FA-50291 / PCM sample encoding / Open access

Pcm channel lifting chain: anchor channel · case 01

Reversible interchannel PCM coding loses its literal first-channel anchor.

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

ROOT CAUSE

Reversible interchannel PCM coding loses its literal first-channel anchor.

VERIFIED REPAIR

Use the stated conversion contract at anchor channel.

Unsuccessful approach: Omitting the anchor makes the channel count and common level unrecoverable.

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=[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	`[[0, 2, 3], [0, 1, 2]]`	`[[3, 2, 3], [1, 1, 2]]`	Failed
oracle 2	`[[0]]`	`[[7]]`	Failed
oracle 3	`[[]]`	`[[]]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[[0, 5, -4, 5]]`	`[[-2, 5, -4, 5]]`	Failed
oracle 6	`[[0, 0, 0], [0, 0, 0]]`	`[[0, 0, 0], [4, 0, 0]]`	Failed
oracle 7	`[[0, 2, -1, 4]]`	`[[1, 2, -1, 4]]`	Failed
variant packet 1	`[[0, 2, 3], [0, 1, 2], [0, 2, 3], [0, 1, 2]]`	`[[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]]`	Failed

SHA-256 / 5ec10b1bd642f3704694aaf27ab0344ff5dc5c4e5410401df028469463158ee3

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=[]
        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	`[[2, 3], [1, 2]]`	`[[3, 2, 3], [1, 1, 2]]`	Failed
oracle 2	`[[]]`	`[[7]]`	Failed
oracle 3	`[[]]`	`[[]]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[[5, -4, 5]]`	`[[-2, 5, -4, 5]]`	Failed
oracle 6	`[[0, 0], [0, 0]]`	`[[0, 0, 0], [4, 0, 0]]`	Failed
oracle 7	`[[2, -1, 4]]`	`[[1, 2, -1, 4]]`	Failed
variant packet 1	`[[2, 3], [1, 2], [2, 3], [1, 2]]`	`[[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]]`	Failed

SHA-256 / c66929bb080402fc170c4a780fd7405fb76afdcf7b6b9ccbecaadcb1d9c54f8f

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 2026-09-29T14:45:07.742954+00:00.

Case digest / 565f6b90e52a443c487a1104dec34b9b1dfc13d01bc73678bc14097ee9204517