FA-49616 / PCM sample encoding / Open access

Pcm subtractive dither: noise phase · case 01

A deterministic PCM dither stream starts at the wrong sample phase.

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

ROOT CAUSE

A deterministic PCM dither stream starts at the wrong sample phase.

THE FAILURE

A deterministic PCM dither stream starts at the wrong sample phase.

Unsuccessful approach: Holding one noise sample replaces the prescribed sequence with a DC offset.

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+1)%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	`[[1, 3], [0, 1], [1, 4], [1, 3]]`	`[[0, 0], [1, 3], [1, 5], [1, 4]]`	Failed
oracle 2	`[[-2, -3], [0, -1], [0, 1], [2, 3]]`	`[[-1, -3], [-1, -1], [1, 1], [1, 3]]`	Failed
oracle 3	`[[0, 2], [0, 0], [1, 2]]`	`[[1, 2], [0, 2], [0, 0]]`	Failed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[[2, 8], [2, 8]]`	`[[2, 8], [2, 8]]`	Passed
oracle 6	`[[1, 2], [0, 1], [2, 2], [1, 1]]`	`[[1, 1], [1, 2], [0, 1], [2, 2]]`	Failed
oracle 7	`[[1, 5], [-1, -4], [1, 4]]`	`[[2, 10], [-1, -7], [1, 8]]`	Failed
variant packet 1	`[[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]]`	Failed

SHA-256 / d5433ce24b7c5a9b2d38c57602c575c3899494d848a606fb40499372619a6fa8

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[0]
        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, 4], [1, 4], [1, 4]]`	`[[0, 0], [1, 3], [1, 5], [1, 4]]`	Failed
oracle 2	`[[-1, -3], [0, -1], [1, 1], [2, 3]]`	`[[-1, -3], [-1, -1], [1, 1], [1, 3]]`	Failed
oracle 3	`[[1, 2], [1, 2], [1, 2]]`	`[[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, 1], [1, 1], [1, 1]]`	`[[1, 1], [1, 2], [0, 1], [2, 2]]`	Failed
oracle 7	`[[2, 10], [-1, -8], [1, 4]]`	`[[2, 10], [-1, -7], [1, 8]]`	Failed
variant packet 1	`[[0, 0], [1, 4], [1, 4], [1, 4], [0, 0], [1, 4], [1, 4], [1, 4]]`	`[[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]]`	Failed

SHA-256 / 4300f9524c753720f0dad20902d75e497295090930addddbd03aa31e55d3699e

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.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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 / e4ee98b9575027e697b5018b0a18ec3ffd1d0849c72afbaba7c302a47e17a1ea