FAILURE MAP
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FA-49161 / PCM sample encoding / Open access

Pcm slot status: payload mask · case 01

Status bits are retained in numerical PCM reconstruction.

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

ROOT CAUSE

Status bits are retained in numerical PCM reconstruction.

THE FAILURE

Status bits are retained in numerical PCM reconstruction.

Unsuccessful approach: Removing the top payload bit loses sample polarity.

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
        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], [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], [31, 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], [4, 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], [511, 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 / 70aaae8076bda39d5d469d240a45673b927a1d8f0d5647677c07db351c33a850

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>>1)
        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[[None, True, False], [7, True, True], [0, True, True], [None, True, False]][[-1, True, True], [None, True, False], [None, True, False], [-8, True, True]]Failed
oracle 3[][]Passed
oracle 4[[0, True, True], [0, True, True], [None, False, False], [None, False, False], [None, True, False], [None, True, False], [None, False, True], [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[[3, True, True], [None, True, False], [None, False, False], [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[[None, True, False], [127, True, True], [None, False, False], [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], [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 / e3cbfd0dba708ec616646ced72b81776cb69f7c920260129d05a4d1937b85c0c

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:44:57.290261+00:00.

Case digest / 82ebeab0089669c6381d2b9a969bc88c946989be4fd9edc59b3f6d8e5551dc42