FA-76271 / Chat ordering and read receipts / Open access
Assign idempotent per-conversation sequence numbers: first sequence · case 01
The first message of a conversation receives seq 0 instead of 1.
ROOT CAUSE
The first sequence decision evaluates `counters.get(conv, -1) + 1` where the contract requires `counters.get(conv, 0) + 1`.
VERIFIED REPAIR
Use `counters.get(conv, 0) + 1` for the first sequence decision and keep every other rule of the model unchanged.
Unsuccessful approach: Skipping the increment only for new conversations still hands out seq 0 first. The attempted `counters.get(conv, 0) + (1 if conv in counters else 0)` still disagrees with a fixture.
Case contract
requests are [conv, sender, nonce] in arrival order; members maps conv -> member list. A sender who is not a member gets "forbidden" and consumes nothing. Each conversation numbers accepted messages 1, 2, 3... A retry with the same (conv, sender, nonce) returns the originally assigned seq without consuming a new one.
Why this case matters
Server sequencing is the backbone of chat ordering; idempotency errors create duplicates or gaps.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(requests, members):
counters = {}
known = {}
out = []
for conv, sender, nonce in requests:
if sender not in members.get(conv, []):
out.append('forbidden')
continue
key = (conv, sender, nonce)
if key in known:
out.append(known[key])
continue
counters[conv] = counters.get(conv, -1) + 1
known[key] = counters[conv]
out.append(counters[conv])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
_CASES = {1: [('nonce reused by another sender', ([['c', 'al', 'n1'], ['c', 'bo', 'n1']], {'c': ['al', 'bo']}), [1, 2]), ('nonce reused in another conversation', ([['d', 'al', 'z'], ['c', 'al', 'n1'], ['d', 'al', 'n1']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('two conversations interleaved', ([['c', 'al', 'a'], ['d', 'al', 'b'], ['c', 'al', 'c']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('retry returns original', ([['c', 'al', 'x'], ['c', 'al', 'y'], ['c', 'al', 'x']], {'c': ['al']}), [1, 2, 1]), ('forbidden sender', ([['c', 'eve', 'z'], ['c', 'al', 'q']], {'c': ['al']}), ['forbidden', 1]), ('burst', ([['c', 'al', 'm0'], ['c', 'al', 'm1']], {'c': ['al']}), [1, 2])], 2: [('nonce reused by another sender', ([['c', 'al', 'n1'], ['c', 'bo', 'n1']], {'c': ['al', 'bo']}), [1, 2]), ('nonce reused in another conversation', ([['d', 'al', 'z'], ['c', 'al', 'n2'], ['d', 'al', 'n2']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('two conversations interleaved', ([['c', 'al', 'a'], ['d', 'al', 'b'], ['c', 'al', 'c']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('retry returns original', ([['c', 'al', 'x'], ['c', 'al', 'y'], ['c', 'al', 'x']], {'c': ['al']}), [1, 2, 1]), ('forbidden sender', ([['c', 'eve', 'z'], ['c', 'al', 'q']], {'c': ['al']}), ['forbidden', 1]), ('burst', ([['c', 'al', 'm0'], ['c', 'al', 'm1'], ['c', 'al', 'm2']], {'c': ['al']}), [1, 2, 3])], 3: [('nonce reused by another sender', ([['c', 'al', 'n1'], ['c', 'bo', 'n1']], {'c': ['al', 'bo']}), [1, 2]), ('nonce reused in another conversation', ([['d', 'al', 'z'], ['c', 'al', 'n3'], ['d', 'al', 'n3']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('two conversations interleaved', ([['c', 'al', 'a'], ['d', 'al', 'b'], ['c', 'al', 'c']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('retry returns original', ([['c', 'al', 'x'], ['c', 'al', 'y'], ['c', 'al', 'x']], {'c': ['al']}), [1, 2, 1]), ('forbidden sender', ([['c', 'eve', 'z'], ['c', 'al', 'q']], {'c': ['al']}), ['forbidden', 1]), ('burst', ([['c', 'al', 'm0'], ['c', 'al', 'm1'], ['c', 'al', 'm2'], ['c', 'al', 'm3']], {'c': ['al']}), [1, 2, 3, 4])], 4: [('nonce reused by another sender', ([['c', 'al', 'n1'], ['c', 'bo', 'n1']], {'c': ['al', 'bo']}), [1, 2]), ('nonce reused in another conversation', ([['d', 'al', 'z'], ['c', 'al', 'n4'], ['d', 'al', 'n4']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('two conversations interleaved', ([['c', 'al', 'a'], ['d', 'al', 'b'], ['c', 'al', 'c']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('retry returns original', ([['c', 'al', 'x'], ['c', 'al', 'y'], ['c', 'al', 'x']], {'c': ['al']}), [1, 2, 1]), ('forbidden sender', ([['c', 'eve', 'z'], ['c', 'al', 'q']], {'c': ['al']}), ['forbidden', 1]), ('burst', ([['c', 'al', 'm0'], ['c', 'al', 'm1'], ['c', 'al', 'm2'], ['c', 'al', 'm3'], ['c', 'al', 'm4']], {'c': ['al']}), [1, 2, 3, 4, 5])], 5: [('nonce reused by another sender', ([['c', 'al', 'n1'], ['c', 'bo', 'n1']], {'c': ['al', 'bo']}), [1, 2]), ('nonce reused in another conversation', ([['d', 'al', 'z'], ['c', 'al', 'n5'], ['d', 'al', 'n5']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('two conversations interleaved', ([['c', 'al', 'a'], ['d', 'al', 'b'], ['c', 'al', 'c']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('retry returns original', ([['c', 'al', 'x'], ['c', 'al', 'y'], ['c', 'al', 'x']], {'c': ['al']}), [1, 2, 1]), ('forbidden sender', ([['c', 'eve', 'z'], ['c', 'al', 'q']], {'c': ['al']}), ['forbidden', 1]), ('burst', ([['c', 'al', 'm0'], ['c', 'al', 'm1'], ['c', 'al', 'm2'], ['c', 'al', 'm3'], ['c', 'al', 'm4'], ['c', 'al', 'm5']], {'c': ['al']}), [1, 2, 3, 4, 5, 6])]}
for _label, _args, _expected in _CASES[N]:
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 |
|---|---|---|---|
| nonce reused by another sender | [0, 1] | [1, 2] | Failed |
| nonce reused in another conversation | [0, 0, 1] | [1, 1, 2] | Failed |
| two conversations interleaved | [0, 0, 1] | [1, 1, 2] | Failed |
| retry returns original | [0, 1, 0] | [1, 2, 1] | Failed |
| forbidden sender | ['forbidden', 0] | ['forbidden', 1] | Failed |
| burst | [0, 1] | [1, 2] | Failed |
SHA-256 / 4f6c5f98c93a2e45c7809b5cc21382671f0c1dc0cd75fdc69bd4cf699e5c454f
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(requests, members):
counters = {}
known = {}
out = []
for conv, sender, nonce in requests:
if sender not in members.get(conv, []):
out.append('forbidden')
continue
key = (conv, sender, nonce)
if key in known:
out.append(known[key])
continue
counters[conv] = counters.get(conv, 0) + (1 if conv in counters else 0)
known[key] = counters[conv]
out.append(counters[conv])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
_CASES = {1: [('nonce reused by another sender', ([['c', 'al', 'n1'], ['c', 'bo', 'n1']], {'c': ['al', 'bo']}), [1, 2]), ('nonce reused in another conversation', ([['d', 'al', 'z'], ['c', 'al', 'n1'], ['d', 'al', 'n1']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('two conversations interleaved', ([['c', 'al', 'a'], ['d', 'al', 'b'], ['c', 'al', 'c']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('retry returns original', ([['c', 'al', 'x'], ['c', 'al', 'y'], ['c', 'al', 'x']], {'c': ['al']}), [1, 2, 1]), ('forbidden sender', ([['c', 'eve', 'z'], ['c', 'al', 'q']], {'c': ['al']}), ['forbidden', 1]), ('burst', ([['c', 'al', 'm0'], ['c', 'al', 'm1']], {'c': ['al']}), [1, 2])], 2: [('nonce reused by another sender', ([['c', 'al', 'n1'], ['c', 'bo', 'n1']], {'c': ['al', 'bo']}), [1, 2]), ('nonce reused in another conversation', ([['d', 'al', 'z'], ['c', 'al', 'n2'], ['d', 'al', 'n2']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('two conversations interleaved', ([['c', 'al', 'a'], ['d', 'al', 'b'], ['c', 'al', 'c']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('retry returns original', ([['c', 'al', 'x'], ['c', 'al', 'y'], ['c', 'al', 'x']], {'c': ['al']}), [1, 2, 1]), ('forbidden sender', ([['c', 'eve', 'z'], ['c', 'al', 'q']], {'c': ['al']}), ['forbidden', 1]), ('burst', ([['c', 'al', 'm0'], ['c', 'al', 'm1'], ['c', 'al', 'm2']], {'c': ['al']}), [1, 2, 3])], 3: [('nonce reused by another sender', ([['c', 'al', 'n1'], ['c', 'bo', 'n1']], {'c': ['al', 'bo']}), [1, 2]), ('nonce reused in another conversation', ([['d', 'al', 'z'], ['c', 'al', 'n3'], ['d', 'al', 'n3']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('two conversations interleaved', ([['c', 'al', 'a'], ['d', 'al', 'b'], ['c', 'al', 'c']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('retry returns original', ([['c', 'al', 'x'], ['c', 'al', 'y'], ['c', 'al', 'x']], {'c': ['al']}), [1, 2, 1]), ('forbidden sender', ([['c', 'eve', 'z'], ['c', 'al', 'q']], {'c': ['al']}), ['forbidden', 1]), ('burst', ([['c', 'al', 'm0'], ['c', 'al', 'm1'], ['c', 'al', 'm2'], ['c', 'al', 'm3']], {'c': ['al']}), [1, 2, 3, 4])], 4: [('nonce reused by another sender', ([['c', 'al', 'n1'], ['c', 'bo', 'n1']], {'c': ['al', 'bo']}), [1, 2]), ('nonce reused in another conversation', ([['d', 'al', 'z'], ['c', 'al', 'n4'], ['d', 'al', 'n4']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('two conversations interleaved', ([['c', 'al', 'a'], ['d', 'al', 'b'], ['c', 'al', 'c']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('retry returns original', ([['c', 'al', 'x'], ['c', 'al', 'y'], ['c', 'al', 'x']], {'c': ['al']}), [1, 2, 1]), ('forbidden sender', ([['c', 'eve', 'z'], ['c', 'al', 'q']], {'c': ['al']}), ['forbidden', 1]), ('burst', ([['c', 'al', 'm0'], ['c', 'al', 'm1'], ['c', 'al', 'm2'], ['c', 'al', 'm3'], ['c', 'al', 'm4']], {'c': ['al']}), [1, 2, 3, 4, 5])], 5: [('nonce reused by another sender', ([['c', 'al', 'n1'], ['c', 'bo', 'n1']], {'c': ['al', 'bo']}), [1, 2]), ('nonce reused in another conversation', ([['d', 'al', 'z'], ['c', 'al', 'n5'], ['d', 'al', 'n5']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('two conversations interleaved', ([['c', 'al', 'a'], ['d', 'al', 'b'], ['c', 'al', 'c']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('retry returns original', ([['c', 'al', 'x'], ['c', 'al', 'y'], ['c', 'al', 'x']], {'c': ['al']}), [1, 2, 1]), ('forbidden sender', ([['c', 'eve', 'z'], ['c', 'al', 'q']], {'c': ['al']}), ['forbidden', 1]), ('burst', ([['c', 'al', 'm0'], ['c', 'al', 'm1'], ['c', 'al', 'm2'], ['c', 'al', 'm3'], ['c', 'al', 'm4'], ['c', 'al', 'm5']], {'c': ['al']}), [1, 2, 3, 4, 5, 6])]}
for _label, _args, _expected in _CASES[N]:
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 |
|---|---|---|---|
| nonce reused by another sender | [0, 1] | [1, 2] | Failed |
| nonce reused in another conversation | [0, 0, 1] | [1, 1, 2] | Failed |
| two conversations interleaved | [0, 0, 1] | [1, 1, 2] | Failed |
| retry returns original | [0, 1, 0] | [1, 2, 1] | Failed |
| forbidden sender | ['forbidden', 0] | ['forbidden', 1] | Failed |
| burst | [0, 1] | [1, 2] | Failed |
SHA-256 / ba33b5dddf77230594093fd2068d59ed9f775175306d9fff79f92ee3fddc2a34
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(requests, members):
counters = {}
known = {}
out = []
for conv, sender, nonce in requests:
if sender not in members.get(conv, []):
out.append('forbidden')
continue
key = (conv, sender, nonce)
if key in known:
out.append(known[key])
continue
counters[conv] = counters.get(conv, 0) + 1
known[key] = counters[conv]
out.append(counters[conv])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
_CASES = {1: [('nonce reused by another sender', ([['c', 'al', 'n1'], ['c', 'bo', 'n1']], {'c': ['al', 'bo']}), [1, 2]), ('nonce reused in another conversation', ([['d', 'al', 'z'], ['c', 'al', 'n1'], ['d', 'al', 'n1']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('two conversations interleaved', ([['c', 'al', 'a'], ['d', 'al', 'b'], ['c', 'al', 'c']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('retry returns original', ([['c', 'al', 'x'], ['c', 'al', 'y'], ['c', 'al', 'x']], {'c': ['al']}), [1, 2, 1]), ('forbidden sender', ([['c', 'eve', 'z'], ['c', 'al', 'q']], {'c': ['al']}), ['forbidden', 1]), ('burst', ([['c', 'al', 'm0'], ['c', 'al', 'm1']], {'c': ['al']}), [1, 2])], 2: [('nonce reused by another sender', ([['c', 'al', 'n1'], ['c', 'bo', 'n1']], {'c': ['al', 'bo']}), [1, 2]), ('nonce reused in another conversation', ([['d', 'al', 'z'], ['c', 'al', 'n2'], ['d', 'al', 'n2']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('two conversations interleaved', ([['c', 'al', 'a'], ['d', 'al', 'b'], ['c', 'al', 'c']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('retry returns original', ([['c', 'al', 'x'], ['c', 'al', 'y'], ['c', 'al', 'x']], {'c': ['al']}), [1, 2, 1]), ('forbidden sender', ([['c', 'eve', 'z'], ['c', 'al', 'q']], {'c': ['al']}), ['forbidden', 1]), ('burst', ([['c', 'al', 'm0'], ['c', 'al', 'm1'], ['c', 'al', 'm2']], {'c': ['al']}), [1, 2, 3])], 3: [('nonce reused by another sender', ([['c', 'al', 'n1'], ['c', 'bo', 'n1']], {'c': ['al', 'bo']}), [1, 2]), ('nonce reused in another conversation', ([['d', 'al', 'z'], ['c', 'al', 'n3'], ['d', 'al', 'n3']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('two conversations interleaved', ([['c', 'al', 'a'], ['d', 'al', 'b'], ['c', 'al', 'c']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('retry returns original', ([['c', 'al', 'x'], ['c', 'al', 'y'], ['c', 'al', 'x']], {'c': ['al']}), [1, 2, 1]), ('forbidden sender', ([['c', 'eve', 'z'], ['c', 'al', 'q']], {'c': ['al']}), ['forbidden', 1]), ('burst', ([['c', 'al', 'm0'], ['c', 'al', 'm1'], ['c', 'al', 'm2'], ['c', 'al', 'm3']], {'c': ['al']}), [1, 2, 3, 4])], 4: [('nonce reused by another sender', ([['c', 'al', 'n1'], ['c', 'bo', 'n1']], {'c': ['al', 'bo']}), [1, 2]), ('nonce reused in another conversation', ([['d', 'al', 'z'], ['c', 'al', 'n4'], ['d', 'al', 'n4']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('two conversations interleaved', ([['c', 'al', 'a'], ['d', 'al', 'b'], ['c', 'al', 'c']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('retry returns original', ([['c', 'al', 'x'], ['c', 'al', 'y'], ['c', 'al', 'x']], {'c': ['al']}), [1, 2, 1]), ('forbidden sender', ([['c', 'eve', 'z'], ['c', 'al', 'q']], {'c': ['al']}), ['forbidden', 1]), ('burst', ([['c', 'al', 'm0'], ['c', 'al', 'm1'], ['c', 'al', 'm2'], ['c', 'al', 'm3'], ['c', 'al', 'm4']], {'c': ['al']}), [1, 2, 3, 4, 5])], 5: [('nonce reused by another sender', ([['c', 'al', 'n1'], ['c', 'bo', 'n1']], {'c': ['al', 'bo']}), [1, 2]), ('nonce reused in another conversation', ([['d', 'al', 'z'], ['c', 'al', 'n5'], ['d', 'al', 'n5']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('two conversations interleaved', ([['c', 'al', 'a'], ['d', 'al', 'b'], ['c', 'al', 'c']], {'c': ['al'], 'd': ['al']}), [1, 1, 2]), ('retry returns original', ([['c', 'al', 'x'], ['c', 'al', 'y'], ['c', 'al', 'x']], {'c': ['al']}), [1, 2, 1]), ('forbidden sender', ([['c', 'eve', 'z'], ['c', 'al', 'q']], {'c': ['al']}), ['forbidden', 1]), ('burst', ([['c', 'al', 'm0'], ['c', 'al', 'm1'], ['c', 'al', 'm2'], ['c', 'al', 'm3'], ['c', 'al', 'm4'], ['c', 'al', 'm5']], {'c': ['al']}), [1, 2, 3, 4, 5, 6])]}
for _label, _args, _expected in _CASES[N]:
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 |
|---|---|---|---|
| nonce reused by another sender | [1, 2] | [1, 2] | Passed |
| nonce reused in another conversation | [1, 1, 2] | [1, 1, 2] | Passed |
| two conversations interleaved | [1, 1, 2] | [1, 1, 2] | Passed |
| retry returns original | [1, 2, 1] | [1, 2, 1] | Passed |
| forbidden sender | ['forbidden', 1] | ['forbidden', 1] | Passed |
| burst | [1, 2] | [1, 2] | Passed |
SHA-256 / 18a59b9a57f8b8a0ae5fc5af3c9fa4f75873d0ea5bdde29102533309423fcc1c
Verification & scope
Stipulated offline chat model; not a complete messaging protocol, client or server implementation. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:49:14.803012+00:00.
Case digest / 8773be0fa535fd9687138e6b7e587f837732be797365f17ec225fb973666cbc5