FA-48961 / PCM sample encoding / Open access
Sign magnitude pcm: sign position · case 01
The sign bit is read beyond the PCM field.
ROOT CAUSE
The sign bit is read beyond the PCM field.
VERIFIED REPAIR
Use the stated conversion contract at sign position.
Unsuccessful approach: Reading the low bit as sign corrupts odd positive magnitudes.
Case contract
Decode sign-magnitude PCM with configurable physical sign-bit polarity and preserve numerical negative zero as a Boolean sideband.
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, invert_sign):
mask=(1<<(width-1))-1
sign=1<<width
values=[]
zeros=[]
for code in codes:
magnitude=code&mask
negative=bool(code&sign)^invert_sign
values.append(-magnitude if negative else magnitude)
zeros.append(bool(negative and magnitude==0))
return [values,zeros]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 1, 7, 8, 9, 15], 4, False)), [[0, 1, 7, 0, -1, -7], [False, False, False, True, False, False]])
check('oracle 2', solve(*([0, 8, 1, 9], 4, True)), [[0, 0, -1, 1], [True, False, False, False]])
check('oracle 3', solve(*([], 4, False)), [[], []])
check('oracle 4', solve(*([0, 3, 4, 7], 3, False)), [[0, 3, 0, -3], [False, False, True, False]])
check('oracle 5', solve(*([0, 128, 255, 127], 8, False)), [[0, 0, -127, 127], [False, True, False, False]])
check('oracle 6', solve(*([1, 2, 3], 4, True)), [[-1, -2, -3], [False, False, False]])
check('oracle 7', solve(*([0, 4], 3, True)), [[0, 0], [True, False]])
if N == 1: check('variant packet 1', solve(*[[0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15], 4, False]), [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [False, False, False, True, False, False, False, False, False, True, False, False]])
if N == 2: check('variant packet 2', solve(*[[0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15], 4, False]), [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False]])
if N == 3: check('variant packet 3', solve(*[[0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15], 4, False]), [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False]])
if N == 4: check('variant packet 4', solve(*[[0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15], 4, False]), [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [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]])
if N == 5: check('variant packet 5', solve(*[[0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15], 4, False]), [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [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, False, False]])
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, 1, 7, 0, 1, 7], [False, False, False, False, False, False]] | [[0, 1, 7, 0, -1, -7], [False, False, False, True, False, False]] | Failed |
| oracle 2 | [[0, 0, -1, -1], [True, True, False, False]] | [[0, 0, -1, 1], [True, False, False, False]] | Failed |
| oracle 3 | [[], []] | [[], []] | Passed |
| oracle 4 | [[0, 3, 0, 3], [False, False, False, False]] | [[0, 3, 0, -3], [False, False, True, False]] | Failed |
| oracle 5 | [[0, 0, 127, 127], [False, False, False, False]] | [[0, 0, -127, 127], [False, True, False, False]] | Failed |
| oracle 6 | [[-1, -2, -3], [False, False, False]] | [[-1, -2, -3], [False, False, False]] | Passed |
| oracle 7 | [[0, 0], [True, True]] | [[0, 0], [True, False]] | Failed |
| variant packet 1 | [[0, 1, 7, 0, 1, 7, 0, 1, 7, 0, 1, 7], [False, False, False, False, False, False, False, False, False, False, False, False]] | [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [False, False, False, True, False, False, False, False, False, True, False, False]] | Failed |
SHA-256 / 0030455b7c02cc9b3c73ab589876bda5620de8be6a0e706122f35e7142fca64f
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(codes, width, invert_sign):
mask=(1<<(width-1))-1
sign=1
values=[]
zeros=[]
for code in codes:
magnitude=code&mask
negative=bool(code&sign)^invert_sign
values.append(-magnitude if negative else magnitude)
zeros.append(bool(negative and magnitude==0))
return [values,zeros]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 1, 7, 8, 9, 15], 4, False)), [[0, 1, 7, 0, -1, -7], [False, False, False, True, False, False]])
check('oracle 2', solve(*([0, 8, 1, 9], 4, True)), [[0, 0, -1, 1], [True, False, False, False]])
check('oracle 3', solve(*([], 4, False)), [[], []])
check('oracle 4', solve(*([0, 3, 4, 7], 3, False)), [[0, 3, 0, -3], [False, False, True, False]])
check('oracle 5', solve(*([0, 128, 255, 127], 8, False)), [[0, 0, -127, 127], [False, True, False, False]])
check('oracle 6', solve(*([1, 2, 3], 4, True)), [[-1, -2, -3], [False, False, False]])
check('oracle 7', solve(*([0, 4], 3, True)), [[0, 0], [True, False]])
if N == 1: check('variant packet 1', solve(*[[0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15], 4, False]), [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [False, False, False, True, False, False, False, False, False, True, False, False]])
if N == 2: check('variant packet 2', solve(*[[0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15], 4, False]), [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False]])
if N == 3: check('variant packet 3', solve(*[[0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15], 4, False]), [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False]])
if N == 4: check('variant packet 4', solve(*[[0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15], 4, False]), [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [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]])
if N == 5: check('variant packet 5', solve(*[[0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15], 4, False]), [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [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, False, False]])
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, -1, -7, 0, -1, -7], [False, False, False, False, False, False]] | [[0, 1, 7, 0, -1, -7], [False, False, False, True, False, False]] | Failed |
| oracle 2 | [[0, 0, 1, 1], [True, True, False, False]] | [[0, 0, -1, 1], [True, False, False, False]] | Failed |
| oracle 3 | [[], []] | [[], []] | Passed |
| oracle 4 | [[0, -3, 0, -3], [False, False, False, False]] | [[0, 3, 0, -3], [False, False, True, False]] | Failed |
| oracle 5 | [[0, 0, -127, -127], [False, False, False, False]] | [[0, 0, -127, 127], [False, True, False, False]] | Failed |
| oracle 6 | [[1, -2, 3], [False, False, False]] | [[-1, -2, -3], [False, False, False]] | Failed |
| oracle 7 | [[0, 0], [True, True]] | [[0, 0], [True, False]] | Failed |
| variant packet 1 | [[0, -1, -7, 0, -1, -7, 0, -1, -7, 0, -1, -7], [False, False, False, False, False, False, False, False, False, False, False, False]] | [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [False, False, False, True, False, False, False, False, False, True, False, False]] | Failed |
SHA-256 / 1f52ef547103cff561e3effb8c6cbb3a16a310eca951a9f5ea8f0b2d7136716b
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(codes, width, invert_sign):
mask=(1<<(width-1))-1
sign=1<<(width-1)
values=[]
zeros=[]
for code in codes:
magnitude=code&mask
negative=bool(code&sign)^invert_sign
values.append(-magnitude if negative else magnitude)
zeros.append(bool(negative and magnitude==0))
return [values,zeros]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 1, 7, 8, 9, 15], 4, False)), [[0, 1, 7, 0, -1, -7], [False, False, False, True, False, False]])
check('oracle 2', solve(*([0, 8, 1, 9], 4, True)), [[0, 0, -1, 1], [True, False, False, False]])
check('oracle 3', solve(*([], 4, False)), [[], []])
check('oracle 4', solve(*([0, 3, 4, 7], 3, False)), [[0, 3, 0, -3], [False, False, True, False]])
check('oracle 5', solve(*([0, 128, 255, 127], 8, False)), [[0, 0, -127, 127], [False, True, False, False]])
check('oracle 6', solve(*([1, 2, 3], 4, True)), [[-1, -2, -3], [False, False, False]])
check('oracle 7', solve(*([0, 4], 3, True)), [[0, 0], [True, False]])
if N == 1: check('variant packet 1', solve(*[[0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15], 4, False]), [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [False, False, False, True, False, False, False, False, False, True, False, False]])
if N == 2: check('variant packet 2', solve(*[[0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15], 4, False]), [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False]])
if N == 3: check('variant packet 3', solve(*[[0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15], 4, False]), [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False]])
if N == 4: check('variant packet 4', solve(*[[0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15], 4, False]), [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [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]])
if N == 5: check('variant packet 5', solve(*[[0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15, 0, 1, 7, 8, 9, 15], 4, False]), [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [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, False, False]])
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, 1, 7, 0, -1, -7], [False, False, False, True, False, False]] | [[0, 1, 7, 0, -1, -7], [False, False, False, True, False, False]] | Passed |
| oracle 2 | [[0, 0, -1, 1], [True, False, False, False]] | [[0, 0, -1, 1], [True, False, False, False]] | Passed |
| oracle 3 | [[], []] | [[], []] | Passed |
| oracle 4 | [[0, 3, 0, -3], [False, False, True, False]] | [[0, 3, 0, -3], [False, False, True, False]] | Passed |
| oracle 5 | [[0, 0, -127, 127], [False, True, False, False]] | [[0, 0, -127, 127], [False, True, False, False]] | Passed |
| oracle 6 | [[-1, -2, -3], [False, False, False]] | [[-1, -2, -3], [False, False, False]] | Passed |
| oracle 7 | [[0, 0], [True, False]] | [[0, 0], [True, False]] | Passed |
| variant packet 1 | [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [False, False, False, True, False, False, False, False, False, True, False, False]] | [[0, 1, 7, 0, -1, -7, 0, 1, 7, 0, -1, -7], [False, False, False, True, False, False, False, False, False, True, False, False]] | Passed |
SHA-256 / a33c066e7eed7956b343ff7323fac4d926c00b17f09c5e607cc2355dfb5d0dd7
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 2026-09-29T14:44:55.571542+00:00.
Case digest / 02fb72cf18726781bd71b5410a0007928b0e4b3732010ddcb93a4930cb8b2fd9