FAILURE MAP
← Case archive

FA-49146 / PCM sample encoding / Open access

Pcm slot status: parity status inclusion · case 01

Parity omits the invalid-status bit carried in the protected slot.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Parity omits the invalid-status bit carried in the protected slot.

VERIFIED REPAIR

Use the stated conversion contract at parity status inclusion.

Unsuccessful approach: Including logical validity instead of the encoded invalid flag reverses parity.

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))&1
        parity_ok=((bin(payload).count("1")+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 fixtureActualExpectedOutcome
oracle 1[[0, True, True], [None, True, False], [1, True, True], [None, False, True], [None, False, False]][[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]]Failed
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, True], [None, False, False], [None, True, False], [-1, True, True], [None, False, False], [None, False, True]][[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], [-1, True, True], [None, False, True], [None, False, False]][[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], [None, True, False], [None, False, True], [None, False, False]][[-1, True, True], [None, True, False], [None, False, False], [None, False, True]]Failed
variant packet 1[[0, True, True], [None, True, False], [1, True, True], [None, False, True], [None, False, False], [0, True, True], [None, True, False], [1, True, True], [None, False, True], [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 / ae29c227d479fae83e3a34cd5f720736654523df63fb5d4e0b3d46173a5e10f7

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>>(width+1))&1
        parity_ok=((bin(payload).count("1")+int(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 fixtureActualExpectedOutcome
oracle 1[[None, True, False], [1, True, True], [None, True, False], [None, False, True], [None, False, False]][[0, True, True], [None, True, False], [1, True, True], [None, False, False], [None, False, True]]Failed
oracle 2[[None, True, False], [-1, True, True], [-8, True, True], [None, True, False]][[-1, True, True], [None, True, False], [None, True, False], [-8, True, True]]Failed
oracle 3[][]Passed
oracle 4[[None, True, False], [-1, True, True], [None, False, True], [None, False, False], [0, True, True], [None, True, False], [None, False, False], [None, False, True]][[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], [None, True, False], [None, False, True], [None, False, False]][[None, True, False], [-1, True, True], [None, False, False], [None, False, True]]Failed
oracle 6[[2, True, True], [None, True, False], [4, True, True], [None, True, False], [None, True, False]][[None, True, False], [3, True, True], [None, True, False], [5, True, True], [6, True, True]]Failed
oracle 7[[None, True, False], [-1, True, True], [None, False, True], [None, False, False]][[-1, True, True], [None, True, False], [None, False, False], [None, False, True]]Failed
variant packet 1[[None, True, False], [1, True, True], [None, True, False], [None, False, True], [None, False, False], [None, True, False], [1, True, True], [None, True, False], [None, False, True], [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 / 84e90fd9c22dfd56ea8916a47aca4d89afce3dfd9f9ac1211ab02caa050b2df0

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 fixtureActualExpectedOutcome
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 2026-09-29T14:44:57.245626+00:00.

Case digest / 270314302f58b8110717c5cac67cb3fa04752488481dfcc6076e592c7618fe69