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FA-74851 / CRDT convergence / Open access

G-Counter gossip: negative increments are admitted into a grow-only slot · case 01

A negative increment lowers a slot, which later merges silently undo, and the rejection count is wrong.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Validation checks only the type of the amount, so non-positive increments enter a grow-only slot.

VERIFIED REPAIR

Reject every amount that is not strictly positive before touching the slot.

Unsuccessful approach: Rejecting only negative amounts still admits zero increments that the contract counts as rejections.

Case contract

Each replica keeps a grow-only map replica->count. ["inc", r, k] adds positive integer k to r's own slot; a non-positive k is rejected and counted. ["sync", src, dst] merges src into dst by pointwise maximum. Return per-replica values (sum of slots), the rejection count, and the first replica's sorted slots.

Why this case matters

State-based counters must converge under repeated, reordered and transitive gossip.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(events, replicas):
    state = {r: {} for r in replicas}
    rejected = 0
    for ev in events:
        if ev[0] == 'inc':
            r, amount = ev[1], ev[2]
            if not isinstance(amount, int):
                rejected += 1
                continue
            state[r][r] = state[r].get(r, 0) + amount
        elif ev[0] == 'sync':
            src, dst = state[ev[1]], state[ev[2]]
            for k, v in src.items():
                dst[k] = max(dst.get(k, 0), v)
    values = [sum(state[r].values()) for r in replicas]
    return {'values': values, 'rejected': rejected, 'state': sorted([k, v] for k, v in state[replicas[0]].items())}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = {
    1: [('repeated sync is idempotent', [[['inc', 'a', 2], ['sync', 'a', 'b'], ['sync', 'a', 'b'], ['inc', 'b', 2], ['sync', 'b', 'a']], ['a', 'b', 'c', 'd']], {'values': [4, 4, 0, 0], 'rejected': 0, 'state': [['a', 2], ['b', 2]]}), ('transitive gossip carries third-party slots', [[['inc', 'a', 1], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['inc', 'c', 1], ['sync', 'c', 'd']], ['a', 'b', 'c', 'd']], {'values': [1, 1, 2, 2], 'rejected': 0, 'state': [['a', 1]]}), ('stale path does not regress a slot', [[['inc', 'a', 1], ['sync', 'a', 'd'], ['inc', 'a', 1], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['sync', 'd', 'c']], ['a', 'b', 'c', 'd']], {'values': [2, 2, 2, 1], 'rejected': 0, 'state': [['a', 2]]}), ('zero and negative amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', -1], ['inc', 'c', 2], ['sync', 'c', 'a'], ['inc', 'a', 3]], ['a', 'b', 'c', 'd']], {'values': [5, 0, 2, 0], 'rejected': 2, 'state': [['a', 3], ['c', 2]]}), ('concurrent increments all survive', [[['inc', 'a', 1], ['inc', 'b', 3], ['inc', 'c', 1], ['sync', 'a', 'b'], ['sync', 'c', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c', 'd']], {'values': [5, 5, 5, 0], 'rejected': 0, 'state': [['a', 1], ['b', 3], ['c', 1]]}), ('empty history', [[], ['a', 'b', 'c', 'd']], {'values': [0, 0, 0, 0], 'rejected': 0, 'state': []}), ('repeated local increments accumulate', [[['inc', 'a', 1], ['sync', 'a', 'a'], ['inc', 'a', 1], ['inc', 'd', 1]], ['a', 'b', 'c', 'd']], {'values': [2, 0, 0, 1], 'rejected': 0, 'state': [['a', 2]]})],
    2: [('repeated sync is idempotent', [[['inc', 'a', 3], ['sync', 'a', 'b'], ['sync', 'a', 'b'], ['inc', 'b', 2], ['sync', 'b', 'a']], ['a', 'b', 'c', 'd']], {'values': [5, 5, 0, 0], 'rejected': 0, 'state': [['a', 3], ['b', 2]]}), ('transitive gossip carries third-party slots', [[['inc', 'a', 2], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['inc', 'c', 1], ['sync', 'c', 'd']], ['a', 'b', 'c', 'd']], {'values': [2, 2, 3, 3], 'rejected': 0, 'state': [['a', 2]]}), ('stale path does not regress a slot', [[['inc', 'a', 1], ['sync', 'a', 'd'], ['inc', 'a', 2], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['sync', 'd', 'c']], ['a', 'b', 'c', 'd']], {'values': [3, 3, 3, 1], 'rejected': 0, 'state': [['a', 3]]}), ('zero and negative amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', -2], ['inc', 'c', 2], ['sync', 'c', 'a'], ['inc', 'a', 3]], ['a', 'b', 'c', 'd']], {'values': [5, 0, 2, 0], 'rejected': 2, 'state': [['a', 3], ['c', 2]]}), ('concurrent increments all survive', [[['inc', 'a', 2], ['inc', 'b', 4], ['inc', 'c', 1], ['sync', 'a', 'b'], ['sync', 'c', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c', 'd']], {'values': [7, 7, 7, 0], 'rejected': 0, 'state': [['a', 2], ['b', 4], ['c', 1]]}), ('empty history', [[], ['a', 'b', 'c', 'd']], {'values': [0, 0, 0, 0], 'rejected': 0, 'state': []}), ('repeated local increments accumulate', [[['inc', 'a', 2], ['sync', 'a', 'a'], ['inc', 'a', 1], ['inc', 'd', 2]], ['a', 'b', 'c', 'd']], {'values': [3, 0, 0, 2], 'rejected': 0, 'state': [['a', 3]]})],
    3: [('repeated sync is idempotent', [[['inc', 'a', 4], ['sync', 'a', 'b'], ['sync', 'a', 'b'], ['inc', 'b', 2], ['sync', 'b', 'a']], ['a', 'b', 'c', 'd']], {'values': [6, 6, 0, 0], 'rejected': 0, 'state': [['a', 4], ['b', 2]]}), ('transitive gossip carries third-party slots', [[['inc', 'a', 3], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['inc', 'c', 1], ['sync', 'c', 'd']], ['a', 'b', 'c', 'd']], {'values': [3, 3, 4, 4], 'rejected': 0, 'state': [['a', 3]]}), ('stale path does not regress a slot', [[['inc', 'a', 1], ['sync', 'a', 'd'], ['inc', 'a', 3], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['sync', 'd', 'c']], ['a', 'b', 'c', 'd']], {'values': [4, 4, 4, 1], 'rejected': 0, 'state': [['a', 4]]}), ('zero and negative amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', -3], ['inc', 'c', 2], ['sync', 'c', 'a'], ['inc', 'a', 3]], ['a', 'b', 'c', 'd']], {'values': [5, 0, 2, 0], 'rejected': 2, 'state': [['a', 3], ['c', 2]]}), ('concurrent increments all survive', [[['inc', 'a', 3], ['inc', 'b', 5], ['inc', 'c', 1], ['sync', 'a', 'b'], ['sync', 'c', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c', 'd']], {'values': [9, 9, 9, 0], 'rejected': 0, 'state': [['a', 3], ['b', 5], ['c', 1]]}), ('empty history', [[], ['a', 'b', 'c', 'd']], {'values': [0, 0, 0, 0], 'rejected': 0, 'state': []}), ('repeated local increments accumulate', [[['inc', 'a', 3], ['sync', 'a', 'a'], ['inc', 'a', 1], ['inc', 'd', 3]], ['a', 'b', 'c', 'd']], {'values': [4, 0, 0, 3], 'rejected': 0, 'state': [['a', 4]]})],
    4: [('repeated sync is idempotent', [[['inc', 'a', 5], ['sync', 'a', 'b'], ['sync', 'a', 'b'], ['inc', 'b', 2], ['sync', 'b', 'a']], ['a', 'b', 'c', 'd']], {'values': [7, 7, 0, 0], 'rejected': 0, 'state': [['a', 5], ['b', 2]]}), ('transitive gossip carries third-party slots', [[['inc', 'a', 4], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['inc', 'c', 1], ['sync', 'c', 'd']], ['a', 'b', 'c', 'd']], {'values': [4, 4, 5, 5], 'rejected': 0, 'state': [['a', 4]]}), ('stale path does not regress a slot', [[['inc', 'a', 1], ['sync', 'a', 'd'], ['inc', 'a', 4], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['sync', 'd', 'c']], ['a', 'b', 'c', 'd']], {'values': [5, 5, 5, 1], 'rejected': 0, 'state': [['a', 5]]}), ('zero and negative amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', -4], ['inc', 'c', 2], ['sync', 'c', 'a'], ['inc', 'a', 3]], ['a', 'b', 'c', 'd']], {'values': [5, 0, 2, 0], 'rejected': 2, 'state': [['a', 3], ['c', 2]]}), ('concurrent increments all survive', [[['inc', 'a', 4], ['inc', 'b', 6], ['inc', 'c', 1], ['sync', 'a', 'b'], ['sync', 'c', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c', 'd']], {'values': [11, 11, 11, 0], 'rejected': 0, 'state': [['a', 4], ['b', 6], ['c', 1]]}), ('empty history', [[], ['a', 'b', 'c', 'd']], {'values': [0, 0, 0, 0], 'rejected': 0, 'state': []}), ('repeated local increments accumulate', [[['inc', 'a', 4], ['sync', 'a', 'a'], ['inc', 'a', 1], ['inc', 'd', 4]], ['a', 'b', 'c', 'd']], {'values': [5, 0, 0, 4], 'rejected': 0, 'state': [['a', 5]]})],
    5: [('repeated sync is idempotent', [[['inc', 'a', 6], ['sync', 'a', 'b'], ['sync', 'a', 'b'], ['inc', 'b', 2], ['sync', 'b', 'a']], ['a', 'b', 'c', 'd']], {'values': [8, 8, 0, 0], 'rejected': 0, 'state': [['a', 6], ['b', 2]]}), ('transitive gossip carries third-party slots', [[['inc', 'a', 5], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['inc', 'c', 1], ['sync', 'c', 'd']], ['a', 'b', 'c', 'd']], {'values': [5, 5, 6, 6], 'rejected': 0, 'state': [['a', 5]]}), ('stale path does not regress a slot', [[['inc', 'a', 1], ['sync', 'a', 'd'], ['inc', 'a', 5], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['sync', 'd', 'c']], ['a', 'b', 'c', 'd']], {'values': [6, 6, 6, 1], 'rejected': 0, 'state': [['a', 6]]}), ('zero and negative amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', -5], ['inc', 'c', 2], ['sync', 'c', 'a'], ['inc', 'a', 3]], ['a', 'b', 'c', 'd']], {'values': [5, 0, 2, 0], 'rejected': 2, 'state': [['a', 3], ['c', 2]]}), ('concurrent increments all survive', [[['inc', 'a', 5], ['inc', 'b', 7], ['inc', 'c', 1], ['sync', 'a', 'b'], ['sync', 'c', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c', 'd']], {'values': [13, 13, 13, 0], 'rejected': 0, 'state': [['a', 5], ['b', 7], ['c', 1]]}), ('empty history', [[], ['a', 'b', 'c', 'd']], {'values': [0, 0, 0, 0], 'rejected': 0, 'state': []}), ('repeated local increments accumulate', [[['inc', 'a', 5], ['sync', 'a', 'a'], ['inc', 'a', 1], ['inc', 'd', 5]], ['a', 'b', 'c', 'd']], {'values': [6, 0, 0, 5], 'rejected': 0, 'state': [['a', 6]]})],
}[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 fixtureActualExpectedOutcome
repeated sync is idempotent{'rejected': 0, 'state': [['a', 2], ['b', 2]], 'values': [4, 4, 0, 0]}{'rejected': 0, 'state': [['a', 2], ['b', 2]], 'values': [4, 4, 0, 0]}Passed
transitive gossip carries third-party slots{'rejected': 0, 'state': [['a', 1]], 'values': [1, 1, 2, 2]}{'rejected': 0, 'state': [['a', 1]], 'values': [1, 1, 2, 2]}Passed
stale path does not regress a slot{'rejected': 0, 'state': [['a', 2]], 'values': [2, 2, 2, 1]}{'rejected': 0, 'state': [['a', 2]], 'values': [2, 2, 2, 1]}Passed
zero and negative amounts are rejected{'rejected': 0, 'state': [['a', 3], ['c', 2]], 'values': [5, -1, 2, 0]}{'rejected': 2, 'state': [['a', 3], ['c', 2]], 'values': [5, 0, 2, 0]}Failed
concurrent increments all survive{'rejected': 0, 'state': [['a', 1], ['b', 3], ['c', 1]], 'values': [5, 5, 5, 0]}{'rejected': 0, 'state': [['a', 1], ['b', 3], ['c', 1]], 'values': [5, 5, 5, 0]}Passed
empty history{'rejected': 0, 'state': [], 'values': [0, 0, 0, 0]}{'rejected': 0, 'state': [], 'values': [0, 0, 0, 0]}Passed
repeated local increments accumulate{'rejected': 0, 'state': [['a', 2]], 'values': [2, 0, 0, 1]}{'rejected': 0, 'state': [['a', 2]], 'values': [2, 0, 0, 1]}Passed

SHA-256 / d219b5a1b383fdb35a970886083bdcf9176dc73e8ed3a122680446eb6043c1fc

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(events, replicas):
    state = {r: {} for r in replicas}
    rejected = 0
    for ev in events:
        if ev[0] == 'inc':
            r, amount = ev[1], ev[2]
            if amount < 0:
                rejected += 1
                continue
            state[r][r] = state[r].get(r, 0) + amount
        elif ev[0] == 'sync':
            src, dst = state[ev[1]], state[ev[2]]
            for k, v in src.items():
                dst[k] = max(dst.get(k, 0), v)
    values = [sum(state[r].values()) for r in replicas]
    return {'values': values, 'rejected': rejected, 'state': sorted([k, v] for k, v in state[replicas[0]].items())}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = {
    1: [('repeated sync is idempotent', [[['inc', 'a', 2], ['sync', 'a', 'b'], ['sync', 'a', 'b'], ['inc', 'b', 2], ['sync', 'b', 'a']], ['a', 'b', 'c', 'd']], {'values': [4, 4, 0, 0], 'rejected': 0, 'state': [['a', 2], ['b', 2]]}), ('transitive gossip carries third-party slots', [[['inc', 'a', 1], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['inc', 'c', 1], ['sync', 'c', 'd']], ['a', 'b', 'c', 'd']], {'values': [1, 1, 2, 2], 'rejected': 0, 'state': [['a', 1]]}), ('stale path does not regress a slot', [[['inc', 'a', 1], ['sync', 'a', 'd'], ['inc', 'a', 1], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['sync', 'd', 'c']], ['a', 'b', 'c', 'd']], {'values': [2, 2, 2, 1], 'rejected': 0, 'state': [['a', 2]]}), ('zero and negative amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', -1], ['inc', 'c', 2], ['sync', 'c', 'a'], ['inc', 'a', 3]], ['a', 'b', 'c', 'd']], {'values': [5, 0, 2, 0], 'rejected': 2, 'state': [['a', 3], ['c', 2]]}), ('concurrent increments all survive', [[['inc', 'a', 1], ['inc', 'b', 3], ['inc', 'c', 1], ['sync', 'a', 'b'], ['sync', 'c', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c', 'd']], {'values': [5, 5, 5, 0], 'rejected': 0, 'state': [['a', 1], ['b', 3], ['c', 1]]}), ('empty history', [[], ['a', 'b', 'c', 'd']], {'values': [0, 0, 0, 0], 'rejected': 0, 'state': []}), ('repeated local increments accumulate', [[['inc', 'a', 1], ['sync', 'a', 'a'], ['inc', 'a', 1], ['inc', 'd', 1]], ['a', 'b', 'c', 'd']], {'values': [2, 0, 0, 1], 'rejected': 0, 'state': [['a', 2]]})],
    2: [('repeated sync is idempotent', [[['inc', 'a', 3], ['sync', 'a', 'b'], ['sync', 'a', 'b'], ['inc', 'b', 2], ['sync', 'b', 'a']], ['a', 'b', 'c', 'd']], {'values': [5, 5, 0, 0], 'rejected': 0, 'state': [['a', 3], ['b', 2]]}), ('transitive gossip carries third-party slots', [[['inc', 'a', 2], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['inc', 'c', 1], ['sync', 'c', 'd']], ['a', 'b', 'c', 'd']], {'values': [2, 2, 3, 3], 'rejected': 0, 'state': [['a', 2]]}), ('stale path does not regress a slot', [[['inc', 'a', 1], ['sync', 'a', 'd'], ['inc', 'a', 2], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['sync', 'd', 'c']], ['a', 'b', 'c', 'd']], {'values': [3, 3, 3, 1], 'rejected': 0, 'state': [['a', 3]]}), ('zero and negative amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', -2], ['inc', 'c', 2], ['sync', 'c', 'a'], ['inc', 'a', 3]], ['a', 'b', 'c', 'd']], {'values': [5, 0, 2, 0], 'rejected': 2, 'state': [['a', 3], ['c', 2]]}), ('concurrent increments all survive', [[['inc', 'a', 2], ['inc', 'b', 4], ['inc', 'c', 1], ['sync', 'a', 'b'], ['sync', 'c', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c', 'd']], {'values': [7, 7, 7, 0], 'rejected': 0, 'state': [['a', 2], ['b', 4], ['c', 1]]}), ('empty history', [[], ['a', 'b', 'c', 'd']], {'values': [0, 0, 0, 0], 'rejected': 0, 'state': []}), ('repeated local increments accumulate', [[['inc', 'a', 2], ['sync', 'a', 'a'], ['inc', 'a', 1], ['inc', 'd', 2]], ['a', 'b', 'c', 'd']], {'values': [3, 0, 0, 2], 'rejected': 0, 'state': [['a', 3]]})],
    3: [('repeated sync is idempotent', [[['inc', 'a', 4], ['sync', 'a', 'b'], ['sync', 'a', 'b'], ['inc', 'b', 2], ['sync', 'b', 'a']], ['a', 'b', 'c', 'd']], {'values': [6, 6, 0, 0], 'rejected': 0, 'state': [['a', 4], ['b', 2]]}), ('transitive gossip carries third-party slots', [[['inc', 'a', 3], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['inc', 'c', 1], ['sync', 'c', 'd']], ['a', 'b', 'c', 'd']], {'values': [3, 3, 4, 4], 'rejected': 0, 'state': [['a', 3]]}), ('stale path does not regress a slot', [[['inc', 'a', 1], ['sync', 'a', 'd'], ['inc', 'a', 3], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['sync', 'd', 'c']], ['a', 'b', 'c', 'd']], {'values': [4, 4, 4, 1], 'rejected': 0, 'state': [['a', 4]]}), ('zero and negative amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', -3], ['inc', 'c', 2], ['sync', 'c', 'a'], ['inc', 'a', 3]], ['a', 'b', 'c', 'd']], {'values': [5, 0, 2, 0], 'rejected': 2, 'state': [['a', 3], ['c', 2]]}), ('concurrent increments all survive', [[['inc', 'a', 3], ['inc', 'b', 5], ['inc', 'c', 1], ['sync', 'a', 'b'], ['sync', 'c', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c', 'd']], {'values': [9, 9, 9, 0], 'rejected': 0, 'state': [['a', 3], ['b', 5], ['c', 1]]}), ('empty history', [[], ['a', 'b', 'c', 'd']], {'values': [0, 0, 0, 0], 'rejected': 0, 'state': []}), ('repeated local increments accumulate', [[['inc', 'a', 3], ['sync', 'a', 'a'], ['inc', 'a', 1], ['inc', 'd', 3]], ['a', 'b', 'c', 'd']], {'values': [4, 0, 0, 3], 'rejected': 0, 'state': [['a', 4]]})],
    4: [('repeated sync is idempotent', [[['inc', 'a', 5], ['sync', 'a', 'b'], ['sync', 'a', 'b'], ['inc', 'b', 2], ['sync', 'b', 'a']], ['a', 'b', 'c', 'd']], {'values': [7, 7, 0, 0], 'rejected': 0, 'state': [['a', 5], ['b', 2]]}), ('transitive gossip carries third-party slots', [[['inc', 'a', 4], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['inc', 'c', 1], ['sync', 'c', 'd']], ['a', 'b', 'c', 'd']], {'values': [4, 4, 5, 5], 'rejected': 0, 'state': [['a', 4]]}), ('stale path does not regress a slot', [[['inc', 'a', 1], ['sync', 'a', 'd'], ['inc', 'a', 4], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['sync', 'd', 'c']], ['a', 'b', 'c', 'd']], {'values': [5, 5, 5, 1], 'rejected': 0, 'state': [['a', 5]]}), ('zero and negative amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', -4], ['inc', 'c', 2], ['sync', 'c', 'a'], ['inc', 'a', 3]], ['a', 'b', 'c', 'd']], {'values': [5, 0, 2, 0], 'rejected': 2, 'state': [['a', 3], ['c', 2]]}), ('concurrent increments all survive', [[['inc', 'a', 4], ['inc', 'b', 6], ['inc', 'c', 1], ['sync', 'a', 'b'], ['sync', 'c', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c', 'd']], {'values': [11, 11, 11, 0], 'rejected': 0, 'state': [['a', 4], ['b', 6], ['c', 1]]}), ('empty history', [[], ['a', 'b', 'c', 'd']], {'values': [0, 0, 0, 0], 'rejected': 0, 'state': []}), ('repeated local increments accumulate', [[['inc', 'a', 4], ['sync', 'a', 'a'], ['inc', 'a', 1], ['inc', 'd', 4]], ['a', 'b', 'c', 'd']], {'values': [5, 0, 0, 4], 'rejected': 0, 'state': [['a', 5]]})],
    5: [('repeated sync is idempotent', [[['inc', 'a', 6], ['sync', 'a', 'b'], ['sync', 'a', 'b'], ['inc', 'b', 2], ['sync', 'b', 'a']], ['a', 'b', 'c', 'd']], {'values': [8, 8, 0, 0], 'rejected': 0, 'state': [['a', 6], ['b', 2]]}), ('transitive gossip carries third-party slots', [[['inc', 'a', 5], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['inc', 'c', 1], ['sync', 'c', 'd']], ['a', 'b', 'c', 'd']], {'values': [5, 5, 6, 6], 'rejected': 0, 'state': [['a', 5]]}), ('stale path does not regress a slot', [[['inc', 'a', 1], ['sync', 'a', 'd'], ['inc', 'a', 5], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['sync', 'd', 'c']], ['a', 'b', 'c', 'd']], {'values': [6, 6, 6, 1], 'rejected': 0, 'state': [['a', 6]]}), ('zero and negative amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', -5], ['inc', 'c', 2], ['sync', 'c', 'a'], ['inc', 'a', 3]], ['a', 'b', 'c', 'd']], {'values': [5, 0, 2, 0], 'rejected': 2, 'state': [['a', 3], ['c', 2]]}), ('concurrent increments all survive', [[['inc', 'a', 5], ['inc', 'b', 7], ['inc', 'c', 1], ['sync', 'a', 'b'], ['sync', 'c', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c', 'd']], {'values': [13, 13, 13, 0], 'rejected': 0, 'state': [['a', 5], ['b', 7], ['c', 1]]}), ('empty history', [[], ['a', 'b', 'c', 'd']], {'values': [0, 0, 0, 0], 'rejected': 0, 'state': []}), ('repeated local increments accumulate', [[['inc', 'a', 5], ['sync', 'a', 'a'], ['inc', 'a', 1], ['inc', 'd', 5]], ['a', 'b', 'c', 'd']], {'values': [6, 0, 0, 5], 'rejected': 0, 'state': [['a', 6]]})],
}[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 fixtureActualExpectedOutcome
repeated sync is idempotent{'rejected': 0, 'state': [['a', 2], ['b', 2]], 'values': [4, 4, 0, 0]}{'rejected': 0, 'state': [['a', 2], ['b', 2]], 'values': [4, 4, 0, 0]}Passed
transitive gossip carries third-party slots{'rejected': 0, 'state': [['a', 1]], 'values': [1, 1, 2, 2]}{'rejected': 0, 'state': [['a', 1]], 'values': [1, 1, 2, 2]}Passed
stale path does not regress a slot{'rejected': 0, 'state': [['a', 2]], 'values': [2, 2, 2, 1]}{'rejected': 0, 'state': [['a', 2]], 'values': [2, 2, 2, 1]}Passed
zero and negative amounts are rejected{'rejected': 1, 'state': [['a', 3], ['c', 2]], 'values': [5, 0, 2, 0]}{'rejected': 2, 'state': [['a', 3], ['c', 2]], 'values': [5, 0, 2, 0]}Failed
concurrent increments all survive{'rejected': 0, 'state': [['a', 1], ['b', 3], ['c', 1]], 'values': [5, 5, 5, 0]}{'rejected': 0, 'state': [['a', 1], ['b', 3], ['c', 1]], 'values': [5, 5, 5, 0]}Passed
empty history{'rejected': 0, 'state': [], 'values': [0, 0, 0, 0]}{'rejected': 0, 'state': [], 'values': [0, 0, 0, 0]}Passed
repeated local increments accumulate{'rejected': 0, 'state': [['a', 2]], 'values': [2, 0, 0, 1]}{'rejected': 0, 'state': [['a', 2]], 'values': [2, 0, 0, 1]}Passed

SHA-256 / 1e54b0ca2dd93f80fe700c081165351665885e525499c8c5aef5d59e448bb09a

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(events, replicas):
    state = {r: {} for r in replicas}
    rejected = 0
    for ev in events:
        if ev[0] == 'inc':
            r, amount = ev[1], ev[2]
            if amount <= 0:
                rejected += 1
                continue
            state[r][r] = state[r].get(r, 0) + amount
        elif ev[0] == 'sync':
            src, dst = state[ev[1]], state[ev[2]]
            for k, v in src.items():
                dst[k] = max(dst.get(k, 0), v)
    values = [sum(state[r].values()) for r in replicas]
    return {'values': values, 'rejected': rejected, 'state': sorted([k, v] for k, v in state[replicas[0]].items())}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = {
    1: [('repeated sync is idempotent', [[['inc', 'a', 2], ['sync', 'a', 'b'], ['sync', 'a', 'b'], ['inc', 'b', 2], ['sync', 'b', 'a']], ['a', 'b', 'c', 'd']], {'values': [4, 4, 0, 0], 'rejected': 0, 'state': [['a', 2], ['b', 2]]}), ('transitive gossip carries third-party slots', [[['inc', 'a', 1], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['inc', 'c', 1], ['sync', 'c', 'd']], ['a', 'b', 'c', 'd']], {'values': [1, 1, 2, 2], 'rejected': 0, 'state': [['a', 1]]}), ('stale path does not regress a slot', [[['inc', 'a', 1], ['sync', 'a', 'd'], ['inc', 'a', 1], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['sync', 'd', 'c']], ['a', 'b', 'c', 'd']], {'values': [2, 2, 2, 1], 'rejected': 0, 'state': [['a', 2]]}), ('zero and negative amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', -1], ['inc', 'c', 2], ['sync', 'c', 'a'], ['inc', 'a', 3]], ['a', 'b', 'c', 'd']], {'values': [5, 0, 2, 0], 'rejected': 2, 'state': [['a', 3], ['c', 2]]}), ('concurrent increments all survive', [[['inc', 'a', 1], ['inc', 'b', 3], ['inc', 'c', 1], ['sync', 'a', 'b'], ['sync', 'c', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c', 'd']], {'values': [5, 5, 5, 0], 'rejected': 0, 'state': [['a', 1], ['b', 3], ['c', 1]]}), ('empty history', [[], ['a', 'b', 'c', 'd']], {'values': [0, 0, 0, 0], 'rejected': 0, 'state': []}), ('repeated local increments accumulate', [[['inc', 'a', 1], ['sync', 'a', 'a'], ['inc', 'a', 1], ['inc', 'd', 1]], ['a', 'b', 'c', 'd']], {'values': [2, 0, 0, 1], 'rejected': 0, 'state': [['a', 2]]})],
    2: [('repeated sync is idempotent', [[['inc', 'a', 3], ['sync', 'a', 'b'], ['sync', 'a', 'b'], ['inc', 'b', 2], ['sync', 'b', 'a']], ['a', 'b', 'c', 'd']], {'values': [5, 5, 0, 0], 'rejected': 0, 'state': [['a', 3], ['b', 2]]}), ('transitive gossip carries third-party slots', [[['inc', 'a', 2], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['inc', 'c', 1], ['sync', 'c', 'd']], ['a', 'b', 'c', 'd']], {'values': [2, 2, 3, 3], 'rejected': 0, 'state': [['a', 2]]}), ('stale path does not regress a slot', [[['inc', 'a', 1], ['sync', 'a', 'd'], ['inc', 'a', 2], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['sync', 'd', 'c']], ['a', 'b', 'c', 'd']], {'values': [3, 3, 3, 1], 'rejected': 0, 'state': [['a', 3]]}), ('zero and negative amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', -2], ['inc', 'c', 2], ['sync', 'c', 'a'], ['inc', 'a', 3]], ['a', 'b', 'c', 'd']], {'values': [5, 0, 2, 0], 'rejected': 2, 'state': [['a', 3], ['c', 2]]}), ('concurrent increments all survive', [[['inc', 'a', 2], ['inc', 'b', 4], ['inc', 'c', 1], ['sync', 'a', 'b'], ['sync', 'c', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c', 'd']], {'values': [7, 7, 7, 0], 'rejected': 0, 'state': [['a', 2], ['b', 4], ['c', 1]]}), ('empty history', [[], ['a', 'b', 'c', 'd']], {'values': [0, 0, 0, 0], 'rejected': 0, 'state': []}), ('repeated local increments accumulate', [[['inc', 'a', 2], ['sync', 'a', 'a'], ['inc', 'a', 1], ['inc', 'd', 2]], ['a', 'b', 'c', 'd']], {'values': [3, 0, 0, 2], 'rejected': 0, 'state': [['a', 3]]})],
    3: [('repeated sync is idempotent', [[['inc', 'a', 4], ['sync', 'a', 'b'], ['sync', 'a', 'b'], ['inc', 'b', 2], ['sync', 'b', 'a']], ['a', 'b', 'c', 'd']], {'values': [6, 6, 0, 0], 'rejected': 0, 'state': [['a', 4], ['b', 2]]}), ('transitive gossip carries third-party slots', [[['inc', 'a', 3], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['inc', 'c', 1], ['sync', 'c', 'd']], ['a', 'b', 'c', 'd']], {'values': [3, 3, 4, 4], 'rejected': 0, 'state': [['a', 3]]}), ('stale path does not regress a slot', [[['inc', 'a', 1], ['sync', 'a', 'd'], ['inc', 'a', 3], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['sync', 'd', 'c']], ['a', 'b', 'c', 'd']], {'values': [4, 4, 4, 1], 'rejected': 0, 'state': [['a', 4]]}), ('zero and negative amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', -3], ['inc', 'c', 2], ['sync', 'c', 'a'], ['inc', 'a', 3]], ['a', 'b', 'c', 'd']], {'values': [5, 0, 2, 0], 'rejected': 2, 'state': [['a', 3], ['c', 2]]}), ('concurrent increments all survive', [[['inc', 'a', 3], ['inc', 'b', 5], ['inc', 'c', 1], ['sync', 'a', 'b'], ['sync', 'c', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c', 'd']], {'values': [9, 9, 9, 0], 'rejected': 0, 'state': [['a', 3], ['b', 5], ['c', 1]]}), ('empty history', [[], ['a', 'b', 'c', 'd']], {'values': [0, 0, 0, 0], 'rejected': 0, 'state': []}), ('repeated local increments accumulate', [[['inc', 'a', 3], ['sync', 'a', 'a'], ['inc', 'a', 1], ['inc', 'd', 3]], ['a', 'b', 'c', 'd']], {'values': [4, 0, 0, 3], 'rejected': 0, 'state': [['a', 4]]})],
    4: [('repeated sync is idempotent', [[['inc', 'a', 5], ['sync', 'a', 'b'], ['sync', 'a', 'b'], ['inc', 'b', 2], ['sync', 'b', 'a']], ['a', 'b', 'c', 'd']], {'values': [7, 7, 0, 0], 'rejected': 0, 'state': [['a', 5], ['b', 2]]}), ('transitive gossip carries third-party slots', [[['inc', 'a', 4], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['inc', 'c', 1], ['sync', 'c', 'd']], ['a', 'b', 'c', 'd']], {'values': [4, 4, 5, 5], 'rejected': 0, 'state': [['a', 4]]}), ('stale path does not regress a slot', [[['inc', 'a', 1], ['sync', 'a', 'd'], ['inc', 'a', 4], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['sync', 'd', 'c']], ['a', 'b', 'c', 'd']], {'values': [5, 5, 5, 1], 'rejected': 0, 'state': [['a', 5]]}), ('zero and negative amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', -4], ['inc', 'c', 2], ['sync', 'c', 'a'], ['inc', 'a', 3]], ['a', 'b', 'c', 'd']], {'values': [5, 0, 2, 0], 'rejected': 2, 'state': [['a', 3], ['c', 2]]}), ('concurrent increments all survive', [[['inc', 'a', 4], ['inc', 'b', 6], ['inc', 'c', 1], ['sync', 'a', 'b'], ['sync', 'c', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c', 'd']], {'values': [11, 11, 11, 0], 'rejected': 0, 'state': [['a', 4], ['b', 6], ['c', 1]]}), ('empty history', [[], ['a', 'b', 'c', 'd']], {'values': [0, 0, 0, 0], 'rejected': 0, 'state': []}), ('repeated local increments accumulate', [[['inc', 'a', 4], ['sync', 'a', 'a'], ['inc', 'a', 1], ['inc', 'd', 4]], ['a', 'b', 'c', 'd']], {'values': [5, 0, 0, 4], 'rejected': 0, 'state': [['a', 5]]})],
    5: [('repeated sync is idempotent', [[['inc', 'a', 6], ['sync', 'a', 'b'], ['sync', 'a', 'b'], ['inc', 'b', 2], ['sync', 'b', 'a']], ['a', 'b', 'c', 'd']], {'values': [8, 8, 0, 0], 'rejected': 0, 'state': [['a', 6], ['b', 2]]}), ('transitive gossip carries third-party slots', [[['inc', 'a', 5], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['inc', 'c', 1], ['sync', 'c', 'd']], ['a', 'b', 'c', 'd']], {'values': [5, 5, 6, 6], 'rejected': 0, 'state': [['a', 5]]}), ('stale path does not regress a slot', [[['inc', 'a', 1], ['sync', 'a', 'd'], ['inc', 'a', 5], ['sync', 'a', 'b'], ['sync', 'b', 'c'], ['sync', 'd', 'c']], ['a', 'b', 'c', 'd']], {'values': [6, 6, 6, 1], 'rejected': 0, 'state': [['a', 6]]}), ('zero and negative amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', -5], ['inc', 'c', 2], ['sync', 'c', 'a'], ['inc', 'a', 3]], ['a', 'b', 'c', 'd']], {'values': [5, 0, 2, 0], 'rejected': 2, 'state': [['a', 3], ['c', 2]]}), ('concurrent increments all survive', [[['inc', 'a', 5], ['inc', 'b', 7], ['inc', 'c', 1], ['sync', 'a', 'b'], ['sync', 'c', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c', 'd']], {'values': [13, 13, 13, 0], 'rejected': 0, 'state': [['a', 5], ['b', 7], ['c', 1]]}), ('empty history', [[], ['a', 'b', 'c', 'd']], {'values': [0, 0, 0, 0], 'rejected': 0, 'state': []}), ('repeated local increments accumulate', [[['inc', 'a', 5], ['sync', 'a', 'a'], ['inc', 'a', 1], ['inc', 'd', 5]], ['a', 'b', 'c', 'd']], {'values': [6, 0, 0, 5], 'rejected': 0, 'state': [['a', 6]]})],
}[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 fixtureActualExpectedOutcome
repeated sync is idempotent{'rejected': 0, 'state': [['a', 2], ['b', 2]], 'values': [4, 4, 0, 0]}{'rejected': 0, 'state': [['a', 2], ['b', 2]], 'values': [4, 4, 0, 0]}Passed
transitive gossip carries third-party slots{'rejected': 0, 'state': [['a', 1]], 'values': [1, 1, 2, 2]}{'rejected': 0, 'state': [['a', 1]], 'values': [1, 1, 2, 2]}Passed
stale path does not regress a slot{'rejected': 0, 'state': [['a', 2]], 'values': [2, 2, 2, 1]}{'rejected': 0, 'state': [['a', 2]], 'values': [2, 2, 2, 1]}Passed
zero and negative amounts are rejected{'rejected': 2, 'state': [['a', 3], ['c', 2]], 'values': [5, 0, 2, 0]}{'rejected': 2, 'state': [['a', 3], ['c', 2]], 'values': [5, 0, 2, 0]}Passed
concurrent increments all survive{'rejected': 0, 'state': [['a', 1], ['b', 3], ['c', 1]], 'values': [5, 5, 5, 0]}{'rejected': 0, 'state': [['a', 1], ['b', 3], ['c', 1]], 'values': [5, 5, 5, 0]}Passed
empty history{'rejected': 0, 'state': [], 'values': [0, 0, 0, 0]}{'rejected': 0, 'state': [], 'values': [0, 0, 0, 0]}Passed
repeated local increments accumulate{'rejected': 0, 'state': [['a', 2]], 'values': [2, 0, 0, 1]}{'rejected': 0, 'state': [['a', 2]], 'values': [2, 0, 0, 1]}Passed

SHA-256 / 9e8069d5c32f505cb53f08f69d496ae2a7e7337ee6340ea7bd3b43e518eb1ce6

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 2026-09-29T14:49:00.481587+00:00.

Case digest / 19b9513afa1b3704a4018d00bb3498a7b5d1af4334e938251a2e2c81e898baa6