FA-49366 / PCM sample encoding / Open access

Pcm channel reconstruction: channel state update · case 01

Residual updates only the first PCM channel accumulator.

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

ROOT CAUSE

Residual updates only the first PCM channel accumulator.

VERIFIED REPAIR

Use the stated conversion contract at channel state update.

Unsuccessful approach: Adding each residual to the original seed prevents accumulation over time.

Case contract

Decode channel-banked residual PCM, resetting predictors only at specified frame boundaries and exporting final per-channel amplitudes.

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, seeds, resets):
    state=list(seeds)
    out=[]
    for index,frame in enumerate(frames):
        if index in resets:
            state=list(seeds)
        reconstructed=[]
        for channel,residual in enumerate(frame):
            state[0]+=residual
            reconstructed.append(state[channel])
        out.append(reconstructed)
    return [out,state]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[3, 2], [2, -1]], [2, 8], [])), [[[5, 10], [7, 9]], [7, 9]])
check('oracle 2', solve(*([[1, 2], [2, 3], [4, 1]], [1, 2], [1])), [[[2, 4], [3, 5], [7, 6]], [7, 6]])
check('oracle 3', solve(*([], [3, 4], [])), [[], [3, 4]])
check('oracle 4', solve(*([[1], [2], [-1]], [0], [2])), [[[1], [3], [-1]], [-1]])
check('oracle 5', solve(*([[-1, -1], [2, -2]], [-1, 4], [])), [[[-2, 3], [0, 1]], [0, 1]])
check('oracle 6', solve(*([[1, 2, 3]], [3, 2, 1], [0])), [[[4, 4, 4]], [4, 4, 4]])
check('oracle 7', solve(*([[0, 0], [0, 0]], [1, -1], [])), [[[1, -1], [1, -1]], [1, -1]])
if N == 1: check('variant packet 1', solve(*[[[3, 2], [2, -1], [3, 2], [2, -1]], [2, 8], []]), [[[5, 10], [7, 9], [10, 11], [12, 10]], [12, 10]])
if N == 2: check('variant packet 2', solve(*[[[3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1]], [2, 8], []]), [[[5, 10], [7, 9], [10, 11], [12, 10], [15, 12], [17, 11]], [17, 11]])
if N == 3: check('variant packet 3', solve(*[[[3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1]], [2, 8], []]), [[[5, 10], [7, 9], [10, 11], [12, 10], [15, 12], [17, 11], [20, 13], [22, 12]], [22, 12]])
if N == 4: check('variant packet 4', solve(*[[[3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1]], [2, 8], []]), [[[5, 10], [7, 9], [10, 11], [12, 10], [15, 12], [17, 11], [20, 13], [22, 12], [25, 14], [27, 13]], [27, 13]])
if N == 5: check('variant packet 5', solve(*[[[3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1]], [2, 8], []]), [[[5, 10], [7, 9], [10, 11], [12, 10], [15, 12], [17, 11], [20, 13], [22, 12], [25, 14], [27, 13], [30, 15], [32, 14]], [32, 14]])
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	`[[[5, 8], [9, 8]], [8, 8]]`	`[[[5, 10], [7, 9]], [7, 9]]`	Failed
oracle 2	`[[[2, 2], [3, 2], [10, 2]], [11, 2]]`	`[[[2, 4], [3, 5], [7, 6]], [7, 6]]`	Failed
oracle 3	`[[], [3, 4]]`	`[[], [3, 4]]`	Passed
oracle 4	`[[[1], [3], [-1]], [-1]]`	`[[[1], [3], [-1]], [-1]]`	Passed
oracle 5	`[[[-2, 4], [-1, 4]], [-3, 4]]`	`[[[-2, 3], [0, 1]], [0, 1]]`	Failed
oracle 6	`[[[4, 2, 1]], [9, 2, 1]]`	`[[[4, 4, 4]], [4, 4, 4]]`	Failed
oracle 7	`[[[1, -1], [1, -1]], [1, -1]]`	`[[[1, -1], [1, -1]], [1, -1]]`	Passed
variant packet 1	`[[[5, 8], [9, 8], [11, 8], [15, 8]], [14, 8]]`	`[[[5, 10], [7, 9], [10, 11], [12, 10]], [12, 10]]`	Failed

SHA-256 / 40bc350478dd52220d9bc797a6e0dd2e7d2ff0055228038ccb4829729f95c3ae

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(frames, seeds, resets):
    state=list(seeds)
    out=[]
    for index,frame in enumerate(frames):
        if index in resets:
            state=list(seeds)
        reconstructed=[]
        for channel,residual in enumerate(frame):
            state[channel]=seeds[channel]+residual
            reconstructed.append(state[channel])
        out.append(reconstructed)
    return [out,state]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[3, 2], [2, -1]], [2, 8], [])), [[[5, 10], [7, 9]], [7, 9]])
check('oracle 2', solve(*([[1, 2], [2, 3], [4, 1]], [1, 2], [1])), [[[2, 4], [3, 5], [7, 6]], [7, 6]])
check('oracle 3', solve(*([], [3, 4], [])), [[], [3, 4]])
check('oracle 4', solve(*([[1], [2], [-1]], [0], [2])), [[[1], [3], [-1]], [-1]])
check('oracle 5', solve(*([[-1, -1], [2, -2]], [-1, 4], [])), [[[-2, 3], [0, 1]], [0, 1]])
check('oracle 6', solve(*([[1, 2, 3]], [3, 2, 1], [0])), [[[4, 4, 4]], [4, 4, 4]])
check('oracle 7', solve(*([[0, 0], [0, 0]], [1, -1], [])), [[[1, -1], [1, -1]], [1, -1]])
if N == 1: check('variant packet 1', solve(*[[[3, 2], [2, -1], [3, 2], [2, -1]], [2, 8], []]), [[[5, 10], [7, 9], [10, 11], [12, 10]], [12, 10]])
if N == 2: check('variant packet 2', solve(*[[[3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1]], [2, 8], []]), [[[5, 10], [7, 9], [10, 11], [12, 10], [15, 12], [17, 11]], [17, 11]])
if N == 3: check('variant packet 3', solve(*[[[3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1]], [2, 8], []]), [[[5, 10], [7, 9], [10, 11], [12, 10], [15, 12], [17, 11], [20, 13], [22, 12]], [22, 12]])
if N == 4: check('variant packet 4', solve(*[[[3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1]], [2, 8], []]), [[[5, 10], [7, 9], [10, 11], [12, 10], [15, 12], [17, 11], [20, 13], [22, 12], [25, 14], [27, 13]], [27, 13]])
if N == 5: check('variant packet 5', solve(*[[[3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1]], [2, 8], []]), [[[5, 10], [7, 9], [10, 11], [12, 10], [15, 12], [17, 11], [20, 13], [22, 12], [25, 14], [27, 13], [30, 15], [32, 14]], [32, 14]])
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	`[[[5, 10], [4, 7]], [4, 7]]`	`[[[5, 10], [7, 9]], [7, 9]]`	Failed
oracle 2	`[[[2, 4], [3, 5], [5, 3]], [5, 3]]`	`[[[2, 4], [3, 5], [7, 6]], [7, 6]]`	Failed
oracle 3	`[[], [3, 4]]`	`[[], [3, 4]]`	Passed
oracle 4	`[[[1], [2], [-1]], [-1]]`	`[[[1], [3], [-1]], [-1]]`	Failed
oracle 5	`[[[-2, 3], [1, 2]], [1, 2]]`	`[[[-2, 3], [0, 1]], [0, 1]]`	Failed
oracle 6	`[[[4, 4, 4]], [4, 4, 4]]`	`[[[4, 4, 4]], [4, 4, 4]]`	Passed
oracle 7	`[[[1, -1], [1, -1]], [1, -1]]`	`[[[1, -1], [1, -1]], [1, -1]]`	Passed
variant packet 1	`[[[5, 10], [4, 7], [5, 10], [4, 7]], [4, 7]]`	`[[[5, 10], [7, 9], [10, 11], [12, 10]], [12, 10]]`	Failed

SHA-256 / d67c3d7f0e320d1e91f99734f29f936c35aead31bb95fb3f63eb432cac46ded9

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(frames, seeds, resets):
    state=list(seeds)
    out=[]
    for index,frame in enumerate(frames):
        if index in resets:
            state=list(seeds)
        reconstructed=[]
        for channel,residual in enumerate(frame):
            state[channel]+=residual
            reconstructed.append(state[channel])
        out.append(reconstructed)
    return [out,state]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[3, 2], [2, -1]], [2, 8], [])), [[[5, 10], [7, 9]], [7, 9]])
check('oracle 2', solve(*([[1, 2], [2, 3], [4, 1]], [1, 2], [1])), [[[2, 4], [3, 5], [7, 6]], [7, 6]])
check('oracle 3', solve(*([], [3, 4], [])), [[], [3, 4]])
check('oracle 4', solve(*([[1], [2], [-1]], [0], [2])), [[[1], [3], [-1]], [-1]])
check('oracle 5', solve(*([[-1, -1], [2, -2]], [-1, 4], [])), [[[-2, 3], [0, 1]], [0, 1]])
check('oracle 6', solve(*([[1, 2, 3]], [3, 2, 1], [0])), [[[4, 4, 4]], [4, 4, 4]])
check('oracle 7', solve(*([[0, 0], [0, 0]], [1, -1], [])), [[[1, -1], [1, -1]], [1, -1]])
if N == 1: check('variant packet 1', solve(*[[[3, 2], [2, -1], [3, 2], [2, -1]], [2, 8], []]), [[[5, 10], [7, 9], [10, 11], [12, 10]], [12, 10]])
if N == 2: check('variant packet 2', solve(*[[[3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1]], [2, 8], []]), [[[5, 10], [7, 9], [10, 11], [12, 10], [15, 12], [17, 11]], [17, 11]])
if N == 3: check('variant packet 3', solve(*[[[3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1]], [2, 8], []]), [[[5, 10], [7, 9], [10, 11], [12, 10], [15, 12], [17, 11], [20, 13], [22, 12]], [22, 12]])
if N == 4: check('variant packet 4', solve(*[[[3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1]], [2, 8], []]), [[[5, 10], [7, 9], [10, 11], [12, 10], [15, 12], [17, 11], [20, 13], [22, 12], [25, 14], [27, 13]], [27, 13]])
if N == 5: check('variant packet 5', solve(*[[[3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1], [3, 2], [2, -1]], [2, 8], []]), [[[5, 10], [7, 9], [10, 11], [12, 10], [15, 12], [17, 11], [20, 13], [22, 12], [25, 14], [27, 13], [30, 15], [32, 14]], [32, 14]])
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	`[[[5, 10], [7, 9]], [7, 9]]`	`[[[5, 10], [7, 9]], [7, 9]]`	Passed
oracle 2	`[[[2, 4], [3, 5], [7, 6]], [7, 6]]`	`[[[2, 4], [3, 5], [7, 6]], [7, 6]]`	Passed
oracle 3	`[[], [3, 4]]`	`[[], [3, 4]]`	Passed
oracle 4	`[[[1], [3], [-1]], [-1]]`	`[[[1], [3], [-1]], [-1]]`	Passed
oracle 5	`[[[-2, 3], [0, 1]], [0, 1]]`	`[[[-2, 3], [0, 1]], [0, 1]]`	Passed
oracle 6	`[[[4, 4, 4]], [4, 4, 4]]`	`[[[4, 4, 4]], [4, 4, 4]]`	Passed
oracle 7	`[[[1, -1], [1, -1]], [1, -1]]`	`[[[1, -1], [1, -1]], [1, -1]]`	Passed
variant packet 1	`[[[5, 10], [7, 9], [10, 11], [12, 10]], [12, 10]]`	`[[[5, 10], [7, 9], [10, 11], [12, 10]], [12, 10]]`	Passed

SHA-256 / bd77d255bc46a03c0e54aefecfad0107d3ab5dcd73e9f1f57c9a170163b565bf

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 2026-09-29T14:44:59.289627+00:00.

Case digest / faea4d20da39b691d2ad5ea8267fd1c46d02cf46d6514d64ee190fdf845cd9aa