FAILURE MAP
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FA-48926 / PCM sample encoding / Open access

Ones complement pcm: positive magnitude · case 01

Positive codes are biased despite the direct positive mapping.

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

ROOT CAUSE

Positive codes are biased despite the direct positive mapping.

THE FAILURE

Positive codes are biased despite the direct positive mapping.

Unsuccessful approach: Subtracting a bias clips low positive samples.

Case contract

Decode bounded ones-complement PCM fields; optionally preserve a per-sample negative-zero sideband while numeric zero stays JSON integer zero.

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(codes, width, preserve_negative_zero):
    mask=(1<<width)-1
    sign=1<<(width-1)
    values=[]
    negative_zero=[]
    for raw in codes:
        code=raw&mask
        magnitude=(~code)&mask if code&sign else code+1
        value=-magnitude if code&sign else magnitude
        values.append(value)
        negative_zero.append(bool(preserve_negative_zero and code==mask))
    return [values,negative_zero]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 1, 7, 8, 14, 15], 4, True)), [[0, 1, 7, -7, -1, 0], [False, False, False, False, False, True]])
check('oracle 2', solve(*([15, 0, 8], 4, False)), [[0, 0, -7], [False, False, False]])
check('oracle 3', solve(*([31, 16, 17], 4, True)), [[0, 0, 1], [True, False, False]])
check('oracle 4', solve(*([], 4, True)), [[], []])
check('oracle 5', solve(*([0, 3, 4, 6, 7], 3, True)), [[0, 3, -3, -1, 0], [False, False, False, False, True]])
check('oracle 6', solve(*([255, 128, 254, 127], 8, False)), [[0, -127, -1, 127], [False, False, False, False]])
check('oracle 7', solve(*([255], 8, True)), [[0], [True]])
if N == 1: check('variant packet 1', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True]])
if N == 2: check('variant packet 2', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True]])
if N == 3: check('variant packet 3', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True]])
if N == 4: check('variant packet 4', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True]])
if N == 5: check('variant packet 5', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True]])
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[[1, 2, 8, -7, -1, 0], [False, False, False, False, False, True]][[0, 1, 7, -7, -1, 0], [False, False, False, False, False, True]]Failed
oracle 2[[0, 1, -7], [False, False, False]][[0, 0, -7], [False, False, False]]Failed
oracle 3[[0, 1, 2], [True, False, False]][[0, 0, 1], [True, False, False]]Failed
oracle 4[[], []][[], []]Passed
oracle 5[[1, 4, -3, -1, 0], [False, False, False, False, True]][[0, 3, -3, -1, 0], [False, False, False, False, True]]Failed
oracle 6[[0, -127, -1, 128], [False, False, False, False]][[0, -127, -1, 127], [False, False, False, False]]Failed
oracle 7[[0], [True]][[0], [True]]Passed
variant packet 1[[1, 2, 8, -7, -1, 0, 1, 2, 8, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True]][[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True]]Failed

SHA-256 / 88e1adcc5ce9bef4d8290188ad276871ca95138832e4c86d0b9ae6aaa89f66d5

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(codes, width, preserve_negative_zero):
    mask=(1<<width)-1
    sign=1<<(width-1)
    values=[]
    negative_zero=[]
    for raw in codes:
        code=raw&mask
        magnitude=(~code)&mask if code&sign else max(0,code-1)
        value=-magnitude if code&sign else magnitude
        values.append(value)
        negative_zero.append(bool(preserve_negative_zero and code==mask))
    return [values,negative_zero]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 1, 7, 8, 14, 15], 4, True)), [[0, 1, 7, -7, -1, 0], [False, False, False, False, False, True]])
check('oracle 2', solve(*([15, 0, 8], 4, False)), [[0, 0, -7], [False, False, False]])
check('oracle 3', solve(*([31, 16, 17], 4, True)), [[0, 0, 1], [True, False, False]])
check('oracle 4', solve(*([], 4, True)), [[], []])
check('oracle 5', solve(*([0, 3, 4, 6, 7], 3, True)), [[0, 3, -3, -1, 0], [False, False, False, False, True]])
check('oracle 6', solve(*([255, 128, 254, 127], 8, False)), [[0, -127, -1, 127], [False, False, False, False]])
check('oracle 7', solve(*([255], 8, True)), [[0], [True]])
if N == 1: check('variant packet 1', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True]])
if N == 2: check('variant packet 2', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True]])
if N == 3: check('variant packet 3', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True]])
if N == 4: check('variant packet 4', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True]])
if N == 5: check('variant packet 5', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True]])
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, 6, -7, -1, 0], [False, False, False, False, False, True]][[0, 1, 7, -7, -1, 0], [False, False, False, False, False, True]]Failed
oracle 2[[0, 0, -7], [False, False, False]][[0, 0, -7], [False, False, False]]Passed
oracle 3[[0, 0, 0], [True, False, False]][[0, 0, 1], [True, False, False]]Failed
oracle 4[[], []][[], []]Passed
oracle 5[[0, 2, -3, -1, 0], [False, False, False, False, True]][[0, 3, -3, -1, 0], [False, False, False, False, True]]Failed
oracle 6[[0, -127, -1, 126], [False, False, False, False]][[0, -127, -1, 127], [False, False, False, False]]Failed
oracle 7[[0], [True]][[0], [True]]Passed
variant packet 1[[0, 0, 6, -7, -1, 0, 0, 0, 6, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True]][[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True]]Failed

SHA-256 / d1a3150b13fb23150fde105e69424c220672af36b41f3c6e1b9aac292939c323

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 2026-09-29T14:44:55.277062+00:00.

Case digest / 9bf46f101addb7dfcaacfe63fbbe298944dacc2f2aeb850ae7b01a086b11b10f