FAILURE MAP
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FA-49061 / PCM sample encoding / Open access

Xor coded pcm: width mask · case 01

A single boundary bit is used where a contiguous field mask is required.

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

ROOT CAUSE

A single boundary bit is used where a contiguous field mask is required.

VERIFIED REPAIR

Use the stated conversion contract at width mask.

Unsuccessful approach: Excluding the sign line during masking erases all negative samples.

Case contract

Undo a per-line XOR inversion map within a signed PCM field before interpreting sign and detecting canonical zero.

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(codes, width, xor_mask):
    field=(1<<width)
    out=[]
    for raw in codes:
        code=(raw^xor_mask)&field
        sign=1<<(width-1)
        value=code-(1<<width) if code&sign else code
        out.append([value, code==0])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 3, 7, 8, 15], 4, 5)), [[5, False], [6, False], [2, False], [-3, False], [-6, False]])
check('oracle 2', solve(*([8, 0, 15], 4, 8)), [[0, True], [-8, False], [7, False]])
check('oracle 3', solve(*([16, 31, 0], 4, 32)), [[0, True], [-1, False], [0, True]])
check('oracle 4', solve(*([0, 255], 8, 85)), [[85, False], [-86, False]])
check('oracle 5', solve(*([], 3, 7)), [])
check('oracle 6', solve(*([0, 1], 1, 1)), [[-1, False], [0, True]])
check('oracle 7', solve(*([3, 4, 7], 3, 2)), [[1, False], [-2, False], [-3, False]])
if N == 1: check('variant packet 1', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 2: check('variant packet 2', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 3: check('variant packet 3', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 4: check('variant packet 4', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 5: check('variant packet 5', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, 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 fixtureActualExpectedOutcome
oracle 1[[0, True], [0, True], [0, True], [0, True], [0, True]][[5, False], [6, False], [2, False], [-3, False], [-6, False]]Failed
oracle 2[[0, True], [0, True], [0, True]][[0, True], [-8, False], [7, False]]Failed
oracle 3[[16, False], [16, False], [0, True]][[0, True], [-1, False], [0, True]]Failed
oracle 4[[0, True], [0, True]][[85, False], [-86, False]]Failed
oracle 5[][]Passed
oracle 6[[0, True], [0, True]][[-1, False], [0, True]]Failed
oracle 7[[0, True], [0, True], [0, True]][[1, False], [-2, False], [-3, False]]Failed
variant packet 1[[0, True], [0, True], [0, True], [0, True], [0, True], [0, True], [0, True], [0, True], [0, True], [0, True]][[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]]Failed

SHA-256 / 79d6fad123afae3c0dc596dda2c4195505b6651059c7c70686f3355eff0ffea3

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(codes, width, xor_mask):
    field=(1<<(width-1))-1
    out=[]
    for raw in codes:
        code=(raw^xor_mask)&field
        sign=1<<(width-1)
        value=code-(1<<width) if code&sign else code
        out.append([value, code==0])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 3, 7, 8, 15], 4, 5)), [[5, False], [6, False], [2, False], [-3, False], [-6, False]])
check('oracle 2', solve(*([8, 0, 15], 4, 8)), [[0, True], [-8, False], [7, False]])
check('oracle 3', solve(*([16, 31, 0], 4, 32)), [[0, True], [-1, False], [0, True]])
check('oracle 4', solve(*([0, 255], 8, 85)), [[85, False], [-86, False]])
check('oracle 5', solve(*([], 3, 7)), [])
check('oracle 6', solve(*([0, 1], 1, 1)), [[-1, False], [0, True]])
check('oracle 7', solve(*([3, 4, 7], 3, 2)), [[1, False], [-2, False], [-3, False]])
if N == 1: check('variant packet 1', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 2: check('variant packet 2', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 3: check('variant packet 3', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 4: check('variant packet 4', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 5: check('variant packet 5', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, 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 fixtureActualExpectedOutcome
oracle 1[[5, False], [6, False], [2, False], [5, False], [2, False]][[5, False], [6, False], [2, False], [-3, False], [-6, False]]Failed
oracle 2[[0, True], [0, True], [7, False]][[0, True], [-8, False], [7, False]]Failed
oracle 3[[0, True], [7, False], [0, True]][[0, True], [-1, False], [0, True]]Failed
oracle 4[[85, False], [42, False]][[85, False], [-86, False]]Failed
oracle 5[][]Passed
oracle 6[[0, True], [0, True]][[-1, False], [0, True]]Failed
oracle 7[[1, False], [2, False], [1, False]][[1, False], [-2, False], [-3, False]]Failed
variant packet 1[[5, False], [6, False], [2, False], [5, False], [2, False], [5, False], [6, False], [2, False], [5, False], [2, False]][[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]]Failed

SHA-256 / 964cec19f243f94757498024ab4b18bfcbad7cee6819e04911278c50a9a519e6

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(codes, width, xor_mask):
    field=(1<<width)-1
    out=[]
    for raw in codes:
        code=(raw^xor_mask)&field
        sign=1<<(width-1)
        value=code-(1<<width) if code&sign else code
        out.append([value, code==0])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 3, 7, 8, 15], 4, 5)), [[5, False], [6, False], [2, False], [-3, False], [-6, False]])
check('oracle 2', solve(*([8, 0, 15], 4, 8)), [[0, True], [-8, False], [7, False]])
check('oracle 3', solve(*([16, 31, 0], 4, 32)), [[0, True], [-1, False], [0, True]])
check('oracle 4', solve(*([0, 255], 8, 85)), [[85, False], [-86, False]])
check('oracle 5', solve(*([], 3, 7)), [])
check('oracle 6', solve(*([0, 1], 1, 1)), [[-1, False], [0, True]])
check('oracle 7', solve(*([3, 4, 7], 3, 2)), [[1, False], [-2, False], [-3, False]])
if N == 1: check('variant packet 1', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 2: check('variant packet 2', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 3: check('variant packet 3', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 4: check('variant packet 4', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 5: check('variant packet 5', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, 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 fixtureActualExpectedOutcome
oracle 1[[5, False], [6, False], [2, False], [-3, False], [-6, False]][[5, False], [6, False], [2, False], [-3, False], [-6, False]]Passed
oracle 2[[0, True], [-8, False], [7, False]][[0, True], [-8, False], [7, False]]Passed
oracle 3[[0, True], [-1, False], [0, True]][[0, True], [-1, False], [0, True]]Passed
oracle 4[[85, False], [-86, False]][[85, False], [-86, False]]Passed
oracle 5[][]Passed
oracle 6[[-1, False], [0, True]][[-1, False], [0, True]]Passed
oracle 7[[1, False], [-2, False], [-3, False]][[1, False], [-2, False], [-3, False]]Passed
variant packet 1[[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]][[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]]Passed

SHA-256 / 677436fbf1c31a2198a83bd1495490a6162935ebca710bd28a5712c0b7f3cf3d

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 2026-09-29T14:44:56.385097+00:00.

Case digest / 82c2ebbb137b7a39a574244700bdf77f0223463b88db81c6fb1bc3b765eb5ba4