FA-12051 / Sensor fusion consistency / Open access
Repeated sensor packet is counted as independent evidence · case 01
Retransmission artificially increases measurement information.
ROOT CAUSE
Every transport delivery contributes inverse variance.
VERIFIED REPAIR
Deduplicate by sensor identity and acquisition sequence.
Unsuccessful approach: Deduplicating sequence alone drops distinct sensors with equal sequence numbers.
Case contract
Sum inverse variances once per (sensor, sequence), returning a reduced fraction string. Repeated identities have equal positive variance.
Why this case matters
Deterministic sensor-fusion model isolating one consistency contract; no hardware or production estimator is simulated.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(records):
return str(sum((Fraction(1,v) for s,q,v in records),Fraction()))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('retransmission', solve([('a',N,2),('a',N,2)]), '1/2')
check('two sensors same sequence', solve([('a',N,2),('b',N,2)]), '1')
check('successive samples', solve([('a',N,2),('a',N+1,2)]), '1')
check('mixed duplicates', solve([('a',N,4),('b',N,4),('a',N,4)]), '1/2')
check('one packet', solve([('a',N,3)]), '1/3')
check('no packet', solve([]), '0')
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 |
|---|---|---|---|
| retransmission | 1 | 1/2 | Failed |
| two sensors same sequence | 1 | 1 | Passed |
| successive samples | 1 | 1 | Passed |
| mixed duplicates | 3/4 | 1/2 | Failed |
| one packet | 1/3 | 1/3 | Passed |
| no packet | 0 | 0 | Passed |
SHA-256 / dbdb9b270c5c01f14816e19c3fd9ce5746c7f229b661edc62975f480e1d8fe6f
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(records):
seen = set(); total = Fraction()
for s,q,v in records:
if q not in seen: total += Fraction(1,v); seen.add(q)
return str(total)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('retransmission', solve([('a',N,2),('a',N,2)]), '1/2')
check('two sensors same sequence', solve([('a',N,2),('b',N,2)]), '1')
check('successive samples', solve([('a',N,2),('a',N+1,2)]), '1')
check('mixed duplicates', solve([('a',N,4),('b',N,4),('a',N,4)]), '1/2')
check('one packet', solve([('a',N,3)]), '1/3')
check('no packet', solve([]), '0')
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 |
|---|---|---|---|
| retransmission | 1/2 | 1/2 | Passed |
| two sensors same sequence | 1/2 | 1 | Failed |
| successive samples | 1 | 1 | Passed |
| mixed duplicates | 1/4 | 1/2 | Failed |
| one packet | 1/3 | 1/3 | Passed |
| no packet | 0 | 0 | Passed |
SHA-256 / aaa62ae6fcb61a75583e86d3865270c87ae59220d39f7ff53c518491a7fa361c
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(records):
seen = set(); total = Fraction()
for s,q,v in records:
if (s,q) not in seen: total += Fraction(1,v); seen.add((s,q))
return str(total)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('retransmission', solve([('a',N,2),('a',N,2)]), '1/2')
check('two sensors same sequence', solve([('a',N,2),('b',N,2)]), '1')
check('successive samples', solve([('a',N,2),('a',N+1,2)]), '1')
check('mixed duplicates', solve([('a',N,4),('b',N,4),('a',N,4)]), '1/2')
check('one packet', solve([('a',N,3)]), '1/3')
check('no packet', solve([]), '0')
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 |
|---|---|---|---|
| retransmission | 1/2 | 1/2 | Passed |
| two sensors same sequence | 1 | 1 | Passed |
| successive samples | 1 | 1 | Passed |
| mixed duplicates | 1/2 | 1/2 | Passed |
| one packet | 1/3 | 1/3 | Passed |
| no packet | 0 | 0 | Passed |
SHA-256 / 0699206efbda23f5c377cef4adee66ba3a81c73fb10e2616077294fc8a8df035
Verification & scope
Exact small scalar or two-axis models; no nonlinear dynamics, numerical conditioning, or real sensor noise simulation. 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 2026-09-29T14:38:53.415381+00:00.
Case digest / 6d08b2b3e577958810c7e9a2d712abe003cfbb01b62e1ac705ea72c99894cb6a