FA-50216 / PCM sample encoding / Open access
Pcm biphase mark payload: boundary transition · case 01
PCM line-code boundary checks the end of the bit cell rather than its first half.
ROOT CAUSE
PCM line-code boundary checks the end of the bit cell rather than its first half.
VERIFIED REPAIR
Use the stated conversion contract at boundary transition.
Unsuccessful approach: Requiring no boundary transition inverts line-code validity.
Case contract
Decode stipulated biphase-mark PCM transport cells: every cell must transition at its start, midcell transition is one, and final physical level carries across packets.
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(cells, initial):
previous=initial
bits=[]
valid=[]
for first,second in cells:
boundary=second!=previous
bit=int(first!=second)
bits.append(bit)
valid.append(boundary)
previous=second
return [bits,valid,previous]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[1, 1], [0, 1], [0, 0]], 0)), [[0, 1, 0], [True, True, True], 0])
check('oracle 2', solve(*([[0, 1], [1, 0]], 1)), [[1, 1], [True, False], 0])
check('oracle 3', solve(*([[0, 0], [1, 1]], 0)), [[0, 0], [False, True], 1])
check('oracle 4', solve(*([], 1)), [[], [], 1])
check('oracle 5', solve(*([[1, 0], [1, 0]], 0)), [[1, 1], [True, True], 0])
check('oracle 6', solve(*([[1, 1]], 1)), [[0], [False], 1])
check('oracle 7', solve(*([[0, 0], [0, 1], [1, 1]], 1)), [[0, 1, 0], [True, False, False], 1])
if N == 1: check('variant packet 1', solve(*[[[1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0]], 0]), [[0, 1, 0, 0, 1, 0], [True, True, True, True, True, True], 0])
if N == 2: check('variant packet 2', solve(*[[[1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0]], 0]), [[0, 1, 0, 0, 1, 0, 0, 1, 0], [True, True, True, True, True, True, True, True, True], 0])
if N == 3: check('variant packet 3', solve(*[[[1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0]], 0]), [[0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [True, True, True, True, True, True, True, True, True, True, True, True], 0])
if N == 4: check('variant packet 4', solve(*[[[1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0]], 0]), [[0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [True, True, True, True, True, True, True, True, True, True, True, True, True, True, True], 0])
if N == 5: check('variant packet 5', solve(*[[[1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0]], 0]), [[0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True], 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, 1, 0], [True, False, True], 0] | [[0, 1, 0], [True, True, True], 0] | Failed |
| oracle 2 | [[1, 1], [False, True], 0] | [[1, 1], [True, False], 0] | Failed |
| oracle 3 | [[0, 0], [False, True], 1] | [[0, 0], [False, True], 1] | Passed |
| oracle 4 | [[], [], 1] | [[], [], 1] | Passed |
| oracle 5 | [[1, 1], [False, False], 0] | [[1, 1], [True, True], 0] | Failed |
| oracle 6 | [[0], [False], 1] | [[0], [False], 1] | Passed |
| oracle 7 | [[0, 1, 0], [True, True, False], 1] | [[0, 1, 0], [True, False, False], 1] | Failed |
| variant packet 1 | [[0, 1, 0, 0, 1, 0], [True, False, True, True, False, True], 0] | [[0, 1, 0, 0, 1, 0], [True, True, True, True, True, True], 0] | Failed |
SHA-256 / cca878e47402d35936ea21f049304124726a610daa53c4e7330703584fe01299
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(cells, initial):
previous=initial
bits=[]
valid=[]
for first,second in cells:
boundary=first==previous
bit=int(first!=second)
bits.append(bit)
valid.append(boundary)
previous=second
return [bits,valid,previous]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[1, 1], [0, 1], [0, 0]], 0)), [[0, 1, 0], [True, True, True], 0])
check('oracle 2', solve(*([[0, 1], [1, 0]], 1)), [[1, 1], [True, False], 0])
check('oracle 3', solve(*([[0, 0], [1, 1]], 0)), [[0, 0], [False, True], 1])
check('oracle 4', solve(*([], 1)), [[], [], 1])
check('oracle 5', solve(*([[1, 0], [1, 0]], 0)), [[1, 1], [True, True], 0])
check('oracle 6', solve(*([[1, 1]], 1)), [[0], [False], 1])
check('oracle 7', solve(*([[0, 0], [0, 1], [1, 1]], 1)), [[0, 1, 0], [True, False, False], 1])
if N == 1: check('variant packet 1', solve(*[[[1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0]], 0]), [[0, 1, 0, 0, 1, 0], [True, True, True, True, True, True], 0])
if N == 2: check('variant packet 2', solve(*[[[1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0]], 0]), [[0, 1, 0, 0, 1, 0, 0, 1, 0], [True, True, True, True, True, True, True, True, True], 0])
if N == 3: check('variant packet 3', solve(*[[[1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0]], 0]), [[0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [True, True, True, True, True, True, True, True, True, True, True, True], 0])
if N == 4: check('variant packet 4', solve(*[[[1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0]], 0]), [[0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [True, True, True, True, True, True, True, True, True, True, True, True, True, True, True], 0])
if N == 5: check('variant packet 5', solve(*[[[1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0]], 0]), [[0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True], 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, 1, 0], [False, False, False], 0] | [[0, 1, 0], [True, True, True], 0] | Failed |
| oracle 2 | [[1, 1], [False, True], 0] | [[1, 1], [True, False], 0] | Failed |
| oracle 3 | [[0, 0], [True, False], 1] | [[0, 0], [False, True], 1] | Failed |
| oracle 4 | [[], [], 1] | [[], [], 1] | Passed |
| oracle 5 | [[1, 1], [False, False], 0] | [[1, 1], [True, True], 0] | Failed |
| oracle 6 | [[0], [True], 1] | [[0], [False], 1] | Failed |
| oracle 7 | [[0, 1, 0], [False, True, True], 1] | [[0, 1, 0], [True, False, False], 1] | Failed |
| variant packet 1 | [[0, 1, 0, 0, 1, 0], [False, False, False, False, False, False], 0] | [[0, 1, 0, 0, 1, 0], [True, True, True, True, True, True], 0] | Failed |
SHA-256 / b1d1e588c6bf85847606e4eeb7f9ea9f01da16afa9f9727723fb721ba985b9f0
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(cells, initial):
previous=initial
bits=[]
valid=[]
for first,second in cells:
boundary=first!=previous
bit=int(first!=second)
bits.append(bit)
valid.append(boundary)
previous=second
return [bits,valid,previous]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[1, 1], [0, 1], [0, 0]], 0)), [[0, 1, 0], [True, True, True], 0])
check('oracle 2', solve(*([[0, 1], [1, 0]], 1)), [[1, 1], [True, False], 0])
check('oracle 3', solve(*([[0, 0], [1, 1]], 0)), [[0, 0], [False, True], 1])
check('oracle 4', solve(*([], 1)), [[], [], 1])
check('oracle 5', solve(*([[1, 0], [1, 0]], 0)), [[1, 1], [True, True], 0])
check('oracle 6', solve(*([[1, 1]], 1)), [[0], [False], 1])
check('oracle 7', solve(*([[0, 0], [0, 1], [1, 1]], 1)), [[0, 1, 0], [True, False, False], 1])
if N == 1: check('variant packet 1', solve(*[[[1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0]], 0]), [[0, 1, 0, 0, 1, 0], [True, True, True, True, True, True], 0])
if N == 2: check('variant packet 2', solve(*[[[1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0]], 0]), [[0, 1, 0, 0, 1, 0, 0, 1, 0], [True, True, True, True, True, True, True, True, True], 0])
if N == 3: check('variant packet 3', solve(*[[[1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0]], 0]), [[0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [True, True, True, True, True, True, True, True, True, True, True, True], 0])
if N == 4: check('variant packet 4', solve(*[[[1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0]], 0]), [[0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [True, True, True, True, True, True, True, True, True, True, True, True, True, True, True], 0])
if N == 5: check('variant packet 5', solve(*[[[1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0], [1, 1], [0, 1], [0, 0]], 0]), [[0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0], [True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True], 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, 1, 0], [True, True, True], 0] | [[0, 1, 0], [True, True, True], 0] | Passed |
| oracle 2 | [[1, 1], [True, False], 0] | [[1, 1], [True, False], 0] | Passed |
| oracle 3 | [[0, 0], [False, True], 1] | [[0, 0], [False, True], 1] | Passed |
| oracle 4 | [[], [], 1] | [[], [], 1] | Passed |
| oracle 5 | [[1, 1], [True, True], 0] | [[1, 1], [True, True], 0] | Passed |
| oracle 6 | [[0], [False], 1] | [[0], [False], 1] | Passed |
| oracle 7 | [[0, 1, 0], [True, False, False], 1] | [[0, 1, 0], [True, False, False], 1] | Passed |
| variant packet 1 | [[0, 1, 0, 0, 1, 0], [True, True, True, True, True, True], 0] | [[0, 1, 0, 0, 1, 0], [True, True, True, True, True, True], 0] | Passed |
SHA-256 / 2a78a2c4ee8991745a7aa4c6cdd8040c7a862353d1154530c88053ccc07cac39
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 2026-09-29T14:45:07.006049+00:00.
Case digest / 114f38c238ae45fe221d5f77c13b67dc3d1bc6260263594d45dda62e16699b73