FA-49056 / PCM sample encoding / Open access
Xor coded pcm: signed field · case 01
Sign is tested before the sign line is uninverted.
ROOT CAUSE
Sign is tested before the sign line is uninverted.
VERIFIED REPAIR
Use the stated conversion contract at signed field.
Unsuccessful approach: Using the inversion mask as sample sign forces a constant polarity interpretation.
Case contract
Undo a per-line XOR inversion map within a signed PCM field before interpreting sign and detecting canonical zero.
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, xor_mask):
field=(1<<width)-1
out=[]
for raw in codes:
code=(raw^xor_mask)&field
sign=1<<(width-1)
value=code-(1<<width) if raw&sign else code
out.append([value, code==0])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 3, 7, 8, 15], 4, 5)), [[5, False], [6, False], [2, False], [-3, False], [-6, False]])
check('oracle 2', solve(*([8, 0, 15], 4, 8)), [[0, True], [-8, False], [7, False]])
check('oracle 3', solve(*([16, 31, 0], 4, 32)), [[0, True], [-1, False], [0, True]])
check('oracle 4', solve(*([0, 255], 8, 85)), [[85, False], [-86, False]])
check('oracle 5', solve(*([], 3, 7)), [])
check('oracle 6', solve(*([0, 1], 1, 1)), [[-1, False], [0, True]])
check('oracle 7', solve(*([3, 4, 7], 3, 2)), [[1, False], [-2, False], [-3, False]])
if N == 1: check('variant packet 1', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 2: check('variant packet 2', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 3: check('variant packet 3', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 4: check('variant packet 4', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 5: check('variant packet 5', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, 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 | [[5, False], [6, False], [2, False], [-3, False], [-6, False]] | [[5, False], [6, False], [2, False], [-3, False], [-6, False]] | Passed |
| oracle 2 | [[-16, True], [8, False], [-9, False]] | [[0, True], [-8, False], [7, False]] | Failed |
| oracle 3 | [[0, True], [-1, False], [0, True]] | [[0, True], [-1, False], [0, True]] | Passed |
| oracle 4 | [[85, False], [-86, False]] | [[85, False], [-86, False]] | Passed |
| oracle 5 | [] | [] | Passed |
| oracle 6 | [[1, False], [-2, True]] | [[-1, False], [0, True]] | Failed |
| oracle 7 | [[1, False], [-2, False], [-3, False]] | [[1, False], [-2, False], [-3, False]] | Passed |
| variant packet 1 | [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]] | [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]] | Passed |
SHA-256 / 3e732a6edc71f25b9b028f5fd63ea8b9e088efafa9415e768f29864eca6ab08f
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(codes, width, xor_mask):
field=(1<<width)-1
out=[]
for raw in codes:
code=(raw^xor_mask)&field
sign=1<<(width-1)
value=code-(1<<width) if xor_mask&sign else code
out.append([value, code==0])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 3, 7, 8, 15], 4, 5)), [[5, False], [6, False], [2, False], [-3, False], [-6, False]])
check('oracle 2', solve(*([8, 0, 15], 4, 8)), [[0, True], [-8, False], [7, False]])
check('oracle 3', solve(*([16, 31, 0], 4, 32)), [[0, True], [-1, False], [0, True]])
check('oracle 4', solve(*([0, 255], 8, 85)), [[85, False], [-86, False]])
check('oracle 5', solve(*([], 3, 7)), [])
check('oracle 6', solve(*([0, 1], 1, 1)), [[-1, False], [0, True]])
check('oracle 7', solve(*([3, 4, 7], 3, 2)), [[1, False], [-2, False], [-3, False]])
if N == 1: check('variant packet 1', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 2: check('variant packet 2', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 3: check('variant packet 3', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 4: check('variant packet 4', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 5: check('variant packet 5', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, 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 | [[5, False], [6, False], [2, False], [13, False], [10, False]] | [[5, False], [6, False], [2, False], [-3, False], [-6, False]] | Failed |
| oracle 2 | [[-16, True], [-8, False], [-9, False]] | [[0, True], [-8, False], [7, False]] | Failed |
| oracle 3 | [[0, True], [15, False], [0, True]] | [[0, True], [-1, False], [0, True]] | Failed |
| oracle 4 | [[85, False], [170, False]] | [[85, False], [-86, False]] | Failed |
| oracle 5 | [] | [] | Passed |
| oracle 6 | [[-1, False], [-2, True]] | [[-1, False], [0, True]] | Failed |
| oracle 7 | [[1, False], [6, False], [5, False]] | [[1, False], [-2, False], [-3, False]] | Failed |
| variant packet 1 | [[5, False], [6, False], [2, False], [13, False], [10, False], [5, False], [6, False], [2, False], [13, False], [10, False]] | [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]] | Failed |
SHA-256 / fa3a0c82a75791366eeaf88fd11e471f553e8c85bffed1e0f5b8d17dfb7e09d8
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(codes, width, xor_mask):
field=(1<<width)-1
out=[]
for raw in codes:
code=(raw^xor_mask)&field
sign=1<<(width-1)
value=code-(1<<width) if code&sign else code
out.append([value, code==0])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 3, 7, 8, 15], 4, 5)), [[5, False], [6, False], [2, False], [-3, False], [-6, False]])
check('oracle 2', solve(*([8, 0, 15], 4, 8)), [[0, True], [-8, False], [7, False]])
check('oracle 3', solve(*([16, 31, 0], 4, 32)), [[0, True], [-1, False], [0, True]])
check('oracle 4', solve(*([0, 255], 8, 85)), [[85, False], [-86, False]])
check('oracle 5', solve(*([], 3, 7)), [])
check('oracle 6', solve(*([0, 1], 1, 1)), [[-1, False], [0, True]])
check('oracle 7', solve(*([3, 4, 7], 3, 2)), [[1, False], [-2, False], [-3, False]])
if N == 1: check('variant packet 1', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 2: check('variant packet 2', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 3: check('variant packet 3', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 4: check('variant packet 4', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])
if N == 5: check('variant packet 5', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, 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 | [[5, False], [6, False], [2, False], [-3, False], [-6, False]] | [[5, False], [6, False], [2, False], [-3, False], [-6, False]] | Passed |
| oracle 2 | [[0, True], [-8, False], [7, False]] | [[0, True], [-8, False], [7, False]] | Passed |
| oracle 3 | [[0, True], [-1, False], [0, True]] | [[0, True], [-1, False], [0, True]] | Passed |
| oracle 4 | [[85, False], [-86, False]] | [[85, False], [-86, False]] | Passed |
| oracle 5 | [] | [] | Passed |
| oracle 6 | [[-1, False], [0, True]] | [[-1, False], [0, True]] | Passed |
| oracle 7 | [[1, False], [-2, False], [-3, False]] | [[1, False], [-2, False], [-3, False]] | Passed |
| variant packet 1 | [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]] | [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]] | Passed |
SHA-256 / 677436fbf1c31a2198a83bd1495490a6162935ebca710bd28a5712c0b7f3cf3d
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 2026-09-29T14:44:56.337805+00:00.
Case digest / acc68a78982edc93e4c816921a6293f778dc4d9378da0f35af8549a88d90e5aa