FA-50301 / PCM sample encoding / Open access

Pcm channel lifting chain: source feedback · case 01

Interchannel lifting feeds an encoded residual back as source amplitude.

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

ROOT CAUSE

Interchannel lifting feeds an encoded residual back as source amplitude.

VERIFIED REPAIR

Use the stated conversion contract at source feedback.

Unsuccessful approach: Resetting to first channel prevents a true adjacent-channel chain.

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-previous)
            previous=sample-previous
        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 fixture	Actual	Expected	Outcome
oracle 1	`[[3, 2, 6], [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, -6, 10]]`	`[[-2, 5, -4, 5]]`	Failed
oracle 6	`[[0, 0, 0], [4, 0, 4]]`	`[[0, 0, 0], [4, 0, 0]]`	Failed
oracle 7	`[[1, 2, 0, 6]]`	`[[1, 2, -1, 4]]`	Failed
variant packet 1	`[[3, 2, 6], [1, 1, 3], [3, 2, 6], [1, 1, 3]]`	`[[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]]`	Failed

SHA-256 / 263086bf271f7755766e431f73802d8c762c7cb23c72fcba63ebf39ff3fe7342

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(sample-previous)
            previous=frame[0]
        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 fixture	Actual	Expected	Outcome
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 / 583019bdb8700b100e5365237fcc77d574ff59006d4e948382cee26cf22091c0

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 fixture	Actual	Expected	Outcome
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 2026-09-29T14:45:07.869798+00:00.

Case digest / be0d91b9b1ceb14a799bbaa7923640814cab49887b39ca7892a283edee24bff0