': [True, False], 'ranges': [[1, 0, 5]]}`	Passed
one-clock gap stays split	`{'hits': [True, True], 'ranges': [[1, 0, 4]]}`	`{'hits': [False, True], 'ranges': [[1, 0, 2], [1, 3, 1]]}`	Failed
contained range does not shrink	`{'hits': [True, False], 'ranges': [[2, 0, 10]]}`	`{'hits': [True, False], 'ranges': [[2, 0, 10]]}`	Passed
overlap extends	`{'hits': [True, True, False], 'ranges': [[3, 5, 6]]}`	`{'hits': [True, True, False], 'ranges': [[3, 5, 6]]}`	Passed
unsorted input	`{'hits': [True, False], 'ranges': [[4, 0, 11]]}`	`{'hits': [True, False], 'ranges': [[4, 0, 11]]}`	Passed
several clients	`{'hits': [True, False, True], 'ranges': [[5, 0, 2], [6, 1, 3]]}`	`{'hits': [True, False, True], 'ranges': [[5, 0, 2], [6, 1, 3]]}`	Passed
long range earlier start sorted after by end	`{'hits': [True, True], 'ranges': [[8, 0, 23]]}`	`{'hits': [False, True], 'ranges': [[8, 0, 20], [8, 21, 2]]}`	Failed
empty input	`{'hits': [False], 'ranges': []}`	`{'hits': [False], 'ranges': []}`	Passed

SHA-256 / 30fe695e4c4ee6d78f29bcb80648ac14282f987e6e41d46ff1d0851ba5d8a85a

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(ranges, queries):
    by = {}
    for c, clk, ln in ranges:
        by.setdefault(c, []).append([clk, ln])
    out = []
    for c in sorted(by):
        rs = sorted(by[c])
        merged = [rs[0][:]]
        for clk, ln in rs[1:]:
            last = merged[-1]
            if clk <= last[0] + last[1]:
                last[1] = max(last[1], clk + ln - last[0])
            else:
                merged.append([clk, ln])
        out.extend([c, a, b] for a, b in merged)
    hits = [any(c == q[0] and a <= q[1] < a + b for c, a, b in out) for q in queries]
    return {'ranges': out, 'hits': hits}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = {
    1: [('adjacent ranges merge', [[[1, 0, 2], [1, 2, 3]], [[1, 4], [1, 5]]], {'ranges': [[1, 0, 5]], 'hits': [True, False]}), ('one-clock gap stays split', [[[1, 0, 2], [1, 3, 1]], [[1, 2], [1, 3]]], {'ranges': [[1, 0, 2], [1, 3, 1]], 'hits': [False, True]}), ('contained range does not shrink', [[[2, 0, 10], [2, 3, 2]], [[2, 9], [2, 10]]], {'ranges': [[2, 0, 10]], 'hits': [True, False]}), ('overlap extends', [[[3, 5, 4], [3, 7, 4]], [[3, 9], [3, 10], [3, 4]]], {'ranges': [[3, 5, 6]], 'hits': [True, True, False]}), ('unsorted input', [[[4, 9, 2], [4, 0, 3], [4, 3, 6]], [[4, 10], [4, 11]]], {'ranges': [[4, 0, 11]], 'hits': [True, False]}), ('several clients', [[[6, 1, 1], [5, 0, 1], [6, 2, 2], [5, 1, 1]], [[5, 1], [6, 0], [6, 3]]], {'ranges': [[5, 0, 2], [6, 1, 3]], 'hits': [True, False, True]}), ('long range earlier start sorted after by end', [[[8, 0, 20], [8, 5, 1], [8, 21, 2]], [[8, 20], [8, 21]]], {'ranges': [[8, 0, 20], [8, 21, 2]], 'hits': [False, True]}), ('empty input', [[], [[1, 0]]], {'ranges': [], 'hits': [False]})],
    2: [('adjacent ranges merge', [[[1, 0, 2], [1, 2, 3]], [[1, 4], [1, 5]]], {'ranges': [[1, 0, 5]], 'hits': [True, False]}), ('one-clock gap stays split', [[[1, 0, 2], [1, 3, 1]], [[1, 2], [1, 3]]], {'ranges': [[1, 0, 2], [1, 3, 1]], 'hits': [False, True]}), ('contained range does not shrink', [[[2, 0, 10], [2, 3, 2]], [[2, 9], [2, 10]]], {'ranges': [[2, 0, 10]], 'hits': [True, False]}), ('overlap extends', [[[3, 5, 4], [3, 7, 5]], [[3, 10], [3, 11], [3, 4]]], {'ranges': [[3, 5, 7]], 'hits': [True, True, False]}), ('unsorted input', [[[4, 9, 2], [4, 0, 3], [4, 3, 6]], [[4, 10], [4, 11]]], {'ranges': [[4, 0, 11]], 'hits': [True, False]}), ('several clients', [[[6, 1, 1], [5, 0, 2], [6, 2, 2], [5, 2, 1]], [[5, 2], [6, 0], [6, 3]]], {'ranges': [[5, 0, 3], [6, 1, 3]], 'hits': [True, False, True]}), ('long range earlier start sorted after by end', [[[8, 0, 20], [8, 5, 1], [8, 21, 2]], [[8, 20], [8, 21]]], {'ranges': [[8, 0, 20], [8, 21, 2]], 'hits': [False, True]}), ('empty input', [[], [[1, 0]]], {'ranges': [], 'hits': [False]})],
    3: [('adjacent ranges merge', [[[1, 0, 2], [1, 2, 3]], [[1, 4], [1, 5]]], {'ranges': [[1, 0, 5]], 'hits': [True, False]}), ('one-clock gap stays split', [[[1, 0, 2], [1, 3, 1]], [[1, 2], [1, 3]]], {'ranges': [[1, 0, 2], [1, 3, 1]], 'hits': [False, True]}), ('contained range does not shrink', [[[2, 0, 10], [2, 3, 2]], [[2, 9], [2, 10]]], {'ranges': [[2, 0, 10]], 'hits': [True, False]}), ('overlap extends', [[[3, 5, 4], [3, 7, 6]], [[3, 11], [3, 12], [3, 4]]], {'ranges': [[3, 5, 8]], 'hits': [True, True, False]}), ('unsorted input', [[[4, 9, 2], [4, 0, 3], [4, 3, 6]], [[4, 10], [4, 11]]], {'ranges': [[4, 0, 11]], 'hits': [True, False]}), ('several clients', [[[6, 1, 1], [5, 0, 3], [6, 2, 2], [5, 3, 1]], [[5, 3], [6, 0], [6, 3]]], {'ranges': [[5, 0, 4], [6, 1, 3]], 'hits': [True, False, True]}), ('long range earlier start sorted after by end', [[[8, 0, 20], [8, 5, 1], [8, 21, 2]], [[8, 20], [8, 21]]], {'ranges': [[8, 0, 20], [8, 21, 2]], 'hits': [False, True]}), ('empty input', [[], [[1, 0]]], {'ranges': [], 'hits': [False]})],
    4: [('adjacent ranges merge', [[[1, 0, 2], [1, 2, 3]], [[1, 4], [1, 5]]], {'ranges': [[1, 0, 5]], 'hits': [True, False]}), ('one-clock gap stays split', [[[1, 0, 2], [1, 3, 1]], [[1, 2], [1, 3]]], {'ranges': [[1, 0, 2], [1, 3, 1]], 'hits': [False, True]}), ('contained range does not shrink', [[[2, 0, 10], [2, 3, 2]], [[2, 9], [2, 10]]], {'ranges': [[2, 0, 10]], 'hits': [True, False]}), ('overlap extends', [[[3, 5, 4], [3, 7, 7]], [[3, 12], [3, 13], [3, 4]]], {'ranges': [[3, 5, 9]], 'hits': [True, True, False]}), ('unsorted input', [[[4, 9, 2], [4, 0, 3], [4, 3, 6]], [[4, 10], [4, 11]]], {'ranges': [[4, 0, 11]], 'hits': [True, False]}), ('several clients', [[[6, 1, 1], [5, 0, 4], [6, 2, 2], [5, 4, 1]], [[5, 4], [6, 0], [6, 3]]], {'ranges': [[5, 0, 5], [6, 1, 3]], 'hits': [True, False, True]}), ('long range earlier start sorted after by end', [[[8, 0, 20], [8, 5, 1], [8, 21, 2]], [[8, 20], [8, 21]]], {'ranges': [[8, 0, 20], [8, 21, 2]], 'hits': [False, True]}), ('empty input', [[], [[1, 0]]], {'ranges': [], 'hits': [False]})],
    5: [('adjacent ranges merge', [[[1, 0, 2], [1, 2, 3]], [[1, 4], [1, 5]]], {'ranges': [[1, 0, 5]], 'hits': [True, False]}), ('one-clock gap stays split', [[[1, 0, 2], [1, 3, 1]], [[1, 2], [1, 3]]], {'ranges': [[1, 0, 2], [1, 3, 1]], 'hits': [False, True]}), ('contained range does not shrink', [[[2, 0, 10], [2, 3, 2]], [[2, 9], [2, 10]]], {'ranges': [[2, 0, 10]], 'hits': [True, False]}), ('overlap extends', [[[3, 5, 4], [3, 7, 8]], [[3, 13], [3, 14], [3, 4]]], {'ranges': [[3, 5, 10]], 'hits': [True, True, False]}), ('unsorted input', [[[4, 9, 2], [4, 0, 3], [4, 3, 6]], [[4, 10], [4, 11]]], {'ranges': [[4, 0, 11]], 'hits': [True, False]}), ('several clients', [[[6, 1, 1], [5, 0, 5], [6, 2, 2], [5, 5, 1]], [[5, 5], [6, 0], [6, 3]]], {'ranges': [[5, 0, 6], [6, 1, 3]], 'hits': [True, False, True]}), ('long range earlier start sorted after by end', [[[8, 0, 20], [8, 5, 1], [8, 21, 2]], [[8, 20], [8, 21]]], {'ranges': [[8, 0, 20], [8, 21, 2]], 'hits': [False, True]}), ('empty input', [[], [[1, 0]]], {'ranges': [], 'hits': [False]})],
}[N]
for label, args, expected in cases:
    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
adjacent ranges merge	`{'hits': [True, False], 'ranges': [[1, 0, 5]]}`	`{'hits': [True, False], 'ranges': [[1, 0, 5]]}`	Passed
one-clock gap stays split	`{'hits': [False, True], 'ranges': [[1, 0, 2], [1, 3, 1]]}`	`{'hits': [False, True], 'ranges': [[1, 0, 2], [1, 3, 1]]}`	Passed
contained range does not shrink	`{'hits': [True, False], 'ranges': [[2, 0, 10]]}`	`{'hits': [True, False], 'ranges': [[2, 0, 10]]}`	Passed
overlap extends	`{'hits': [True, True, False], 'ranges': [[3, 5, 6]]}`	`{'hits': [True, True, False], 'ranges': [[3, 5, 6]]}`	Passed
unsorted input	`{'hits': [True, False], 'ranges': [[4, 0, 11]]}`	`{'hits': [True, False], 'ranges': [[4, 0, 11]]}`	Passed
several clients	`{'hits': [True, False, True], 'ranges': [[5, 0, 2], [6, 1, 3]]}`	`{'hits': [True, False, True], 'ranges': [[5, 0, 2], [6, 1, 3]]}`	Passed
long range earlier start sorted after by end	`{'hits': [False, True], 'ranges': [[8, 0, 20], [8, 21, 2]]}`	`{'hits': [False, True], 'ranges': [[8, 0, 20], [8, 21, 2]]}`	Passed
empty input	`{'hits': [False], 'ranges': []}`	`{'hits': [False], 'ranges': []}`	Passed

SHA-256 / d56fbc60856d774d390799787a14c39164ac12816ab600995fab894f7065f355

Verification & scope

A deterministic, bounded teaching model of one replicated data type with stipulated operation and merge rules; it is not a production CRDT library and makes no claim of conformance to any specific published design. 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 2026-09-29T14:49:05.311211+00:00.

Case digest / 5a73a426ac684deb5e31c526f08c966b87d8cf4b30ef377ea637b547cb2fcd73