FA-49051 / PCM sample encoding / Open access
Xor coded pcm: zero detection · case 01
Silence detection uses the encoded electrical bits.
ROOT CAUSE
Silence detection uses the encoded electrical bits.
VERIFIED REPAIR
Use the stated conversion contract at zero detection.
Unsuccessful approach: Comparing corrected bits to the electrical inversion map double-applies coding.
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 code&sign else code
out.append([value, raw==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, True], [6, False], [2, False], [-3, False], [-6, False]] | [[5, False], [6, False], [2, False], [-3, False], [-6, False]] | Failed |
| oracle 2 | [[0, False], [-8, True], [7, False]] | [[0, True], [-8, False], [7, False]] | Failed |
| oracle 3 | [[0, False], [-1, False], [0, True]] | [[0, True], [-1, False], [0, True]] | Failed |
| oracle 4 | [[85, True], [-86, False]] | [[85, False], [-86, False]] | Failed |
| oracle 5 | [] | [] | Passed |
| oracle 6 | [[-1, True], [0, False]] | [[-1, False], [0, True]] | Failed |
| oracle 7 | [[1, False], [-2, False], [-3, False]] | [[1, False], [-2, False], [-3, False]] | Passed |
| variant packet 1 | [[5, True], [6, False], [2, False], [-3, False], [-6, False], [5, True], [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]] | Failed |
SHA-256 / 2f9c7b7154120d2e24e3447dd805b109cabbe16fd67262d7ac0e9831092315fc
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 code&sign else code
out.append([value, code==xor_mask])
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, True], [6, False], [2, False], [-3, False], [-6, False]] | [[5, False], [6, False], [2, False], [-3, False], [-6, False]] | Failed |
| oracle 2 | [[0, False], [-8, True], [7, False]] | [[0, True], [-8, False], [7, False]] | Failed |
| oracle 3 | [[0, False], [-1, False], [0, False]] | [[0, True], [-1, False], [0, True]] | Failed |
| oracle 4 | [[85, True], [-86, False]] | [[85, False], [-86, False]] | Failed |
| oracle 5 | [] | [] | Passed |
| oracle 6 | [[-1, True], [0, False]] | [[-1, False], [0, True]] | Failed |
| oracle 7 | [[1, False], [-2, False], [-3, False]] | [[1, False], [-2, False], [-3, False]] | Passed |
| variant packet 1 | [[5, True], [6, False], [2, False], [-3, False], [-6, False], [5, True], [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]] | Failed |
SHA-256 / 43062f8b40080c61604fb975c45353d6ed6d5b75da74433508c94c97fb45e538
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 2026-09-29T14:44:56.336662+00:00.
Case digest / fbcd8a4100bb676e4e3905dfa059c80be3242771adabed4b8df91652826b1524