FA-49776 / PCM sample encoding / Open access
Pcm nibble block order: low mask · case 01
Low nibble loses its adaptive sign bit.
ROOT CAUSE
Low nibble loses its adaptive sign bit.
VERIFIED REPAIR
Use the stated conversion contract at low mask.
Unsuccessful approach: Leaving the entire octet mixes neighboring sample codes.
Case contract
Extract adaptive PCM nibble codes in declared within-octet order; valid count is in nibbles and remaining codes are returned separately as padding.
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(octets, high_first, valid_nibbles):
values=[]
for byte in octets:
high=(byte>>4)&15
low=byte&7
values.extend([high,low] if high_first else [low,high])
count=min(max(valid_nibbles,0),len(values))
return [values[:count],values[count:]]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([24, 242], True, 3)), [[1, 8, 15], [2]])
check('oracle 2', solve(*([18, 52], False, 4)), [[2, 1, 4, 3], []])
check('oracle 3', solve(*([427], True, 2)), [[10, 11], []])
check('oracle 4', solve(*([], False, 0)), [[], []])
check('oracle 5', solve(*([128], False, 1)), [[0], [8]])
check('oracle 6', solve(*([255], True, 0)), [[], [15, 15]])
check('oracle 7', solve(*([87, 121], False, 8)), [[7, 5, 9, 7], []])
if N == 1: check('variant packet 1', solve(*[[24, 242, 24, 242], True, 6]), [[1, 8, 15, 2, 1, 8], [15, 2]])
if N == 2: check('variant packet 2', solve(*[[24, 242, 24, 242, 24, 242], True, 9]), [[1, 8, 15, 2, 1, 8, 15, 2, 1], [8, 15, 2]])
if N == 3: check('variant packet 3', solve(*[[24, 242, 24, 242, 24, 242, 24, 242], True, 12]), [[1, 8, 15, 2, 1, 8, 15, 2, 1, 8, 15, 2], [1, 8, 15, 2]])
if N == 4: check('variant packet 4', solve(*[[24, 242, 24, 242, 24, 242, 24, 242, 24, 242], True, 15]), [[1, 8, 15, 2, 1, 8, 15, 2, 1, 8, 15, 2, 1, 8, 15], [2, 1, 8, 15, 2]])
if N == 5: check('variant packet 5', solve(*[[24, 242, 24, 242, 24, 242, 24, 242, 24, 242, 24, 242], True, 18]), [[1, 8, 15, 2, 1, 8, 15, 2, 1, 8, 15, 2, 1, 8, 15, 2, 1, 8], [15, 2, 1, 8, 15, 2]])
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 | [[1, 0, 15], [2]] | [[1, 8, 15], [2]] | Failed |
| oracle 2 | [[2, 1, 4, 3], []] | [[2, 1, 4, 3], []] | Passed |
| oracle 3 | [[10, 3], []] | [[10, 11], []] | Failed |
| oracle 4 | [[], []] | [[], []] | Passed |
| oracle 5 | [[0], [8]] | [[0], [8]] | Passed |
| oracle 6 | [[], [15, 7]] | [[], [15, 15]] | Failed |
| oracle 7 | [[7, 5, 1, 7], []] | [[7, 5, 9, 7], []] | Failed |
| variant packet 1 | [[1, 0, 15, 2, 1, 0], [15, 2]] | [[1, 8, 15, 2, 1, 8], [15, 2]] | Failed |
SHA-256 / 0cb6d5aba6251820c14e137daeebd7f24d278209d7e708e2563421985e524342
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(octets, high_first, valid_nibbles):
values=[]
for byte in octets:
high=(byte>>4)&15
low=byte&255
values.extend([high,low] if high_first else [low,high])
count=min(max(valid_nibbles,0),len(values))
return [values[:count],values[count:]]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([24, 242], True, 3)), [[1, 8, 15], [2]])
check('oracle 2', solve(*([18, 52], False, 4)), [[2, 1, 4, 3], []])
check('oracle 3', solve(*([427], True, 2)), [[10, 11], []])
check('oracle 4', solve(*([], False, 0)), [[], []])
check('oracle 5', solve(*([128], False, 1)), [[0], [8]])
check('oracle 6', solve(*([255], True, 0)), [[], [15, 15]])
check('oracle 7', solve(*([87, 121], False, 8)), [[7, 5, 9, 7], []])
if N == 1: check('variant packet 1', solve(*[[24, 242, 24, 242], True, 6]), [[1, 8, 15, 2, 1, 8], [15, 2]])
if N == 2: check('variant packet 2', solve(*[[24, 242, 24, 242, 24, 242], True, 9]), [[1, 8, 15, 2, 1, 8, 15, 2, 1], [8, 15, 2]])
if N == 3: check('variant packet 3', solve(*[[24, 242, 24, 242, 24, 242, 24, 242], True, 12]), [[1, 8, 15, 2, 1, 8, 15, 2, 1, 8, 15, 2], [1, 8, 15, 2]])
if N == 4: check('variant packet 4', solve(*[[24, 242, 24, 242, 24, 242, 24, 242, 24, 242], True, 15]), [[1, 8, 15, 2, 1, 8, 15, 2, 1, 8, 15, 2, 1, 8, 15], [2, 1, 8, 15, 2]])
if N == 5: check('variant packet 5', solve(*[[24, 242, 24, 242, 24, 242, 24, 242, 24, 242, 24, 242], True, 18]), [[1, 8, 15, 2, 1, 8, 15, 2, 1, 8, 15, 2, 1, 8, 15, 2, 1, 8], [15, 2, 1, 8, 15, 2]])
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 | [[1, 24, 15], [242]] | [[1, 8, 15], [2]] | Failed |
| oracle 2 | [[18, 1, 52, 3], []] | [[2, 1, 4, 3], []] | Failed |
| oracle 3 | [[10, 171], []] | [[10, 11], []] | Failed |
| oracle 4 | [[], []] | [[], []] | Passed |
| oracle 5 | [[128], [8]] | [[0], [8]] | Failed |
| oracle 6 | [[], [15, 255]] | [[], [15, 15]] | Failed |
| oracle 7 | [[87, 5, 121, 7], []] | [[7, 5, 9, 7], []] | Failed |
| variant packet 1 | [[1, 24, 15, 242, 1, 24], [15, 242]] | [[1, 8, 15, 2, 1, 8], [15, 2]] | Failed |
SHA-256 / 675e59cefa5085f0a7759203842447d603a5dfbf17baf4f7afc91fcc85269576
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(octets, high_first, valid_nibbles):
values=[]
for byte in octets:
high=(byte>>4)&15
low=byte&15
values.extend([high,low] if high_first else [low,high])
count=min(max(valid_nibbles,0),len(values))
return [values[:count],values[count:]]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([24, 242], True, 3)), [[1, 8, 15], [2]])
check('oracle 2', solve(*([18, 52], False, 4)), [[2, 1, 4, 3], []])
check('oracle 3', solve(*([427], True, 2)), [[10, 11], []])
check('oracle 4', solve(*([], False, 0)), [[], []])
check('oracle 5', solve(*([128], False, 1)), [[0], [8]])
check('oracle 6', solve(*([255], True, 0)), [[], [15, 15]])
check('oracle 7', solve(*([87, 121], False, 8)), [[7, 5, 9, 7], []])
if N == 1: check('variant packet 1', solve(*[[24, 242, 24, 242], True, 6]), [[1, 8, 15, 2, 1, 8], [15, 2]])
if N == 2: check('variant packet 2', solve(*[[24, 242, 24, 242, 24, 242], True, 9]), [[1, 8, 15, 2, 1, 8, 15, 2, 1], [8, 15, 2]])
if N == 3: check('variant packet 3', solve(*[[24, 242, 24, 242, 24, 242, 24, 242], True, 12]), [[1, 8, 15, 2, 1, 8, 15, 2, 1, 8, 15, 2], [1, 8, 15, 2]])
if N == 4: check('variant packet 4', solve(*[[24, 242, 24, 242, 24, 242, 24, 242, 24, 242], True, 15]), [[1, 8, 15, 2, 1, 8, 15, 2, 1, 8, 15, 2, 1, 8, 15], [2, 1, 8, 15, 2]])
if N == 5: check('variant packet 5', solve(*[[24, 242, 24, 242, 24, 242, 24, 242, 24, 242, 24, 242], True, 18]), [[1, 8, 15, 2, 1, 8, 15, 2, 1, 8, 15, 2, 1, 8, 15, 2, 1, 8], [15, 2, 1, 8, 15, 2]])
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 | [[1, 8, 15], [2]] | [[1, 8, 15], [2]] | Passed |
| oracle 2 | [[2, 1, 4, 3], []] | [[2, 1, 4, 3], []] | Passed |
| oracle 3 | [[10, 11], []] | [[10, 11], []] | Passed |
| oracle 4 | [[], []] | [[], []] | Passed |
| oracle 5 | [[0], [8]] | [[0], [8]] | Passed |
| oracle 6 | [[], [15, 15]] | [[], [15, 15]] | Passed |
| oracle 7 | [[7, 5, 9, 7], []] | [[7, 5, 9, 7], []] | Passed |
| variant packet 1 | [[1, 8, 15, 2, 1, 8], [15, 2]] | [[1, 8, 15, 2, 1, 8], [15, 2]] | Passed |
SHA-256 / 4f6a87c43584421013fac17a5e9bec4afd624413bad1362e9bea4f2fd23f9dba
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 2026-09-29T14:45:03.055465+00:00.
Case digest / 74a4e781ede90d9eaa71f174a01af006671e6fb692b696a72a4e60aad624bd6e