FAILURE MAP
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FA-50296 / PCM sample encoding / Open access

Pcm channel lifting chain: residual reference · case 01

Adjacent-channel lifting always references first channel instead of its immediate predecessor.

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

ROOT CAUSE

Adjacent-channel lifting always references first channel instead of its immediate predecessor.

VERIFIED REPAIR

Use the stated conversion contract at residual reference.

Unsuccessful approach: Reversing residual orientation disagrees with inverse chain reconstruction.

Case contract

Losslessly represent each PCM frame as a first-channel anchor followed by differences from immediately preceding original channels; preserve empty and mono frames.

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(frames):
    out=[]
    for frame in frames:
        if not frame:
            out.append([])
            continue
        transformed=[frame[0]]
        previous=frame[0]
        for sample in frame[1:]:
            transformed.append(sample-frame[0])
            previous=sample
        out.append(transformed)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[3, 5, 8], [1, 2, 4]],)), [[3, 2, 3], [1, 1, 2]])
check('oracle 2', solve(*([[7]],)), [[7]])
check('oracle 3', solve(*([[]],)), [[]])
check('oracle 4', solve(*([],)), [])
check('oracle 5', solve(*([[-2, 3, -1, 4]],)), [[-2, 5, -4, 5]])
check('oracle 6', solve(*([[0, 0, 0], [4, 4, 4]],)), [[0, 0, 0], [4, 0, 0]])
check('oracle 7', solve(*([[1, 3, 2, 6]],)), [[1, 2, -1, 4]])
if N == 1: check('variant packet 1', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])
if N == 2: check('variant packet 2', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])
if N == 3: check('variant packet 3', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])
if N == 4: check('variant packet 4', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])
if N == 5: check('variant packet 5', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])
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[[3, 2, 5], [1, 1, 3]][[3, 2, 3], [1, 1, 2]]Failed
oracle 2[[7]][[7]]Passed
oracle 3[[]][[]]Passed
oracle 4[][]Passed
oracle 5[[-2, 5, 1, 6]][[-2, 5, -4, 5]]Failed
oracle 6[[0, 0, 0], [4, 0, 0]][[0, 0, 0], [4, 0, 0]]Passed
oracle 7[[1, 2, 1, 5]][[1, 2, -1, 4]]Failed
variant packet 1[[3, 2, 5], [1, 1, 3], [3, 2, 5], [1, 1, 3]][[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]]Failed

SHA-256 / 2d956681aba89864db79097b990038e29312f8f358966bbf920855557527af14

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(frames):
    out=[]
    for frame in frames:
        if not frame:
            out.append([])
            continue
        transformed=[frame[0]]
        previous=frame[0]
        for sample in frame[1:]:
            transformed.append(previous-sample)
            previous=sample
        out.append(transformed)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[3, 5, 8], [1, 2, 4]],)), [[3, 2, 3], [1, 1, 2]])
check('oracle 2', solve(*([[7]],)), [[7]])
check('oracle 3', solve(*([[]],)), [[]])
check('oracle 4', solve(*([],)), [])
check('oracle 5', solve(*([[-2, 3, -1, 4]],)), [[-2, 5, -4, 5]])
check('oracle 6', solve(*([[0, 0, 0], [4, 4, 4]],)), [[0, 0, 0], [4, 0, 0]])
check('oracle 7', solve(*([[1, 3, 2, 6]],)), [[1, 2, -1, 4]])
if N == 1: check('variant packet 1', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])
if N == 2: check('variant packet 2', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])
if N == 3: check('variant packet 3', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])
if N == 4: check('variant packet 4', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])
if N == 5: check('variant packet 5', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])
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[[3, -2, -3], [1, -1, -2]][[3, 2, 3], [1, 1, 2]]Failed
oracle 2[[7]][[7]]Passed
oracle 3[[]][[]]Passed
oracle 4[][]Passed
oracle 5[[-2, -5, 4, -5]][[-2, 5, -4, 5]]Failed
oracle 6[[0, 0, 0], [4, 0, 0]][[0, 0, 0], [4, 0, 0]]Passed
oracle 7[[1, -2, 1, -4]][[1, 2, -1, 4]]Failed
variant packet 1[[3, -2, -3], [1, -1, -2], [3, -2, -3], [1, -1, -2]][[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]]Failed

SHA-256 / 450ec5e8cde8ee675c5a41137d2cf1ebe0f84eefe685dfdf914711bb371d1964

3 / The verified repair

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

N = 1
observations = []
def solve(frames):
    out=[]
    for frame in frames:
        if not frame:
            out.append([])
            continue
        transformed=[frame[0]]
        previous=frame[0]
        for sample in frame[1:]:
            transformed.append(sample-previous)
            previous=sample
        out.append(transformed)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[3, 5, 8], [1, 2, 4]],)), [[3, 2, 3], [1, 1, 2]])
check('oracle 2', solve(*([[7]],)), [[7]])
check('oracle 3', solve(*([[]],)), [[]])
check('oracle 4', solve(*([],)), [])
check('oracle 5', solve(*([[-2, 3, -1, 4]],)), [[-2, 5, -4, 5]])
check('oracle 6', solve(*([[0, 0, 0], [4, 4, 4]],)), [[0, 0, 0], [4, 0, 0]])
check('oracle 7', solve(*([[1, 3, 2, 6]],)), [[1, 2, -1, 4]])
if N == 1: check('variant packet 1', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])
if N == 2: check('variant packet 2', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])
if N == 3: check('variant packet 3', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])
if N == 4: check('variant packet 4', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])
if N == 5: check('variant packet 5', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])
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[[3, 2, 3], [1, 1, 2]][[3, 2, 3], [1, 1, 2]]Passed
oracle 2[[7]][[7]]Passed
oracle 3[[]][[]]Passed
oracle 4[][]Passed
oracle 5[[-2, 5, -4, 5]][[-2, 5, -4, 5]]Passed
oracle 6[[0, 0, 0], [4, 0, 0]][[0, 0, 0], [4, 0, 0]]Passed
oracle 7[[1, 2, -1, 4]][[1, 2, -1, 4]]Passed
variant packet 1[[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]][[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]]Passed

SHA-256 / 26fd14af573ca2a19bba5ac989e4bf14157d913c7eb51f640848db2afe1de033

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 2026-09-29T14:45:07.782771+00:00.

Case digest / 792cb234acac68cde8ab46dfb6694346ef8f93754494290c32deb24d4cf25c3e