FAILURE MAP
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FA-49631 / PCM sample encoding / Open access

Pcm subtractive dither: quantizer step · case 01

Dithered amplitude is emitted without division into PCM code bins.

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

ROOT CAUSE

Dithered amplitude is emitted without division into PCM code bins.

THE FAILURE

Dithered amplitude is emitted without division into PCM code bins.

Unsuccessful approach: Doubling the quantization step changes the agreed reconstruction scale.

Case contract

Stipulated subtractive-dither PCM converter with a repeating explicit integer noise sequence, even quantizer step, and both wire codes and reconstructed 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(samples, noises, step):
    out=[]
    for index,sample in enumerate(samples):
        noise=noises[index%len(noises)]
        driven=sample+noise
        code=(driven+step//2)
        restored=code*step-noise
        out.append([code,restored])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, 2, 3, 4], [0, 1, -1], 4)), [[0, 0], [1, 3], [1, 5], [1, 4]])
check('oracle 2', solve(*([-3, -1, 1, 3], [1, -1], 2)), [[-1, -3], [-1, -1], [1, 1], [1, 3]])
check('oracle 3', solve(*([0, 0, 0], [2, -2, 0], 4)), [[1, 2], [0, 2], [0, 0]])
check('oracle 4', solve(*([], [1], 4)), [])
check('oracle 5', solve(*([8, 9], [0], 4)), [[2, 8], [2, 8]])
check('oracle 6', solve(*([1, 1, 1, 1], [1, 0, -1, 2], 2)), [[1, 1], [1, 2], [0, 1], [2, 2]])
check('oracle 7', solve(*([7, -7, 5], [2, 1, -2], 6)), [[2, 10], [-1, -7], [1, 8]])
if N == 1: check('variant packet 1', solve(*[[1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]])
if N == 2: check('variant packet 2', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5]])
if N == 3: check('variant packet 3', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5], [0, 0], [1, 3], [1, 5], [1, 4]])
if N == 4: check('variant packet 4', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5], [0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]])
if N == 5: check('variant packet 5', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5], [0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5]])
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, 12], [5, 19], [4, 17], [6, 24]][[0, 0], [1, 3], [1, 5], [1, 4]]Failed
oracle 2[[-1, -3], [-1, -1], [3, 5], [3, 7]][[-1, -3], [-1, -1], [1, 1], [1, 3]]Failed
oracle 3[[4, 14], [0, 2], [2, 8]][[1, 2], [0, 2], [0, 0]]Failed
oracle 4[][]Passed
oracle 5[[10, 40], [11, 44]][[2, 8], [2, 8]]Failed
oracle 6[[3, 5], [2, 4], [1, 3], [4, 6]][[1, 1], [1, 2], [0, 1], [2, 2]]Failed
oracle 7[[12, 70], [-3, -19], [6, 38]][[2, 10], [-1, -7], [1, 8]]Failed
variant packet 1[[3, 12], [5, 19], [4, 17], [6, 24], [4, 15], [3, 13], [5, 20], [7, 27]][[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]]Failed

SHA-256 / 54637750f201c824612ee2543ebaea1732f8319ae7827c59f1cefa2a8cdcdc37

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(samples, noises, step):
    out=[]
    for index,sample in enumerate(samples):
        noise=noises[index%len(noises)]
        driven=sample+noise
        code=(driven+step//2)//(step*2)
        restored=code*step-noise
        out.append([code,restored])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, 2, 3, 4], [0, 1, -1], 4)), [[0, 0], [1, 3], [1, 5], [1, 4]])
check('oracle 2', solve(*([-3, -1, 1, 3], [1, -1], 2)), [[-1, -3], [-1, -1], [1, 1], [1, 3]])
check('oracle 3', solve(*([0, 0, 0], [2, -2, 0], 4)), [[1, 2], [0, 2], [0, 0]])
check('oracle 4', solve(*([], [1], 4)), [])
check('oracle 5', solve(*([8, 9], [0], 4)), [[2, 8], [2, 8]])
check('oracle 6', solve(*([1, 1, 1, 1], [1, 0, -1, 2], 2)), [[1, 1], [1, 2], [0, 1], [2, 2]])
check('oracle 7', solve(*([7, -7, 5], [2, 1, -2], 6)), [[2, 10], [-1, -7], [1, 8]])
if N == 1: check('variant packet 1', solve(*[[1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]])
if N == 2: check('variant packet 2', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5]])
if N == 3: check('variant packet 3', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5], [0, 0], [1, 3], [1, 5], [1, 4]])
if N == 4: check('variant packet 4', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5], [0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]])
if N == 5: check('variant packet 5', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5], [0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5]])
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, 0], [0, -1], [0, 1], [0, 0]][[0, 0], [1, 3], [1, 5], [1, 4]]Failed
oracle 2[[-1, -3], [-1, -1], [0, -1], [0, 1]][[-1, -3], [-1, -1], [1, 1], [1, 3]]Failed
oracle 3[[0, -2], [0, 2], [0, 0]][[1, 2], [0, 2], [0, 0]]Failed
oracle 4[][]Passed
oracle 5[[1, 4], [1, 4]][[2, 8], [2, 8]]Failed
oracle 6[[0, -1], [0, 0], [0, 1], [1, 0]][[1, 1], [1, 2], [0, 1], [2, 2]]Failed
oracle 7[[1, 4], [-1, -7], [0, 2]][[2, 10], [-1, -7], [1, 8]]Failed
variant packet 1[[0, 0], [0, -1], [0, 1], [0, 0], [0, -1], [0, 1], [0, 0], [0, -1]][[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]]Failed

SHA-256 / 8dc146e6b802dc8551080e4942b3ee2b8db81d7ee02da214bbbeaa53ccc81db8

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:45:01.798045+00:00.

Case digest / 90615bc88b6e2edf4d939ac8949ce66e68df5c07335f69cd126e53783d961d46