FAILURE MAP
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FA-49106 / PCM sample encoding / Open access

Pcm bitplane restore: plane combine · case 01

Each incoming plane overwrites all previously restored signal bits.

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

ROOT CAUSE

Each incoming plane overwrites all previously restored signal bits.

VERIFIED REPAIR

Use the stated conversion contract at plane combine.

Unsuccessful approach: Adding unshifted bits counts set bits instead of restoring magnitude.

Case contract

Restore signed PCM sample integers from least-significant-bit-first bitplanes; sample index selects a bit inside each plane, and extra planes are ignored.

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(planes, samples, width):
    out=[0]*samples
    for bit,plane in enumerate(planes[:width]):
        for i in range(samples):
            value=(plane>>i)&1
            out[i]=value<<bit
    sign=1<<(width-1)
    return [x-(1<<width) if x&sign else x for x in out]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([5, 6, 3], 3, 3)), [-3, -2, 3])
check('oracle 2', solve(*([1, 2, 4, 7], 3, 3)), [1, 2, -4])
check('oracle 3', solve(*([0, 0, 7], 3, 3)), [-4, -4, -4])
check('oracle 4', solve(*([3, 0], 2, 2)), [1, 1])
check('oracle 5', solve(*([], 0, 4)), [])
check('oracle 6', solve(*([1], 1, 1)), [-1])
check('oracle 7', solve(*([0, 1, 0, 0], 1, 3)), [2])
if N == 1: check('variant packet 1', solve(*[[5, 6, 3], 4, 3]), [-3, -2, 3, 0])
if N == 2: check('variant packet 2', solve(*[[5, 6, 3], 5, 3]), [-3, -2, 3, 0, 0])
if N == 3: check('variant packet 3', solve(*[[5, 6, 3], 6, 3]), [-3, -2, 3, 0, 0, 0])
if N == 4: check('variant packet 4', solve(*[[5, 6, 3], 7, 3]), [-3, -2, 3, 0, 0, 0, 0])
if N == 5: check('variant packet 5', solve(*[[5, 6, 3], 8, 3]), [-3, -2, 3, 0, 0, 0, 0, 0])
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[-4, -4, 0][-3, -2, 3]Failed
oracle 2[0, 0, -4][1, 2, -4]Failed
oracle 3[-4, -4, -4][-4, -4, -4]Passed
oracle 4[0, 0][1, 1]Failed
oracle 5[][]Passed
oracle 6[-1][-1]Passed
oracle 7[0][2]Failed
variant packet 1[-4, -4, 0, 0][-3, -2, 3, 0]Failed

SHA-256 / 661f6bcfc82884a7cd18f33bcbeb34473acc9625eae7f1ab7cf4f62d624722b1

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(planes, samples, width):
    out=[0]*samples
    for bit,plane in enumerate(planes[:width]):
        for i in range(samples):
            value=(plane>>i)&1
            out[i]+=value
    sign=1<<(width-1)
    return [x-(1<<width) if x&sign else x for x in out]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([5, 6, 3], 3, 3)), [-3, -2, 3])
check('oracle 2', solve(*([1, 2, 4, 7], 3, 3)), [1, 2, -4])
check('oracle 3', solve(*([0, 0, 7], 3, 3)), [-4, -4, -4])
check('oracle 4', solve(*([3, 0], 2, 2)), [1, 1])
check('oracle 5', solve(*([], 0, 4)), [])
check('oracle 6', solve(*([1], 1, 1)), [-1])
check('oracle 7', solve(*([0, 1, 0, 0], 1, 3)), [2])
if N == 1: check('variant packet 1', solve(*[[5, 6, 3], 4, 3]), [-3, -2, 3, 0])
if N == 2: check('variant packet 2', solve(*[[5, 6, 3], 5, 3]), [-3, -2, 3, 0, 0])
if N == 3: check('variant packet 3', solve(*[[5, 6, 3], 6, 3]), [-3, -2, 3, 0, 0, 0])
if N == 4: check('variant packet 4', solve(*[[5, 6, 3], 7, 3]), [-3, -2, 3, 0, 0, 0, 0])
if N == 5: check('variant packet 5', solve(*[[5, 6, 3], 8, 3]), [-3, -2, 3, 0, 0, 0, 0, 0])
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[2, 2, 2][-3, -2, 3]Failed
oracle 2[1, 1, 1][1, 2, -4]Failed
oracle 3[1, 1, 1][-4, -4, -4]Failed
oracle 4[1, 1][1, 1]Passed
oracle 5[][]Passed
oracle 6[-1][-1]Passed
oracle 7[1][2]Failed
variant packet 1[2, 2, 2, 0][-3, -2, 3, 0]Failed

SHA-256 / 2fea28aa893218592ddb49dcd7611bc488384abad8a9bcd7e8c3eb8eeeeb41e1

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(planes, samples, width):
    out=[0]*samples
    for bit,plane in enumerate(planes[:width]):
        for i in range(samples):
            value=(plane>>i)&1
            out[i]|=value<<bit
    sign=1<<(width-1)
    return [x-(1<<width) if x&sign else x for x in out]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([5, 6, 3], 3, 3)), [-3, -2, 3])
check('oracle 2', solve(*([1, 2, 4, 7], 3, 3)), [1, 2, -4])
check('oracle 3', solve(*([0, 0, 7], 3, 3)), [-4, -4, -4])
check('oracle 4', solve(*([3, 0], 2, 2)), [1, 1])
check('oracle 5', solve(*([], 0, 4)), [])
check('oracle 6', solve(*([1], 1, 1)), [-1])
check('oracle 7', solve(*([0, 1, 0, 0], 1, 3)), [2])
if N == 1: check('variant packet 1', solve(*[[5, 6, 3], 4, 3]), [-3, -2, 3, 0])
if N == 2: check('variant packet 2', solve(*[[5, 6, 3], 5, 3]), [-3, -2, 3, 0, 0])
if N == 3: check('variant packet 3', solve(*[[5, 6, 3], 6, 3]), [-3, -2, 3, 0, 0, 0])
if N == 4: check('variant packet 4', solve(*[[5, 6, 3], 7, 3]), [-3, -2, 3, 0, 0, 0, 0])
if N == 5: check('variant packet 5', solve(*[[5, 6, 3], 8, 3]), [-3, -2, 3, 0, 0, 0, 0, 0])
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, -2, 3][-3, -2, 3]Passed
oracle 2[1, 2, -4][1, 2, -4]Passed
oracle 3[-4, -4, -4][-4, -4, -4]Passed
oracle 4[1, 1][1, 1]Passed
oracle 5[][]Passed
oracle 6[-1][-1]Passed
oracle 7[2][2]Passed
variant packet 1[-3, -2, 3, 0][-3, -2, 3, 0]Passed

SHA-256 / cb5e306770f4573e44c7fd7312950e2ffdb93eba88fb38af0d27e1c5303d8b58

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 2026-09-29T14:44:56.937180+00:00.

Case digest / 78db46d946250970073d9a2c9f41aad8bc6b8f22ed21176168e623ee7152fe64