FAILURE MAP
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FA-49041 / PCM sample encoding / Open access

Xor coded pcm: mask operation · case 01

A hardware line-inversion map is applied as a bit-set mask.

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

ROOT CAUSE

A hardware line-inversion map is applied as a bit-set mask.

VERIFIED REPAIR

Use the stated conversion contract at mask operation.

Unsuccessful approach: AND filtering destroys every non-inverted signal line.

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)-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], [7, False], [7, False], [-3, False], [-1, False]][[5, False], [6, False], [2, False], [-3, False], [-6, False]]Failed
oracle 2[[-8, False], [-8, False], [-1, False]][[0, True], [-8, False], [7, False]]Failed
oracle 3[[0, True], [-1, False], [0, True]][[0, True], [-1, False], [0, True]]Passed
oracle 4[[85, False], [-1, False]][[85, False], [-86, False]]Failed
oracle 5[][]Passed
oracle 6[[-1, False], [-1, False]][[-1, False], [0, True]]Failed
oracle 7[[3, False], [-2, False], [-1, False]][[1, False], [-2, False], [-3, False]]Failed
variant packet 1[[5, False], [7, False], [7, False], [-3, False], [-1, False], [5, False], [7, False], [7, False], [-3, False], [-1, False]][[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]]Failed

SHA-256 / 2142d41c37290a7382fd652a52d8946f015b22060f72c2b9578d2791e549dd72

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
    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], [1, False], [5, False], [0, True], [5, False]][[5, False], [6, False], [2, False], [-3, False], [-6, False]]Failed
oracle 2[[-8, False], [0, True], [-8, False]][[0, True], [-8, False], [7, False]]Failed
oracle 3[[0, True], [0, True], [0, True]][[0, True], [-1, False], [0, True]]Failed
oracle 4[[0, True], [85, False]][[85, False], [-86, False]]Failed
oracle 5[][]Passed
oracle 6[[0, True], [-1, False]][[-1, False], [0, True]]Failed
oracle 7[[2, False], [0, True], [2, False]][[1, False], [-2, False], [-3, False]]Failed
variant packet 1[[0, True], [1, False], [5, False], [0, True], [5, False], [0, True], [1, False], [5, False], [0, True], [5, False]][[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]]Failed

SHA-256 / 3bd2e14577e7525415702be2a5a7640a404a6ac69485e98aaca57625ac244e07

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 2026-09-29T14:44:56.253192+00:00.

Case digest / a554036bf7ee2bcfb730af2059a323cf4e964253303202019b78155c574fa981