FA-49621 / PCM sample encoding / Open access

Pcm subtractive dither: prequantizer noise · case 01

Dither is omitted before PCM precision reduction.

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

ROOT CAUSE

Dither is omitted before PCM precision reduction.

VERIFIED REPAIR

Use the stated conversion contract at prequantizer noise.

Unsuccessful approach: Subtracting noise uses the inverse sequence but decoder still subtracts original noise.

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
        code=(driven+step//2)//step
        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 fixture	Actual	Expected	Outcome
oracle 1	`[[0, 0], [1, 3], [1, 5], [1, 4]]`	`[[0, 0], [1, 3], [1, 5], [1, 4]]`	Passed
oracle 2	`[[-1, -3], [0, 1], [1, 1], [2, 5]]`	`[[-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	`[[2, 8], [2, 8]]`	`[[2, 8], [2, 8]]`	Passed
oracle 6	`[[1, 1], [1, 2], [1, 3], [1, 0]]`	`[[1, 1], [1, 2], [0, 1], [2, 2]]`	Failed
oracle 7	`[[1, 4], [-1, -7], [1, 8]]`	`[[2, 10], [-1, -7], [1, 8]]`	Failed
variant packet 1	`[[0, 0], [1, 3], [1, 5], [1, 4], [0, -1], [1, 5], [1, 4], [1, 3]]`	`[[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]]`	Failed

SHA-256 / 070d00f8dbeae010a2f4d396cbf1cc1e5d6d1811133340493aa377346e0b363b

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
        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 fixture	Actual	Expected	Outcome
oracle 1	`[[0, 0], [0, -1], [1, 5], [1, 4]]`	`[[0, 0], [1, 3], [1, 5], [1, 4]]`	Failed
oracle 2	`[[-2, -5], [0, 1], [0, -1], [2, 5]]`	`[[-1, -3], [-1, -1], [1, 1], [1, 3]]`	Failed
oracle 3	`[[0, -2], [1, 6], [0, 0]]`	`[[1, 2], [0, 2], [0, 0]]`	Failed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[[2, 8], [2, 8]]`	`[[2, 8], [2, 8]]`	Passed
oracle 6	`[[0, -1], [1, 2], [1, 3], [0, -2]]`	`[[1, 1], [1, 2], [0, 1], [2, 2]]`	Failed
oracle 7	`[[1, 4], [-1, -7], [1, 8]]`	`[[2, 10], [-1, -7], [1, 8]]`	Failed
variant packet 1	`[[0, 0], [0, -1], [1, 5], [1, 4], [0, -1], [1, 5], [1, 4], [1, 3]]`	`[[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]]`	Failed

SHA-256 / aac15bb02c7d1c88cd7703c583a19a956a959bbd57ae3b4b01bf19e3a421d16d

3 / The verified repair

Exit 0

"""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
        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 fixture	Actual	Expected	Outcome
oracle 1	`[[0, 0], [1, 3], [1, 5], [1, 4]]`	`[[0, 0], [1, 3], [1, 5], [1, 4]]`	Passed
oracle 2	`[[-1, -3], [-1, -1], [1, 1], [1, 3]]`	`[[-1, -3], [-1, -1], [1, 1], [1, 3]]`	Passed
oracle 3	`[[1, 2], [0, 2], [0, 0]]`	`[[1, 2], [0, 2], [0, 0]]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[[2, 8], [2, 8]]`	`[[2, 8], [2, 8]]`	Passed
oracle 6	`[[1, 1], [1, 2], [0, 1], [2, 2]]`	`[[1, 1], [1, 2], [0, 1], [2, 2]]`	Passed
oracle 7	`[[2, 10], [-1, -7], [1, 8]]`	`[[2, 10], [-1, -7], [1, 8]]`	Passed
variant packet 1	`[[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]]`	`[[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]]`	Passed

SHA-256 / 5564ae7a3d9537d69cbc47015aeeba2a38a760af253d10d894e0bb5507adc3cb

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 2026-09-29T14:45:01.639440+00:00.

Case digest / 5aadbfd51f6f3cefd9922b01bfeb95c3d2218d25b38221a39fb70fb2f16b6105