FAILURE MAP
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FA-49111 / PCM sample encoding / Open access

Pcm bitplane restore: field sign · case 01

Sign is inferred from a low-order plane instead of reconstructed sample.

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

ROOT CAUSE

Sign is inferred from a low-order plane instead of reconstructed sample.

VERIFIED REPAIR

Use the stated conversion contract at field sign.

Unsuccessful approach: Using strict greater-than loses the most negative code.

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 planes and planes[0]&(1<<i) 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, -5][-3, -2, 3]Failed
oracle 2[1, 2, 4][1, 2, -4]Failed
oracle 3[4, 4, 4][-4, -4, -4]Failed
oracle 4[-3, -3][1, 1]Failed
oracle 5[][]Passed
oracle 6[-1][-1]Passed
oracle 7[2][2]Passed
variant packet 1[5, 6, 3, 0][-3, -2, 3, 0]Failed

SHA-256 / 306272353b167430c5c5b8da842c8ce3ac5301dd50cef216d9281da67e3f6d0e

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<<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]Failed
oracle 3[4, 4, 4][-4, -4, -4]Failed
oracle 4[1, 1][1, 1]Passed
oracle 5[][]Passed
oracle 6[1][-1]Failed
oracle 7[2][2]Passed
variant packet 1[-3, -2, 3, 0][-3, -2, 3, 0]Passed

SHA-256 / 4869ce5fe8c381f1af2d5057d525a86868e4a802a147d0732ad72c2b9f2a30a0

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 2026-09-29T14:44:56.938680+00:00.

Case digest / 086115deacf7e75524e4a040c3b2006f1fdc2c63bbfd3e1848a756dbd165a063