FA-49151 / PCM sample encoding / Open access
Pcm slot status: parity location · case 01
The invalid bit is reused as parity.
ROOT CAUSE
The invalid bit is reused as parity.
VERIFIED REPAIR
Use the stated conversion contract at parity location.
Unsuccessful approach: The sample low bit cannot stand in for the parity lane.
Case contract
Decode a stipulated slot: signed payload, one invalid bit, then even parity covering payload and invalid bit; invalid or corrupt samples return null plus status.
Why this case matters
Offline PCM interchange uses these exact bounded packet and sample representation decisions.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(slots, width):
out=[]
mask=(1<<width)-1
for slot in slots:
payload=slot&mask
valid=not bool(slot&(1<<width))
parity=(slot>>width)&1
parity_ok=((bin(payload).count("1")+int(not valid)+parity)%2)==0
sample=payload-(1<<width) if payload&(1<<(width-1)) else payload
out.append([sample if valid and parity_ok else None,valid,parity_ok])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 1, 33, 16, 48], 4)), [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]])
check('oracle 2', solve(*([15, 47, 8, 40], 4)), [[-1, True, True], [None, True, False], [None, True, False], [-8, True, True]])
check('oracle 3', solve(*([], 4)), [])
check('oracle 4', solve(*([0, 1, 2, 3, 4, 5, 6, 7], 1)), [[0, True, True], [None, True, False], [None, False, False], [None, False, True], [None, True, False], [-1, True, True], [None, False, True], [None, False, False]])
check('oracle 5', solve(*([7, 23, 8, 24], 3)), [[None, True, False], [-1, True, True], [None, False, False], [None, False, True]])
check('oracle 6', solve(*([2, 3, 4, 5, 6], 4)), [[None, True, False], [3, True, True], [None, True, False], [5, True, True], [6, True, True]])
check('oracle 7', solve(*([255, 767, 256, 768], 8)), [[-1, True, True], [None, True, False], [None, False, False], [None, False, True]])
if N == 1: check('variant packet 1', solve(*[[0, 1, 33, 16, 48, 0, 1, 33, 16, 48], 4]), [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]])
if N == 2: check('variant packet 2', solve(*[[0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48], 4]), [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]])
if N == 3: check('variant packet 3', solve(*[[0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48], 4]), [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]])
if N == 4: check('variant packet 4', solve(*[[0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48], 4]), [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]])
if N == 5: check('variant packet 5', solve(*[[0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48], 4]), [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]])
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 |
|---|---|---|---|
| oracle 1 | [[0, True, True], [None, True, False], [None, True, False], [None, False, True], [None, False, True]] | [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]] | Failed |
| oracle 2 | [[-1, True, True], [-1, True, True], [None, True, False], [None, True, False]] | [[-1, True, True], [None, True, False], [None, True, False], [-8, True, True]] | Failed |
| oracle 3 | [] | [] | Passed |
| oracle 4 | [[0, True, True], [None, True, False], [None, False, True], [None, False, False], [0, True, True], [None, True, False], [None, False, True], [None, False, False]] | [[0, True, True], [None, True, False], [None, False, False], [None, False, True], [None, True, False], [-1, True, True], [None, False, True], [None, False, False]] | Failed |
| oracle 5 | [[None, True, False], [None, True, False], [None, False, True], [None, False, True]] | [[None, True, False], [-1, True, True], [None, False, False], [None, False, True]] | Failed |
| oracle 6 | [[None, True, False], [3, True, True], [None, True, False], [5, True, True], [6, True, True]] | [[None, True, False], [3, True, True], [None, True, False], [5, True, True], [6, True, True]] | Passed |
| oracle 7 | [[-1, True, True], [-1, True, True], [None, False, True], [None, False, True]] | [[-1, True, True], [None, True, False], [None, False, False], [None, False, True]] | Failed |
| variant packet 1 | [[0, True, True], [None, True, False], [None, True, False], [None, False, True], [None, False, True], [0, True, True], [None, True, False], [None, True, False], [None, False, True], [None, False, True]] | [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]] | Failed |
SHA-256 / 9e0ccfcbda11d869caa39db0383f61adb556293213f1fff85c387ffd4a1b36c1
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(slots, width):
out=[]
mask=(1<<width)-1
for slot in slots:
payload=slot&mask
valid=not bool(slot&(1<<width))
parity=slot&1
parity_ok=((bin(payload).count("1")+int(not valid)+parity)%2)==0
sample=payload-(1<<width) if payload&(1<<(width-1)) else payload
out.append([sample if valid and parity_ok else None,valid,parity_ok])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 1, 33, 16, 48], 4)), [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]])
check('oracle 2', solve(*([15, 47, 8, 40], 4)), [[-1, True, True], [None, True, False], [None, True, False], [-8, True, True]])
check('oracle 3', solve(*([], 4)), [])
check('oracle 4', solve(*([0, 1, 2, 3, 4, 5, 6, 7], 1)), [[0, True, True], [None, True, False], [None, False, False], [None, False, True], [None, True, False], [-1, True, True], [None, False, True], [None, False, False]])
check('oracle 5', solve(*([7, 23, 8, 24], 3)), [[None, True, False], [-1, True, True], [None, False, False], [None, False, True]])
check('oracle 6', solve(*([2, 3, 4, 5, 6], 4)), [[None, True, False], [3, True, True], [None, True, False], [5, True, True], [6, True, True]])
check('oracle 7', solve(*([255, 767, 256, 768], 8)), [[-1, True, True], [None, True, False], [None, False, False], [None, False, True]])
if N == 1: check('variant packet 1', solve(*[[0, 1, 33, 16, 48, 0, 1, 33, 16, 48], 4]), [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]])
if N == 2: check('variant packet 2', solve(*[[0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48], 4]), [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]])
if N == 3: check('variant packet 3', solve(*[[0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48], 4]), [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]])
if N == 4: check('variant packet 4', solve(*[[0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48], 4]), [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]])
if N == 5: check('variant packet 5', solve(*[[0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48], 4]), [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]])
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 |
|---|---|---|---|
| oracle 1 | [[0, True, True], [1, True, True], [1, True, True], [None, False, False], [None, False, False]] | [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]] | Failed |
| oracle 2 | [[None, True, False], [None, True, False], [None, True, False], [None, True, False]] | [[-1, True, True], [None, True, False], [None, True, False], [-8, True, True]] | Failed |
| oracle 3 | [] | [] | Passed |
| oracle 4 | [[0, True, True], [-1, True, True], [None, False, False], [None, False, False], [0, True, True], [-1, True, True], [None, False, False], [None, False, False]] | [[0, True, True], [None, True, False], [None, False, False], [None, False, True], [None, True, False], [-1, True, True], [None, False, True], [None, False, False]] | Failed |
| oracle 5 | [[-1, True, True], [-1, True, True], [None, False, False], [None, False, False]] | [[None, True, False], [-1, True, True], [None, False, False], [None, False, True]] | Failed |
| oracle 6 | [[None, True, False], [None, True, False], [None, True, False], [None, True, False], [6, True, True]] | [[None, True, False], [3, True, True], [None, True, False], [5, True, True], [6, True, True]] | Failed |
| oracle 7 | [[None, True, False], [None, True, False], [None, False, False], [None, False, False]] | [[-1, True, True], [None, True, False], [None, False, False], [None, False, True]] | Failed |
| variant packet 1 | [[0, True, True], [1, True, True], [1, True, True], [None, False, False], [None, False, False], [0, True, True], [1, True, True], [1, True, True], [None, False, False], [None, False, False]] | [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]] | Failed |
SHA-256 / 7e09b61c450e91ae5b9a89db124b51164b13d0ce982f116a04dada0d5b8d24da
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(slots, width):
out=[]
mask=(1<<width)-1
for slot in slots:
payload=slot&mask
valid=not bool(slot&(1<<width))
parity=(slot>>(width+1))&1
parity_ok=((bin(payload).count("1")+int(not valid)+parity)%2)==0
sample=payload-(1<<width) if payload&(1<<(width-1)) else payload
out.append([sample if valid and parity_ok else None,valid,parity_ok])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 1, 33, 16, 48], 4)), [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]])
check('oracle 2', solve(*([15, 47, 8, 40], 4)), [[-1, True, True], [None, True, False], [None, True, False], [-8, True, True]])
check('oracle 3', solve(*([], 4)), [])
check('oracle 4', solve(*([0, 1, 2, 3, 4, 5, 6, 7], 1)), [[0, True, True], [None, True, False], [None, False, False], [None, False, True], [None, True, False], [-1, True, True], [None, False, True], [None, False, False]])
check('oracle 5', solve(*([7, 23, 8, 24], 3)), [[None, True, False], [-1, True, True], [None, False, False], [None, False, True]])
check('oracle 6', solve(*([2, 3, 4, 5, 6], 4)), [[None, True, False], [3, True, True], [None, True, False], [5, True, True], [6, True, True]])
check('oracle 7', solve(*([255, 767, 256, 768], 8)), [[-1, True, True], [None, True, False], [None, False, False], [None, False, True]])
if N == 1: check('variant packet 1', solve(*[[0, 1, 33, 16, 48, 0, 1, 33, 16, 48], 4]), [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]])
if N == 2: check('variant packet 2', solve(*[[0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48], 4]), [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]])
if N == 3: check('variant packet 3', solve(*[[0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48], 4]), [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]])
if N == 4: check('variant packet 4', solve(*[[0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48], 4]), [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]])
if N == 5: check('variant packet 5', solve(*[[0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48, 0, 1, 33, 16, 48], 4]), [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]])
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 |
|---|---|---|---|
| oracle 1 | [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]] | [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]] | Passed |
| oracle 2 | [[-1, True, True], [None, True, False], [None, True, False], [-8, True, True]] | [[-1, True, True], [None, True, False], [None, True, False], [-8, True, True]] | Passed |
| oracle 3 | [] | [] | Passed |
| oracle 4 | [[0, True, True], [None, True, False], [None, False, False], [None, False, True], [None, True, False], [-1, True, True], [None, False, True], [None, False, False]] | [[0, True, True], [None, True, False], [None, False, False], [None, False, True], [None, True, False], [-1, True, True], [None, False, True], [None, False, False]] | Passed |
| oracle 5 | [[None, True, False], [-1, True, True], [None, False, False], [None, False, True]] | [[None, True, False], [-1, True, True], [None, False, False], [None, False, True]] | Passed |
| oracle 6 | [[None, True, False], [3, True, True], [None, True, False], [5, True, True], [6, True, True]] | [[None, True, False], [3, True, True], [None, True, False], [5, True, True], [6, True, True]] | Passed |
| oracle 7 | [[-1, True, True], [None, True, False], [None, False, False], [None, False, True]] | [[-1, True, True], [None, True, False], [None, False, False], [None, False, True]] | Passed |
| variant packet 1 | [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]] | [[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True], [0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]] | Passed |
SHA-256 / 898fdb7733ffec8b0307105871c3f75c9420c3c20f29d769a3c8257da617da82
Verification & scope
Stipulated finite model; no claim of hardware timing or full file-format conformance. 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 2026-09-29T14:44:57.263377+00:00.
Case digest / 9ec30c75c5e528e1a5e296c1ae8dc6963a4b81e305a59a3764708f1e02609c96