FA-49096 / PCM sample encoding / Open access
Pcm bitplane restore: sample bit offset · case 01
Samples within each PCM bitplane are read in reverse order.
ROOT CAUSE
Samples within each PCM bitplane are read in reverse order.
VERIFIED REPAIR
Use the stated conversion contract at sample bit offset.
Unsuccessful approach: Reusing the first sample bit repeats the first waveform value.
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>>(samples-1-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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| oracle 1 | [3, -2, -3] | [-3, -2, 3] | Failed |
| oracle 2 | [-4, 2, 1] | [1, 2, -4] | Failed |
| 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 | [0, 3, -2, -3] | [-3, -2, 3, 0] | Failed |
SHA-256 / bec33d8c859b9ff1b0e23d10d7248ac4e965a2c25fc94005be78d19b757a3606
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&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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| oracle 1 | [-3, -3, -3] | [-3, -2, 3] | Failed |
| oracle 2 | [1, 1, 1] | [1, 2, -4] | Failed |
| 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, -3, -3, -3] | [-3, -2, 3, 0] | Failed |
SHA-256 / 544f837a1871ed284eb0fd06ab87b18820fcc076cb1045ff93450155afe42566
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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| 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 2026-09-29T14:44:56.711695+00:00.
Case digest / 0242f5ee30ff18ee6b96bbd24ece1245d67203e7beea8ea9f78db7ce04c394b3