FA-541 / Consensus / Open access

Choose a value after prepare responses: Prepare responses from different ballots are combined · case 01

The proposal adoption operation is admitted even though prepare responses from different ballots are combined.

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

ROOT CAUSE

The admission path omits the responses ballot invariant while validating the other operation preconditions.

VERIFIED REPAIR

Require all(x == r['responses_ballot'][0] for x in r['responses_ballot'][1]) together with every other stated precondition before accepting the operation.

Unsuccessful approach: Adding the responses ballot check repairs the reported defect, but replacing the adjacent ballot identity check loses that independent invariant.

Case contract

Return a Boolean admission decision for choose a value after prepare responses. The record r must satisfy all of: len(set(r['promise_quorum'][0])) >= r['promise_quorum'][1]; r['highest_accepted'][0] == max(r['highest_accepted'][1]); r['accepted_value'][0] == r['accepted_value'][1]; all(x == r['responses_ballot'][0] for x in r['responses_ballot'][1]); len(r['ballot_identity']) == len(set(tuple(x) for x in r['ballot_identity'])). Extra tracing fields are ignored; validation does not mutate the record.

Why this case matters

A deterministic local contract for consensus. Each negative fixture violates exactly one invariant. No transport timing, persistence, cryptographic verification, or full protocol implementation is claimed.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(r):
    return (len(set(r['promise_quorum'][0])) >= r['promise_quorum'][1]) and (r['highest_accepted'][0] == max(r['highest_accepted'][1])) and (r['accepted_value'][0] == r['accepted_value'][1]) and (len(r['ballot_identity']) == len(set(tuple(x) for x in r['ballot_identity'])))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
r = {'promise_quorum': [[1, 2], 2], 'highest_accepted': [7, [2, 7, 5]], 'accepted_value': ['old', 'old'], 'responses_ballot': [8, [8, 8]], 'ballot_identity': [[8, 'a'], [8, 'b']]}
check('valid operation', solve(r), True)
check('A proposer proceeds with too few distinct promises', solve(dict(r, **{'promise_quorum': [[1, 1], 2]})), False)
check('A proposer ignores the highest previously accepted ballot', solve(dict(r, **{'highest_accepted': [5, [2, 7, 5]]})), False)
check('A proposer replaces the adopted value with its client value', solve(dict(r, **{'accepted_value': ['new', 'old']})), False)
check('Prepare responses from different ballots are combined', solve(dict(r, **{'responses_ballot': [8, [7, 8]]})), False)
check('Two proposers reuse one ballot identity', solve(dict(r, **{'ballot_identity': [[8, 'a'], [8, 'a']]})), False)
check('unrelated tracing metadata', solve(dict(r, trace='run-'+str(N))), True)
check('repeat validation is pure', solve(r), True)
invalid = {'promise_quorum': [[1, 1], 2], 'highest_accepted': [5, [2, 7, 5]], 'accepted_value': ['new', 'old'], 'responses_ballot': [8, [7, 8]], 'ballot_identity': [[8, 'a'], [8, 'a']]}
keys = list(invalid)
pair = {keys[N % len(keys)]: invalid[keys[N % len(keys)]], keys[(N+1) % len(keys)]: invalid[keys[(N+1) % len(keys)]]}
check('two independent violations in variant', solve(dict(r, **pair)), False)
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
valid operation	`True`	`True`	Passed
A proposer proceeds with too few distinct promises	`False`	`False`	Passed
A proposer ignores the highest previously accepted ballot	`False`	`False`	Passed
A proposer replaces the adopted value with its client value	`False`	`False`	Passed
Prepare responses from different ballots are combined	`True`	`False`	Failed
Two proposers reuse one ballot identity	`False`	`False`	Passed
unrelated tracing metadata	`True`	`True`	Passed
repeat validation is pure	`True`	`True`	Passed
two independent violations in variant	`False`	`False`	Passed

SHA-256 / 9160392747f1025eb8ac05acc52030dd782a82ad3d811f0dc62cfbea7ffca4a5

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(r):
    return (len(set(r['promise_quorum'][0])) >= r['promise_quorum'][1]) and (r['highest_accepted'][0] == max(r['highest_accepted'][1])) and (r['accepted_value'][0] == r['accepted_value'][1]) and (all(x == r['responses_ballot'][0] for x in r['responses_ballot'][1]))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
r = {'promise_quorum': [[1, 2], 2], 'highest_accepted': [7, [2, 7, 5]], 'accepted_value': ['old', 'old'], 'responses_ballot': [8, [8, 8]], 'ballot_identity': [[8, 'a'], [8, 'b']]}
check('valid operation', solve(r), True)
check('A proposer proceeds with too few distinct promises', solve(dict(r, **{'promise_quorum': [[1, 1], 2]})), False)
check('A proposer ignores the highest previously accepted ballot', solve(dict(r, **{'highest_accepted': [5, [2, 7, 5]]})), False)
check('A proposer replaces the adopted value with its client value', solve(dict(r, **{'accepted_value': ['new', 'old']})), False)
check('Prepare responses from different ballots are combined', solve(dict(r, **{'responses_ballot': [8, [7, 8]]})), False)
check('Two proposers reuse one ballot identity', solve(dict(r, **{'ballot_identity': [[8, 'a'], [8, 'a']]})), False)
check('unrelated tracing metadata', solve(dict(r, trace='run-'+str(N))), True)
check('repeat validation is pure', solve(r), True)
invalid = {'promise_quorum': [[1, 1], 2], 'highest_accepted': [5, [2, 7, 5]], 'accepted_value': ['new', 'old'], 'responses_ballot': [8, [7, 8]], 'ballot_identity': [[8, 'a'], [8, 'a']]}
keys = list(invalid)
pair = {keys[N % len(keys)]: invalid[keys[N % len(keys)]], keys[(N+1) % len(keys)]: invalid[keys[(N+1) % len(keys)]]}
check('two independent violations in variant', solve(dict(r, **pair)), False)
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
valid operation	`True`	`True`	Passed
A proposer proceeds with too few distinct promises	`False`	`False`	Passed
A proposer ignores the highest previously accepted ballot	`False`	`False`	Passed
A proposer replaces the adopted value with its client value	`False`	`False`	Passed
Prepare responses from different ballots are combined	`False`	`False`	Passed
Two proposers reuse one ballot identity	`True`	`False`	Failed
unrelated tracing metadata	`True`	`True`	Passed
repeat validation is pure	`True`	`True`	Passed
two independent violations in variant	`False`	`False`	Passed

SHA-256 / 6b09e8d15c68d7ed6631ae427575c48dcd9e525d890d665046a7499f43aa2b6d

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(r):
    return (len(set(r['promise_quorum'][0])) >= r['promise_quorum'][1]) and (r['highest_accepted'][0] == max(r['highest_accepted'][1])) and (r['accepted_value'][0] == r['accepted_value'][1]) and (all(x == r['responses_ballot'][0] for x in r['responses_ballot'][1])) and (len(r['ballot_identity']) == len(set(tuple(x) for x in r['ballot_identity'])))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
r = {'promise_quorum': [[1, 2], 2], 'highest_accepted': [7, [2, 7, 5]], 'accepted_value': ['old', 'old'], 'responses_ballot': [8, [8, 8]], 'ballot_identity': [[8, 'a'], [8, 'b']]}
check('valid operation', solve(r), True)
check('A proposer proceeds with too few distinct promises', solve(dict(r, **{'promise_quorum': [[1, 1], 2]})), False)
check('A proposer ignores the highest previously accepted ballot', solve(dict(r, **{'highest_accepted': [5, [2, 7, 5]]})), False)
check('A proposer replaces the adopted value with its client value', solve(dict(r, **{'accepted_value': ['new', 'old']})), False)
check('Prepare responses from different ballots are combined', solve(dict(r, **{'responses_ballot': [8, [7, 8]]})), False)
check('Two proposers reuse one ballot identity', solve(dict(r, **{'ballot_identity': [[8, 'a'], [8, 'a']]})), False)
check('unrelated tracing metadata', solve(dict(r, trace='run-'+str(N))), True)
check('repeat validation is pure', solve(r), True)
invalid = {'promise_quorum': [[1, 1], 2], 'highest_accepted': [5, [2, 7, 5]], 'accepted_value': ['new', 'old'], 'responses_ballot': [8, [7, 8]], 'ballot_identity': [[8, 'a'], [8, 'a']]}
keys = list(invalid)
pair = {keys[N % len(keys)]: invalid[keys[N % len(keys)]], keys[(N+1) % len(keys)]: invalid[keys[(N+1) % len(keys)]]}
check('two independent violations in variant', solve(dict(r, **pair)), False)
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
valid operation	`True`	`True`	Passed
A proposer proceeds with too few distinct promises	`False`	`False`	Passed
A proposer ignores the highest previously accepted ballot	`False`	`False`	Passed
A proposer replaces the adopted value with its client value	`False`	`False`	Passed
Prepare responses from different ballots are combined	`False`	`False`	Passed
Two proposers reuse one ballot identity	`False`	`False`	Passed
unrelated tracing metadata	`True`	`True`	Passed
repeat validation is pure	`True`	`True`	Passed
two independent violations in variant	`False`	`False`	Passed

SHA-256 / 85329280e82a2f5e4b2e69296171dd2eb6eb7ec01abf2a8ba66d23cd59063f3f

Verification & scope

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 2026-09-29T14:36:53.806865+00:00.

Case digest / fa3942fb7fc1d5fa8354ea3eb95577af7bd46305f9db49c1e519601470f5f463