FA-48891 / PCM sample encoding / Open access
Validbit left container: left padding shift · case 01
Left justified sample bits are interpreted as right justified.
ROOT CAUSE
Left justified sample bits are interpreted as right justified.
VERIFIED REPAIR
Use the stated conversion contract at left padding shift.
Unsuccessful approach: Shifting by the valid width removes the wrong number of pad bits.
Case contract
Extract a signed valid-bit field left justified in an unsigned container; ignore bits above the container and separately return low unused pad bits. valid<container.
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(words, valid, container):
shift=0
mask=(1<<valid)-1
values=[]
for word in words:
code=(word>>shift)&mask
sign=1<<(valid-1)
values.append(code-(1<<valid) if code&sign else code)
unused=[word&((1<<shift)-1) for word in words]
return [values,unused]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([3840, 1792, 256], 4, 12)), [[-1, 7, 1], [0, 0, 0]])
check('oracle 2', solve(*([128, 112, 0], 4, 8)), [[-8, 7, 0], [0, 0, 0]])
check('oracle 3', solve(*([384, 496], 4, 8)), [[-8, -1], [0, 0]])
check('oracle 4', solve(*([129, 114], 4, 8)), [[-8, 7], [1, 2]])
check('oracle 5', solve(*([], 3, 8)), [[], []])
check('oracle 6', solve(*([224, 32], 3, 8)), [[-1, 1], [0, 0]])
check('oracle 7', solve(*([4092, 4], 10, 12)), [[-1, 1], [0, 0]])
if N == 1: check('variant packet 1', solve(*[[3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0]])
if N == 2: check('variant packet 2', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0]])
if N == 3: check('variant packet 3', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
if N == 4: check('variant packet 4', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
if N == 5: check('variant packet 5', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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 | [[0, 0, 0], [0, 0, 0]] | [[-1, 7, 1], [0, 0, 0]] | Failed |
| oracle 2 | [[0, 0, 0], [0, 0, 0]] | [[-8, 7, 0], [0, 0, 0]] | Failed |
| oracle 3 | [[0, 0], [0, 0]] | [[-8, -1], [0, 0]] | Failed |
| oracle 4 | [[1, 2], [0, 0]] | [[-8, 7], [1, 2]] | Failed |
| oracle 5 | [[], []] | [[], []] | Passed |
| oracle 6 | [[0, 0], [0, 0]] | [[-1, 1], [0, 0]] | Failed |
| oracle 7 | [[-4, 4], [0, 0]] | [[-1, 1], [0, 0]] | Failed |
| variant packet 1 | [[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]] | [[-1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0]] | Failed |
SHA-256 / 2a2aae687ebe1b346e736ef440406dd474690cd370af429bedee498a4542aeb6
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(words, valid, container):
shift=valid
mask=(1<<valid)-1
values=[]
for word in words:
code=(word>>shift)&mask
sign=1<<(valid-1)
values.append(code-(1<<valid) if code&sign else code)
unused=[word&((1<<shift)-1) for word in words]
return [values,unused]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([3840, 1792, 256], 4, 12)), [[-1, 7, 1], [0, 0, 0]])
check('oracle 2', solve(*([128, 112, 0], 4, 8)), [[-8, 7, 0], [0, 0, 0]])
check('oracle 3', solve(*([384, 496], 4, 8)), [[-8, -1], [0, 0]])
check('oracle 4', solve(*([129, 114], 4, 8)), [[-8, 7], [1, 2]])
check('oracle 5', solve(*([], 3, 8)), [[], []])
check('oracle 6', solve(*([224, 32], 3, 8)), [[-1, 1], [0, 0]])
check('oracle 7', solve(*([4092, 4], 10, 12)), [[-1, 1], [0, 0]])
if N == 1: check('variant packet 1', solve(*[[3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0]])
if N == 2: check('variant packet 2', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0]])
if N == 3: check('variant packet 3', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
if N == 4: check('variant packet 4', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
if N == 5: check('variant packet 5', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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 | [[0, 0, 0], [0, 0, 0]] | [[-1, 7, 1], [0, 0, 0]] | Failed |
| oracle 2 | [[-8, 7, 0], [0, 0, 0]] | [[-8, 7, 0], [0, 0, 0]] | Passed |
| oracle 3 | [[-8, -1], [0, 0]] | [[-8, -1], [0, 0]] | Passed |
| oracle 4 | [[-8, 7], [1, 2]] | [[-8, 7], [1, 2]] | Passed |
| oracle 5 | [[], []] | [[], []] | Passed |
| oracle 6 | [[-4, -4], [0, 0]] | [[-1, 1], [0, 0]] | Failed |
| oracle 7 | [[3, 0], [1020, 4]] | [[-1, 1], [0, 0]] | Failed |
| variant packet 1 | [[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]] | [[-1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0]] | Failed |
SHA-256 / c6fbf10edc1cc00baddbb730177710b5a627f7e591442b4db39cc096c7ee4ff1
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(words, valid, container):
shift=container-valid
mask=(1<<valid)-1
values=[]
for word in words:
code=(word>>shift)&mask
sign=1<<(valid-1)
values.append(code-(1<<valid) if code&sign else code)
unused=[word&((1<<shift)-1) for word in words]
return [values,unused]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([3840, 1792, 256], 4, 12)), [[-1, 7, 1], [0, 0, 0]])
check('oracle 2', solve(*([128, 112, 0], 4, 8)), [[-8, 7, 0], [0, 0, 0]])
check('oracle 3', solve(*([384, 496], 4, 8)), [[-8, -1], [0, 0]])
check('oracle 4', solve(*([129, 114], 4, 8)), [[-8, 7], [1, 2]])
check('oracle 5', solve(*([], 3, 8)), [[], []])
check('oracle 6', solve(*([224, 32], 3, 8)), [[-1, 1], [0, 0]])
check('oracle 7', solve(*([4092, 4], 10, 12)), [[-1, 1], [0, 0]])
if N == 1: check('variant packet 1', solve(*[[3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0]])
if N == 2: check('variant packet 2', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0]])
if N == 3: check('variant packet 3', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
if N == 4: check('variant packet 4', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
if N == 5: check('variant packet 5', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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 | [[-1, 7, 1], [0, 0, 0]] | [[-1, 7, 1], [0, 0, 0]] | Passed |
| oracle 2 | [[-8, 7, 0], [0, 0, 0]] | [[-8, 7, 0], [0, 0, 0]] | Passed |
| oracle 3 | [[-8, -1], [0, 0]] | [[-8, -1], [0, 0]] | Passed |
| oracle 4 | [[-8, 7], [1, 2]] | [[-8, 7], [1, 2]] | Passed |
| oracle 5 | [[], []] | [[], []] | Passed |
| oracle 6 | [[-1, 1], [0, 0]] | [[-1, 1], [0, 0]] | Passed |
| oracle 7 | [[-1, 1], [0, 0]] | [[-1, 1], [0, 0]] | Passed |
| variant packet 1 | [[-1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0]] | [[-1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0]] | Passed |
SHA-256 / ca7293e7026af013c2db0a94ce1e628036256a4a01402c3fc8b3e0204e17275f
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 2026-09-29T14:44:54.943551+00:00.
Case digest / 65cf4e7967c4954d07826da01293d4a901018a28371eb7775983c30d31f64022