FAILURE MAP
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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.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

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 fixtureActualExpectedOutcome
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 fixtureActualExpectedOutcome
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 fixtureActualExpectedOutcome
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