FA-48901 / PCM sample encoding / Open access
Validbit left container: sign position · case 01
The container sign position is tested after valid-bit extraction.
ROOT CAUSE
The container sign position is tested after valid-bit extraction.
VERIFIED REPAIR
Use the stated conversion contract at sign position.
Unsuccessful approach: Testing one bit beyond the extracted field still misses negativity.
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=container-valid
mask=(1<<valid)-1
values=[]
for word in words:
code=(word>>shift)&mask
sign=1<<(container-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 | [[15, 7, 1], [0, 0, 0]] | [[-1, 7, 1], [0, 0, 0]] | Failed |
| oracle 2 | [[8, 7, 0], [0, 0, 0]] | [[-8, 7, 0], [0, 0, 0]] | Failed |
| oracle 3 | [[8, 15], [0, 0]] | [[-8, -1], [0, 0]] | Failed |
| oracle 4 | [[8, 7], [1, 2]] | [[-8, 7], [1, 2]] | Failed |
| oracle 5 | [[], []] | [[], []] | Passed |
| oracle 6 | [[7, 1], [0, 0]] | [[-1, 1], [0, 0]] | Failed |
| oracle 7 | [[1023, 1], [0, 0]] | [[-1, 1], [0, 0]] | Failed |
| variant packet 1 | [[15, 7, 1, 15, 7, 1], [0, 0, 0, 0, 0, 0]] | [[-1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0]] | Failed |
SHA-256 / 33ca6280aaaa18ac501f90483c347ca1e52d40d959d8c569cbb5f6d54e721a6c
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=container-valid
mask=(1<<valid)-1
values=[]
for word in words:
code=(word>>shift)&mask
sign=1<<valid
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 | [[15, 7, 1], [0, 0, 0]] | [[-1, 7, 1], [0, 0, 0]] | Failed |
| oracle 2 | [[8, 7, 0], [0, 0, 0]] | [[-8, 7, 0], [0, 0, 0]] | Failed |
| oracle 3 | [[8, 15], [0, 0]] | [[-8, -1], [0, 0]] | Failed |
| oracle 4 | [[8, 7], [1, 2]] | [[-8, 7], [1, 2]] | Failed |
| oracle 5 | [[], []] | [[], []] | Passed |
| oracle 6 | [[7, 1], [0, 0]] | [[-1, 1], [0, 0]] | Failed |
| oracle 7 | [[1023, 1], [0, 0]] | [[-1, 1], [0, 0]] | Failed |
| variant packet 1 | [[15, 7, 1, 15, 7, 1], [0, 0, 0, 0, 0, 0]] | [[-1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0]] | Failed |
SHA-256 / 11d5cc9da5a7d86eca06680482432decd0c89a381867f799fc51aeef569228ed
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 2026-09-29T14:44:54.980017+00:00.
Case digest / 367dab4bd4f3e45d9da599e0a920939d57a2118c4789704a7261e6b6391c2de1