FAILURE MAP
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FA-74871 / CRDT convergence / Open access

PN-Counter with local floor: the negative map merges by minimum · case 01

Decrements never propagate; other replicas keep reporting the undecremented value.

Verified by executionVariant 1 · 9 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The negative map is merged with min against a zero default, so remote decrement slots collapse to zero.

VERIFIED REPAIR

Both maps are grow-only and must merge by pointwise maximum.

Unsuccessful approach: Copying only slots that are absent propagates the first decrement but never later growth of the same slot.

Case contract

Replicas keep a positive map and a negative map (replica->total). ["inc", r, k] and ["dec", r, k] need k > 0, otherwise the event index is rejected. A decrement is also rejected when r's locally observed value is below k. ["sync", src, dst] merges both maps of src into dst by pointwise maximum. Return values and rejected indices.

Why this case matters

Positive/negative counters are the standard way to support decrements in a state-based counter.

1 / The failure

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

N = 1
observations = []
def solve(events, replicas):
    pos = {r: {} for r in replicas}
    neg = {r: {} for r in replicas}
    rejected = []
    def value(r):
        return sum(pos[r].values()) - sum(neg[r].values())
    for i, ev in enumerate(events):
        kind = ev[0]
        if kind == 'sync':
            s, d = ev[1], ev[2]
            for k, v in pos[s].items():
                pos[d][k] = max(pos[d].get(k, 0), v)
            for k, v in neg[s].items():
                neg[d][k] = min(neg[d].get(k, 0), v)
            continue
        r, amt = ev[1], ev[2]
        if amt <= 0:
            rejected.append(i)
            continue
        if kind == 'inc':
            pos[r][r] = pos[r].get(r, 0) + amt
        else:
            if value(r) < amt:
                rejected.append(i)
                continue
            neg[r][r] = neg[r].get(r, 0) + amt
    return {'values': [value(r) for r in replicas], 'rejected': rejected}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = {
    1: [('decrement to exactly zero is allowed', [[['inc', 'a', 1], ['dec', 'a', 1]], ['a', 'b', 'c']], {'values': [0, 0, 0], 'rejected': []}), ('decrement beyond local view is rejected', [[['inc', 'a', 1], ['dec', 'b', 1], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [1, 0, 0], 'rejected': [1, 2]}), ('decrement funded by learned increments', [[['inc', 'a', 3], ['sync', 'a', 'b'], ['dec', 'b', 2], ['sync', 'b', 'a'], ['sync', 'b', 'c'], ['sync', 'a', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []}), ('concurrent decrements converge', [[['inc', 'a', 4], ['sync', 'a', 'b'], ['dec', 'a', 1], ['dec', 'b', 2], ['sync', 'a', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []}), ('zero amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', 3], ['dec', 'b', 0], ['dec', 'b', 1]], ['a', 'b', 'c']], {'values': [0, 2, 0], 'rejected': [0, 2]}), ('repeated decrement slot is refreshed', [[['inc', 'c', 4], ['dec', 'c', 1], ['sync', 'c', 'a'], ['dec', 'c', 1], ['sync', 'c', 'a'], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [2, 2, 2], 'rejected': []}), ('second decrement cannot pass the floor', [[['inc', 'a', 2], ['dec', 'a', 1], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [1, 0, 0], 'rejected': [2]}), ('one-way sync does not pull from the receiver', [[['inc', 'a', 1], ['inc', 'b', 1], ['dec', 'b', 1], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [1, 1, 0], 'rejected': []}), ('mixed history', [[['inc', 'a', 3], ['dec', 'a', 1], ['sync', 'a', 'b'], ['inc', 'b', 1], ['dec', 'b', 2], ['sync', 'b', 'a'], ['sync', 'a', 'c'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []})],
    2: [('decrement to exactly zero is allowed', [[['inc', 'a', 2], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [0, 0, 0], 'rejected': []}), ('decrement beyond local view is rejected', [[['inc', 'a', 2], ['dec', 'b', 1], ['dec', 'a', 3]], ['a', 'b', 'c']], {'values': [2, 0, 0], 'rejected': [1, 2]}), ('decrement funded by learned increments', [[['inc', 'a', 4], ['sync', 'a', 'b'], ['dec', 'b', 3], ['sync', 'b', 'a'], ['sync', 'b', 'c'], ['sync', 'a', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []}), ('concurrent decrements converge', [[['inc', 'a', 6], ['sync', 'a', 'b'], ['dec', 'a', 1], ['dec', 'b', 2], ['sync', 'a', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [3, 3, 3], 'rejected': []}), ('zero amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', 3], ['dec', 'b', 0], ['dec', 'b', 1]], ['a', 'b', 'c']], {'values': [0, 2, 0], 'rejected': [0, 2]}), ('repeated decrement slot is refreshed', [[['inc', 'c', 5], ['dec', 'c', 1], ['sync', 'c', 'a'], ['dec', 'c', 1], ['sync', 'c', 'a'], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [3, 3, 3], 'rejected': []}), ('second decrement cannot pass the floor', [[['inc', 'a', 3], ['dec', 'a', 2], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [1, 0, 0], 'rejected': [2]}), ('one-way sync does not pull from the receiver', [[['inc', 'a', 2], ['inc', 'b', 2], ['dec', 'b', 1], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [2, 3, 0], 'rejected': []}), ('mixed history', [[['inc', 'a', 3], ['dec', 'a', 1], ['sync', 'a', 'b'], ['inc', 'b', 2], ['dec', 'b', 2], ['sync', 'b', 'a'], ['sync', 'a', 'c'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [2, 2, 2], 'rejected': []})],
    3: [('decrement to exactly zero is allowed', [[['inc', 'a', 3], ['dec', 'a', 3]], ['a', 'b', 'c']], {'values': [0, 0, 0], 'rejected': []}), ('decrement beyond local view is rejected', [[['inc', 'a', 3], ['dec', 'b', 1], ['dec', 'a', 4]], ['a', 'b', 'c']], {'values': [3, 0, 0], 'rejected': [1, 2]}), ('decrement funded by learned increments', [[['inc', 'a', 5], ['sync', 'a', 'b'], ['dec', 'b', 4], ['sync', 'b', 'a'], ['sync', 'b', 'c'], ['sync', 'a', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []}), ('concurrent decrements converge', [[['inc', 'a', 8], ['sync', 'a', 'b'], ['dec', 'a', 1], ['dec', 'b', 2], ['sync', 'a', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [5, 5, 5], 'rejected': []}), ('zero amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', 3], ['dec', 'b', 0], ['dec', 'b', 1]], ['a', 'b', 'c']], {'values': [0, 2, 0], 'rejected': [0, 2]}), ('repeated decrement slot is refreshed', [[['inc', 'c', 6], ['dec', 'c', 1], ['sync', 'c', 'a'], ['dec', 'c', 1], ['sync', 'c', 'a'], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [4, 4, 4], 'rejected': []}), ('second decrement cannot pass the floor', [[['inc', 'a', 4], ['dec', 'a', 3], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [1, 0, 0], 'rejected': [2]}), ('one-way sync does not pull from the receiver', [[['inc', 'a', 3], ['inc', 'b', 3], ['dec', 'b', 1], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [3, 5, 0], 'rejected': []}), ('mixed history', [[['inc', 'a', 3], ['dec', 'a', 1], ['sync', 'a', 'b'], ['inc', 'b', 3], ['dec', 'b', 2], ['sync', 'b', 'a'], ['sync', 'a', 'c'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [3, 3, 3], 'rejected': []})],
    4: [('decrement to exactly zero is allowed', [[['inc', 'a', 4], ['dec', 'a', 4]], ['a', 'b', 'c']], {'values': [0, 0, 0], 'rejected': []}), ('decrement beyond local view is rejected', [[['inc', 'a', 4], ['dec', 'b', 1], ['dec', 'a', 5]], ['a', 'b', 'c']], {'values': [4, 0, 0], 'rejected': [1, 2]}), ('decrement funded by learned increments', [[['inc', 'a', 6], ['sync', 'a', 'b'], ['dec', 'b', 5], ['sync', 'b', 'a'], ['sync', 'b', 'c'], ['sync', 'a', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []}), ('concurrent decrements converge', [[['inc', 'a', 10], ['sync', 'a', 'b'], ['dec', 'a', 1], ['dec', 'b', 2], ['sync', 'a', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [7, 7, 7], 'rejected': []}), ('zero amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', 3], ['dec', 'b', 0], ['dec', 'b', 1]], ['a', 'b', 'c']], {'values': [0, 2, 0], 'rejected': [0, 2]}), ('repeated decrement slot is refreshed', [[['inc', 'c', 7], ['dec', 'c', 1], ['sync', 'c', 'a'], ['dec', 'c', 1], ['sync', 'c', 'a'], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [5, 5, 5], 'rejected': []}), ('second decrement cannot pass the floor', [[['inc', 'a', 5], ['dec', 'a', 4], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [1, 0, 0], 'rejected': [2]}), ('one-way sync does not pull from the receiver', [[['inc', 'a', 4], ['inc', 'b', 4], ['dec', 'b', 1], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [4, 7, 0], 'rejected': []}), ('mixed history', [[['inc', 'a', 3], ['dec', 'a', 1], ['sync', 'a', 'b'], ['inc', 'b', 4], ['dec', 'b', 2], ['sync', 'b', 'a'], ['sync', 'a', 'c'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [4, 4, 4], 'rejected': []})],
    5: [('decrement to exactly zero is allowed', [[['inc', 'a', 5], ['dec', 'a', 5]], ['a', 'b', 'c']], {'values': [0, 0, 0], 'rejected': []}), ('decrement beyond local view is rejected', [[['inc', 'a', 5], ['dec', 'b', 1], ['dec', 'a', 6]], ['a', 'b', 'c']], {'values': [5, 0, 0], 'rejected': [1, 2]}), ('decrement funded by learned increments', [[['inc', 'a', 7], ['sync', 'a', 'b'], ['dec', 'b', 6], ['sync', 'b', 'a'], ['sync', 'b', 'c'], ['sync', 'a', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []}), ('concurrent decrements converge', [[['inc', 'a', 12], ['sync', 'a', 'b'], ['dec', 'a', 1], ['dec', 'b', 2], ['sync', 'a', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [9, 9, 9], 'rejected': []}), ('zero amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', 3], ['dec', 'b', 0], ['dec', 'b', 1]], ['a', 'b', 'c']], {'values': [0, 2, 0], 'rejected': [0, 2]}), ('repeated decrement slot is refreshed', [[['inc', 'c', 8], ['dec', 'c', 1], ['sync', 'c', 'a'], ['dec', 'c', 1], ['sync', 'c', 'a'], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [6, 6, 6], 'rejected': []}), ('second decrement cannot pass the floor', [[['inc', 'a', 6], ['dec', 'a', 5], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [1, 0, 0], 'rejected': [2]}), ('one-way sync does not pull from the receiver', [[['inc', 'a', 5], ['inc', 'b', 5], ['dec', 'b', 1], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [5, 9, 0], 'rejected': []}), ('mixed history', [[['inc', 'a', 3], ['dec', 'a', 1], ['sync', 'a', 'b'], ['inc', 'b', 5], ['dec', 'b', 2], ['sync', 'b', 'a'], ['sync', 'a', 'c'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [5, 5, 5], 'rejected': []})],
}[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
decrement to exactly zero is allowed{'rejected': [], 'values': [0, 0, 0]}{'rejected': [], 'values': [0, 0, 0]}Passed
decrement beyond local view is rejected{'rejected': [1, 2], 'values': [1, 0, 0]}{'rejected': [1, 2], 'values': [1, 0, 0]}Passed
decrement funded by learned increments{'rejected': [], 'values': [3, 1, 3]}{'rejected': [], 'values': [1, 1, 1]}Failed
concurrent decrements converge{'rejected': [], 'values': [4, 2, 4]}{'rejected': [], 'values': [1, 1, 1]}Failed
zero amounts are rejected{'rejected': [0, 2], 'values': [0, 2, 0]}{'rejected': [0, 2], 'values': [0, 2, 0]}Passed
repeated decrement slot is refreshed{'rejected': [], 'values': [4, 4, 2]}{'rejected': [], 'values': [2, 2, 2]}Failed
second decrement cannot pass the floor{'rejected': [2], 'values': [1, 0, 0]}{'rejected': [2], 'values': [1, 0, 0]}Passed
one-way sync does not pull from the receiver{'rejected': [], 'values': [1, 1, 0]}{'rejected': [], 'values': [1, 1, 0]}Passed
mixed history{'rejected': [], 'values': [4, 2, 4]}{'rejected': [], 'values': [1, 1, 1]}Failed

SHA-256 / 696d765dae56786cd239e94b1984e8f8f949c7d845b3a73e77aadcf6dc1729a4

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(events, replicas):
    pos = {r: {} for r in replicas}
    neg = {r: {} for r in replicas}
    rejected = []
    def value(r):
        return sum(pos[r].values()) - sum(neg[r].values())
    for i, ev in enumerate(events):
        kind = ev[0]
        if kind == 'sync':
            s, d = ev[1], ev[2]
            for k, v in pos[s].items():
                pos[d][k] = max(pos[d].get(k, 0), v)
            for k, v in neg[s].items():
                if k not in neg[d]:
                    neg[d][k] = v
            continue
        r, amt = ev[1], ev[2]
        if amt <= 0:
            rejected.append(i)
            continue
        if kind == 'inc':
            pos[r][r] = pos[r].get(r, 0) + amt
        else:
            if value(r) < amt:
                rejected.append(i)
                continue
            neg[r][r] = neg[r].get(r, 0) + amt
    return {'values': [value(r) for r in replicas], 'rejected': rejected}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = {
    1: [('decrement to exactly zero is allowed', [[['inc', 'a', 1], ['dec', 'a', 1]], ['a', 'b', 'c']], {'values': [0, 0, 0], 'rejected': []}), ('decrement beyond local view is rejected', [[['inc', 'a', 1], ['dec', 'b', 1], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [1, 0, 0], 'rejected': [1, 2]}), ('decrement funded by learned increments', [[['inc', 'a', 3], ['sync', 'a', 'b'], ['dec', 'b', 2], ['sync', 'b', 'a'], ['sync', 'b', 'c'], ['sync', 'a', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []}), ('concurrent decrements converge', [[['inc', 'a', 4], ['sync', 'a', 'b'], ['dec', 'a', 1], ['dec', 'b', 2], ['sync', 'a', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []}), ('zero amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', 3], ['dec', 'b', 0], ['dec', 'b', 1]], ['a', 'b', 'c']], {'values': [0, 2, 0], 'rejected': [0, 2]}), ('repeated decrement slot is refreshed', [[['inc', 'c', 4], ['dec', 'c', 1], ['sync', 'c', 'a'], ['dec', 'c', 1], ['sync', 'c', 'a'], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [2, 2, 2], 'rejected': []}), ('second decrement cannot pass the floor', [[['inc', 'a', 2], ['dec', 'a', 1], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [1, 0, 0], 'rejected': [2]}), ('one-way sync does not pull from the receiver', [[['inc', 'a', 1], ['inc', 'b', 1], ['dec', 'b', 1], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [1, 1, 0], 'rejected': []}), ('mixed history', [[['inc', 'a', 3], ['dec', 'a', 1], ['sync', 'a', 'b'], ['inc', 'b', 1], ['dec', 'b', 2], ['sync', 'b', 'a'], ['sync', 'a', 'c'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []})],
    2: [('decrement to exactly zero is allowed', [[['inc', 'a', 2], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [0, 0, 0], 'rejected': []}), ('decrement beyond local view is rejected', [[['inc', 'a', 2], ['dec', 'b', 1], ['dec', 'a', 3]], ['a', 'b', 'c']], {'values': [2, 0, 0], 'rejected': [1, 2]}), ('decrement funded by learned increments', [[['inc', 'a', 4], ['sync', 'a', 'b'], ['dec', 'b', 3], ['sync', 'b', 'a'], ['sync', 'b', 'c'], ['sync', 'a', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []}), ('concurrent decrements converge', [[['inc', 'a', 6], ['sync', 'a', 'b'], ['dec', 'a', 1], ['dec', 'b', 2], ['sync', 'a', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [3, 3, 3], 'rejected': []}), ('zero amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', 3], ['dec', 'b', 0], ['dec', 'b', 1]], ['a', 'b', 'c']], {'values': [0, 2, 0], 'rejected': [0, 2]}), ('repeated decrement slot is refreshed', [[['inc', 'c', 5], ['dec', 'c', 1], ['sync', 'c', 'a'], ['dec', 'c', 1], ['sync', 'c', 'a'], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [3, 3, 3], 'rejected': []}), ('second decrement cannot pass the floor', [[['inc', 'a', 3], ['dec', 'a', 2], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [1, 0, 0], 'rejected': [2]}), ('one-way sync does not pull from the receiver', [[['inc', 'a', 2], ['inc', 'b', 2], ['dec', 'b', 1], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [2, 3, 0], 'rejected': []}), ('mixed history', [[['inc', 'a', 3], ['dec', 'a', 1], ['sync', 'a', 'b'], ['inc', 'b', 2], ['dec', 'b', 2], ['sync', 'b', 'a'], ['sync', 'a', 'c'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [2, 2, 2], 'rejected': []})],
    3: [('decrement to exactly zero is allowed', [[['inc', 'a', 3], ['dec', 'a', 3]], ['a', 'b', 'c']], {'values': [0, 0, 0], 'rejected': []}), ('decrement beyond local view is rejected', [[['inc', 'a', 3], ['dec', 'b', 1], ['dec', 'a', 4]], ['a', 'b', 'c']], {'values': [3, 0, 0], 'rejected': [1, 2]}), ('decrement funded by learned increments', [[['inc', 'a', 5], ['sync', 'a', 'b'], ['dec', 'b', 4], ['sync', 'b', 'a'], ['sync', 'b', 'c'], ['sync', 'a', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []}), ('concurrent decrements converge', [[['inc', 'a', 8], ['sync', 'a', 'b'], ['dec', 'a', 1], ['dec', 'b', 2], ['sync', 'a', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [5, 5, 5], 'rejected': []}), ('zero amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', 3], ['dec', 'b', 0], ['dec', 'b', 1]], ['a', 'b', 'c']], {'values': [0, 2, 0], 'rejected': [0, 2]}), ('repeated decrement slot is refreshed', [[['inc', 'c', 6], ['dec', 'c', 1], ['sync', 'c', 'a'], ['dec', 'c', 1], ['sync', 'c', 'a'], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [4, 4, 4], 'rejected': []}), ('second decrement cannot pass the floor', [[['inc', 'a', 4], ['dec', 'a', 3], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [1, 0, 0], 'rejected': [2]}), ('one-way sync does not pull from the receiver', [[['inc', 'a', 3], ['inc', 'b', 3], ['dec', 'b', 1], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [3, 5, 0], 'rejected': []}), ('mixed history', [[['inc', 'a', 3], ['dec', 'a', 1], ['sync', 'a', 'b'], ['inc', 'b', 3], ['dec', 'b', 2], ['sync', 'b', 'a'], ['sync', 'a', 'c'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [3, 3, 3], 'rejected': []})],
    4: [('decrement to exactly zero is allowed', [[['inc', 'a', 4], ['dec', 'a', 4]], ['a', 'b', 'c']], {'values': [0, 0, 0], 'rejected': []}), ('decrement beyond local view is rejected', [[['inc', 'a', 4], ['dec', 'b', 1], ['dec', 'a', 5]], ['a', 'b', 'c']], {'values': [4, 0, 0], 'rejected': [1, 2]}), ('decrement funded by learned increments', [[['inc', 'a', 6], ['sync', 'a', 'b'], ['dec', 'b', 5], ['sync', 'b', 'a'], ['sync', 'b', 'c'], ['sync', 'a', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []}), ('concurrent decrements converge', [[['inc', 'a', 10], ['sync', 'a', 'b'], ['dec', 'a', 1], ['dec', 'b', 2], ['sync', 'a', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [7, 7, 7], 'rejected': []}), ('zero amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', 3], ['dec', 'b', 0], ['dec', 'b', 1]], ['a', 'b', 'c']], {'values': [0, 2, 0], 'rejected': [0, 2]}), ('repeated decrement slot is refreshed', [[['inc', 'c', 7], ['dec', 'c', 1], ['sync', 'c', 'a'], ['dec', 'c', 1], ['sync', 'c', 'a'], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [5, 5, 5], 'rejected': []}), ('second decrement cannot pass the floor', [[['inc', 'a', 5], ['dec', 'a', 4], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [1, 0, 0], 'rejected': [2]}), ('one-way sync does not pull from the receiver', [[['inc', 'a', 4], ['inc', 'b', 4], ['dec', 'b', 1], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [4, 7, 0], 'rejected': []}), ('mixed history', [[['inc', 'a', 3], ['dec', 'a', 1], ['sync', 'a', 'b'], ['inc', 'b', 4], ['dec', 'b', 2], ['sync', 'b', 'a'], ['sync', 'a', 'c'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [4, 4, 4], 'rejected': []})],
    5: [('decrement to exactly zero is allowed', [[['inc', 'a', 5], ['dec', 'a', 5]], ['a', 'b', 'c']], {'values': [0, 0, 0], 'rejected': []}), ('decrement beyond local view is rejected', [[['inc', 'a', 5], ['dec', 'b', 1], ['dec', 'a', 6]], ['a', 'b', 'c']], {'values': [5, 0, 0], 'rejected': [1, 2]}), ('decrement funded by learned increments', [[['inc', 'a', 7], ['sync', 'a', 'b'], ['dec', 'b', 6], ['sync', 'b', 'a'], ['sync', 'b', 'c'], ['sync', 'a', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []}), ('concurrent decrements converge', [[['inc', 'a', 12], ['sync', 'a', 'b'], ['dec', 'a', 1], ['dec', 'b', 2], ['sync', 'a', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [9, 9, 9], 'rejected': []}), ('zero amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', 3], ['dec', 'b', 0], ['dec', 'b', 1]], ['a', 'b', 'c']], {'values': [0, 2, 0], 'rejected': [0, 2]}), ('repeated decrement slot is refreshed', [[['inc', 'c', 8], ['dec', 'c', 1], ['sync', 'c', 'a'], ['dec', 'c', 1], ['sync', 'c', 'a'], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [6, 6, 6], 'rejected': []}), ('second decrement cannot pass the floor', [[['inc', 'a', 6], ['dec', 'a', 5], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [1, 0, 0], 'rejected': [2]}), ('one-way sync does not pull from the receiver', [[['inc', 'a', 5], ['inc', 'b', 5], ['dec', 'b', 1], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [5, 9, 0], 'rejected': []}), ('mixed history', [[['inc', 'a', 3], ['dec', 'a', 1], ['sync', 'a', 'b'], ['inc', 'b', 5], ['dec', 'b', 2], ['sync', 'b', 'a'], ['sync', 'a', 'c'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [5, 5, 5], 'rejected': []})],
}[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
decrement to exactly zero is allowed{'rejected': [], 'values': [0, 0, 0]}{'rejected': [], 'values': [0, 0, 0]}Passed
decrement beyond local view is rejected{'rejected': [1, 2], 'values': [1, 0, 0]}{'rejected': [1, 2], 'values': [1, 0, 0]}Passed
decrement funded by learned increments{'rejected': [], 'values': [1, 1, 1]}{'rejected': [], 'values': [1, 1, 1]}Passed
concurrent decrements converge{'rejected': [], 'values': [1, 1, 1]}{'rejected': [], 'values': [1, 1, 1]}Passed
zero amounts are rejected{'rejected': [0, 2], 'values': [0, 2, 0]}{'rejected': [0, 2], 'values': [0, 2, 0]}Passed
repeated decrement slot is refreshed{'rejected': [], 'values': [3, 3, 2]}{'rejected': [], 'values': [2, 2, 2]}Failed
second decrement cannot pass the floor{'rejected': [2], 'values': [1, 0, 0]}{'rejected': [2], 'values': [1, 0, 0]}Passed
one-way sync does not pull from the receiver{'rejected': [], 'values': [1, 1, 0]}{'rejected': [], 'values': [1, 1, 0]}Passed
mixed history{'rejected': [], 'values': [1, 1, 1]}{'rejected': [], 'values': [1, 1, 1]}Passed

SHA-256 / 33d10a001f943c725fc0299f393d2127e33415ad8732bf9cc10638603bee8610

3 / The verified repair

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

N = 1
observations = []
def solve(events, replicas):
    pos = {r: {} for r in replicas}
    neg = {r: {} for r in replicas}
    rejected = []
    def value(r):
        return sum(pos[r].values()) - sum(neg[r].values())
    for i, ev in enumerate(events):
        kind = ev[0]
        if kind == 'sync':
            s, d = ev[1], ev[2]
            for k, v in pos[s].items():
                pos[d][k] = max(pos[d].get(k, 0), v)
            for k, v in neg[s].items():
                neg[d][k] = max(neg[d].get(k, 0), v)
            continue
        r, amt = ev[1], ev[2]
        if amt <= 0:
            rejected.append(i)
            continue
        if kind == 'inc':
            pos[r][r] = pos[r].get(r, 0) + amt
        else:
            if value(r) < amt:
                rejected.append(i)
                continue
            neg[r][r] = neg[r].get(r, 0) + amt
    return {'values': [value(r) for r in replicas], 'rejected': rejected}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = {
    1: [('decrement to exactly zero is allowed', [[['inc', 'a', 1], ['dec', 'a', 1]], ['a', 'b', 'c']], {'values': [0, 0, 0], 'rejected': []}), ('decrement beyond local view is rejected', [[['inc', 'a', 1], ['dec', 'b', 1], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [1, 0, 0], 'rejected': [1, 2]}), ('decrement funded by learned increments', [[['inc', 'a', 3], ['sync', 'a', 'b'], ['dec', 'b', 2], ['sync', 'b', 'a'], ['sync', 'b', 'c'], ['sync', 'a', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []}), ('concurrent decrements converge', [[['inc', 'a', 4], ['sync', 'a', 'b'], ['dec', 'a', 1], ['dec', 'b', 2], ['sync', 'a', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []}), ('zero amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', 3], ['dec', 'b', 0], ['dec', 'b', 1]], ['a', 'b', 'c']], {'values': [0, 2, 0], 'rejected': [0, 2]}), ('repeated decrement slot is refreshed', [[['inc', 'c', 4], ['dec', 'c', 1], ['sync', 'c', 'a'], ['dec', 'c', 1], ['sync', 'c', 'a'], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [2, 2, 2], 'rejected': []}), ('second decrement cannot pass the floor', [[['inc', 'a', 2], ['dec', 'a', 1], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [1, 0, 0], 'rejected': [2]}), ('one-way sync does not pull from the receiver', [[['inc', 'a', 1], ['inc', 'b', 1], ['dec', 'b', 1], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [1, 1, 0], 'rejected': []}), ('mixed history', [[['inc', 'a', 3], ['dec', 'a', 1], ['sync', 'a', 'b'], ['inc', 'b', 1], ['dec', 'b', 2], ['sync', 'b', 'a'], ['sync', 'a', 'c'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []})],
    2: [('decrement to exactly zero is allowed', [[['inc', 'a', 2], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [0, 0, 0], 'rejected': []}), ('decrement beyond local view is rejected', [[['inc', 'a', 2], ['dec', 'b', 1], ['dec', 'a', 3]], ['a', 'b', 'c']], {'values': [2, 0, 0], 'rejected': [1, 2]}), ('decrement funded by learned increments', [[['inc', 'a', 4], ['sync', 'a', 'b'], ['dec', 'b', 3], ['sync', 'b', 'a'], ['sync', 'b', 'c'], ['sync', 'a', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []}), ('concurrent decrements converge', [[['inc', 'a', 6], ['sync', 'a', 'b'], ['dec', 'a', 1], ['dec', 'b', 2], ['sync', 'a', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [3, 3, 3], 'rejected': []}), ('zero amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', 3], ['dec', 'b', 0], ['dec', 'b', 1]], ['a', 'b', 'c']], {'values': [0, 2, 0], 'rejected': [0, 2]}), ('repeated decrement slot is refreshed', [[['inc', 'c', 5], ['dec', 'c', 1], ['sync', 'c', 'a'], ['dec', 'c', 1], ['sync', 'c', 'a'], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [3, 3, 3], 'rejected': []}), ('second decrement cannot pass the floor', [[['inc', 'a', 3], ['dec', 'a', 2], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [1, 0, 0], 'rejected': [2]}), ('one-way sync does not pull from the receiver', [[['inc', 'a', 2], ['inc', 'b', 2], ['dec', 'b', 1], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [2, 3, 0], 'rejected': []}), ('mixed history', [[['inc', 'a', 3], ['dec', 'a', 1], ['sync', 'a', 'b'], ['inc', 'b', 2], ['dec', 'b', 2], ['sync', 'b', 'a'], ['sync', 'a', 'c'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [2, 2, 2], 'rejected': []})],
    3: [('decrement to exactly zero is allowed', [[['inc', 'a', 3], ['dec', 'a', 3]], ['a', 'b', 'c']], {'values': [0, 0, 0], 'rejected': []}), ('decrement beyond local view is rejected', [[['inc', 'a', 3], ['dec', 'b', 1], ['dec', 'a', 4]], ['a', 'b', 'c']], {'values': [3, 0, 0], 'rejected': [1, 2]}), ('decrement funded by learned increments', [[['inc', 'a', 5], ['sync', 'a', 'b'], ['dec', 'b', 4], ['sync', 'b', 'a'], ['sync', 'b', 'c'], ['sync', 'a', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []}), ('concurrent decrements converge', [[['inc', 'a', 8], ['sync', 'a', 'b'], ['dec', 'a', 1], ['dec', 'b', 2], ['sync', 'a', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [5, 5, 5], 'rejected': []}), ('zero amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', 3], ['dec', 'b', 0], ['dec', 'b', 1]], ['a', 'b', 'c']], {'values': [0, 2, 0], 'rejected': [0, 2]}), ('repeated decrement slot is refreshed', [[['inc', 'c', 6], ['dec', 'c', 1], ['sync', 'c', 'a'], ['dec', 'c', 1], ['sync', 'c', 'a'], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [4, 4, 4], 'rejected': []}), ('second decrement cannot pass the floor', [[['inc', 'a', 4], ['dec', 'a', 3], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [1, 0, 0], 'rejected': [2]}), ('one-way sync does not pull from the receiver', [[['inc', 'a', 3], ['inc', 'b', 3], ['dec', 'b', 1], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [3, 5, 0], 'rejected': []}), ('mixed history', [[['inc', 'a', 3], ['dec', 'a', 1], ['sync', 'a', 'b'], ['inc', 'b', 3], ['dec', 'b', 2], ['sync', 'b', 'a'], ['sync', 'a', 'c'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [3, 3, 3], 'rejected': []})],
    4: [('decrement to exactly zero is allowed', [[['inc', 'a', 4], ['dec', 'a', 4]], ['a', 'b', 'c']], {'values': [0, 0, 0], 'rejected': []}), ('decrement beyond local view is rejected', [[['inc', 'a', 4], ['dec', 'b', 1], ['dec', 'a', 5]], ['a', 'b', 'c']], {'values': [4, 0, 0], 'rejected': [1, 2]}), ('decrement funded by learned increments', [[['inc', 'a', 6], ['sync', 'a', 'b'], ['dec', 'b', 5], ['sync', 'b', 'a'], ['sync', 'b', 'c'], ['sync', 'a', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []}), ('concurrent decrements converge', [[['inc', 'a', 10], ['sync', 'a', 'b'], ['dec', 'a', 1], ['dec', 'b', 2], ['sync', 'a', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [7, 7, 7], 'rejected': []}), ('zero amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', 3], ['dec', 'b', 0], ['dec', 'b', 1]], ['a', 'b', 'c']], {'values': [0, 2, 0], 'rejected': [0, 2]}), ('repeated decrement slot is refreshed', [[['inc', 'c', 7], ['dec', 'c', 1], ['sync', 'c', 'a'], ['dec', 'c', 1], ['sync', 'c', 'a'], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [5, 5, 5], 'rejected': []}), ('second decrement cannot pass the floor', [[['inc', 'a', 5], ['dec', 'a', 4], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [1, 0, 0], 'rejected': [2]}), ('one-way sync does not pull from the receiver', [[['inc', 'a', 4], ['inc', 'b', 4], ['dec', 'b', 1], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [4, 7, 0], 'rejected': []}), ('mixed history', [[['inc', 'a', 3], ['dec', 'a', 1], ['sync', 'a', 'b'], ['inc', 'b', 4], ['dec', 'b', 2], ['sync', 'b', 'a'], ['sync', 'a', 'c'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [4, 4, 4], 'rejected': []})],
    5: [('decrement to exactly zero is allowed', [[['inc', 'a', 5], ['dec', 'a', 5]], ['a', 'b', 'c']], {'values': [0, 0, 0], 'rejected': []}), ('decrement beyond local view is rejected', [[['inc', 'a', 5], ['dec', 'b', 1], ['dec', 'a', 6]], ['a', 'b', 'c']], {'values': [5, 0, 0], 'rejected': [1, 2]}), ('decrement funded by learned increments', [[['inc', 'a', 7], ['sync', 'a', 'b'], ['dec', 'b', 6], ['sync', 'b', 'a'], ['sync', 'b', 'c'], ['sync', 'a', 'c']], ['a', 'b', 'c']], {'values': [1, 1, 1], 'rejected': []}), ('concurrent decrements converge', [[['inc', 'a', 12], ['sync', 'a', 'b'], ['dec', 'a', 1], ['dec', 'b', 2], ['sync', 'a', 'b'], ['sync', 'b', 'a'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [9, 9, 9], 'rejected': []}), ('zero amounts are rejected', [[['inc', 'a', 0], ['inc', 'b', 3], ['dec', 'b', 0], ['dec', 'b', 1]], ['a', 'b', 'c']], {'values': [0, 2, 0], 'rejected': [0, 2]}), ('repeated decrement slot is refreshed', [[['inc', 'c', 8], ['dec', 'c', 1], ['sync', 'c', 'a'], ['dec', 'c', 1], ['sync', 'c', 'a'], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [6, 6, 6], 'rejected': []}), ('second decrement cannot pass the floor', [[['inc', 'a', 6], ['dec', 'a', 5], ['dec', 'a', 2]], ['a', 'b', 'c']], {'values': [1, 0, 0], 'rejected': [2]}), ('one-way sync does not pull from the receiver', [[['inc', 'a', 5], ['inc', 'b', 5], ['dec', 'b', 1], ['sync', 'a', 'b']], ['a', 'b', 'c']], {'values': [5, 9, 0], 'rejected': []}), ('mixed history', [[['inc', 'a', 3], ['dec', 'a', 1], ['sync', 'a', 'b'], ['inc', 'b', 5], ['dec', 'b', 2], ['sync', 'b', 'a'], ['sync', 'a', 'c'], ['sync', 'b', 'c']], ['a', 'b', 'c']], {'values': [5, 5, 5], 'rejected': []})],
}[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
decrement to exactly zero is allowed{'rejected': [], 'values': [0, 0, 0]}{'rejected': [], 'values': [0, 0, 0]}Passed
decrement beyond local view is rejected{'rejected': [1, 2], 'values': [1, 0, 0]}{'rejected': [1, 2], 'values': [1, 0, 0]}Passed
decrement funded by learned increments{'rejected': [], 'values': [1, 1, 1]}{'rejected': [], 'values': [1, 1, 1]}Passed
concurrent decrements converge{'rejected': [], 'values': [1, 1, 1]}{'rejected': [], 'values': [1, 1, 1]}Passed
zero amounts are rejected{'rejected': [0, 2], 'values': [0, 2, 0]}{'rejected': [0, 2], 'values': [0, 2, 0]}Passed
repeated decrement slot is refreshed{'rejected': [], 'values': [2, 2, 2]}{'rejected': [], 'values': [2, 2, 2]}Passed
second decrement cannot pass the floor{'rejected': [2], 'values': [1, 0, 0]}{'rejected': [2], 'values': [1, 0, 0]}Passed
one-way sync does not pull from the receiver{'rejected': [], 'values': [1, 1, 0]}{'rejected': [], 'values': [1, 1, 0]}Passed
mixed history{'rejected': [], 'values': [1, 1, 1]}{'rejected': [], 'values': [1, 1, 1]}Passed

SHA-256 / 3adf2aa219bbf8f7be38ef729ec20b58a77ed0d029c1bf2975b91368aacc6a4b

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 2026-09-29T14:49:00.871957+00:00.

Case digest / e849b0d87e1f1066226e1728f3eaf59fd5370735eeee2ba68ae52b668085d58e