FAILURE MAP
← Case archive

FA-49171 / PCM sample encoding / Open access

Pcm frame sequence: gap threshold · case 01

The ambiguous half-cycle packet is accepted as a forward gap.

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

ROOT CAUSE

The ambiguous half-cycle packet is accepted as a forward gap.

VERIFIED REPAIR

Use the stated conversion contract at gap threshold.

Unsuccessful approach: Accepting all nonzero distances replays old packets after huge gaps.

Case contract

Bounded PCM packet sequence adapter with one null marker per lost packet (not per lost sample); reject old or half-cycle-ambiguous packets and retain modular cursor.

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(packets, start, modulus):
    expected=start
    out=[]
    for sequence,samples in packets:
        delta=(sequence-expected)%modulus
        if delta==0:
            out.extend(samples)
            expected=(expected+1)%modulus
        elif delta<=modulus//2:
            out.extend([None]*delta)
            out.extend(samples)
            expected=(sequence+1)%modulus
    return [out,expected]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[7, [4]], [0, [5]], [1, [6]]], 7, 8)), [[4, 5, 6], 2])
check('oracle 2', solve(*([[0, [1]], [2, [3]], [3, [4]]], 0, 8)), [[1, None, 3, 4], 4])
check('oracle 3', solve(*([[4, [9]], [0, [2]]], 0, 8)), [[2], 1])
check('oracle 4', solve(*([[7, [9]], [0, [1]]], 0, 8)), [[1], 1])
check('oracle 5', solve(*([], 3, 8)), [[], 3])
check('oracle 6', solve(*([[6, [1]], [1, [2]]], 6, 8)), [[1, None, None, 2], 2])
check('oracle 7', solve(*([[0, [1, 2]], [0, [3]], [1, [4]]], 0, 8)), [[1, 2, 4], 2])
if N == 1: check('variant packet 1', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])
if N == 2: check('variant packet 2', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])
if N == 3: check('variant packet 3', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])
if N == 4: check('variant packet 4', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])
if N == 5: check('variant packet 5', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])
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[[4, 5, 6], 2][[4, 5, 6], 2]Passed
oracle 2[[1, None, 3, 4], 4][[1, None, 3, 4], 4]Passed
oracle 3[[None, None, None, None, 9, None, None, None, 2], 1][[2], 1]Failed
oracle 4[[1], 1][[1], 1]Passed
oracle 5[[], 3][[], 3]Passed
oracle 6[[1, None, None, 2], 2][[1, None, None, 2], 2]Passed
oracle 7[[1, 2, 4], 2][[1, 2, 4], 2]Passed
variant packet 1[[4, 5, 6], 2][[4, 5, 6], 2]Passed

SHA-256 / 19068f924cbd0c773fb52dabfabfbb0961ec09289fd9103261ecccd2524aa94d

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(packets, start, modulus):
    expected=start
    out=[]
    for sequence,samples in packets:
        delta=(sequence-expected)%modulus
        if delta==0:
            out.extend(samples)
            expected=(expected+1)%modulus
        elif delta<modulus:
            out.extend([None]*delta)
            out.extend(samples)
            expected=(sequence+1)%modulus
    return [out,expected]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[7, [4]], [0, [5]], [1, [6]]], 7, 8)), [[4, 5, 6], 2])
check('oracle 2', solve(*([[0, [1]], [2, [3]], [3, [4]]], 0, 8)), [[1, None, 3, 4], 4])
check('oracle 3', solve(*([[4, [9]], [0, [2]]], 0, 8)), [[2], 1])
check('oracle 4', solve(*([[7, [9]], [0, [1]]], 0, 8)), [[1], 1])
check('oracle 5', solve(*([], 3, 8)), [[], 3])
check('oracle 6', solve(*([[6, [1]], [1, [2]]], 6, 8)), [[1, None, None, 2], 2])
check('oracle 7', solve(*([[0, [1, 2]], [0, [3]], [1, [4]]], 0, 8)), [[1, 2, 4], 2])
if N == 1: check('variant packet 1', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])
if N == 2: check('variant packet 2', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])
if N == 3: check('variant packet 3', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])
if N == 4: check('variant packet 4', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])
if N == 5: check('variant packet 5', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])
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[[4, 5, 6], 2][[4, 5, 6], 2]Passed
oracle 2[[1, None, 3, 4], 4][[1, None, 3, 4], 4]Passed
oracle 3[[None, None, None, None, 9, None, None, None, 2], 1][[2], 1]Failed
oracle 4[[None, None, None, None, None, None, None, 9, 1], 1][[1], 1]Failed
oracle 5[[], 3][[], 3]Passed
oracle 6[[1, None, None, 2], 2][[1, None, None, 2], 2]Passed
oracle 7[[1, 2, None, None, None, None, None, None, None, 3, 4], 2][[1, 2, 4], 2]Failed
variant packet 1[[4, 5, 6, None, None, None, None, None, 4, 5, 6], 2][[4, 5, 6], 2]Failed

SHA-256 / 1fc22e649fc3fccfc4fca0494b607e712c7bbdecd16195bb74da6fd325881ebe

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(packets, start, modulus):
    expected=start
    out=[]
    for sequence,samples in packets:
        delta=(sequence-expected)%modulus
        if delta==0:
            out.extend(samples)
            expected=(expected+1)%modulus
        elif delta<modulus//2:
            out.extend([None]*delta)
            out.extend(samples)
            expected=(sequence+1)%modulus
    return [out,expected]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[7, [4]], [0, [5]], [1, [6]]], 7, 8)), [[4, 5, 6], 2])
check('oracle 2', solve(*([[0, [1]], [2, [3]], [3, [4]]], 0, 8)), [[1, None, 3, 4], 4])
check('oracle 3', solve(*([[4, [9]], [0, [2]]], 0, 8)), [[2], 1])
check('oracle 4', solve(*([[7, [9]], [0, [1]]], 0, 8)), [[1], 1])
check('oracle 5', solve(*([], 3, 8)), [[], 3])
check('oracle 6', solve(*([[6, [1]], [1, [2]]], 6, 8)), [[1, None, None, 2], 2])
check('oracle 7', solve(*([[0, [1, 2]], [0, [3]], [1, [4]]], 0, 8)), [[1, 2, 4], 2])
if N == 1: check('variant packet 1', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])
if N == 2: check('variant packet 2', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])
if N == 3: check('variant packet 3', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])
if N == 4: check('variant packet 4', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])
if N == 5: check('variant packet 5', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])
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[[4, 5, 6], 2][[4, 5, 6], 2]Passed
oracle 2[[1, None, 3, 4], 4][[1, None, 3, 4], 4]Passed
oracle 3[[2], 1][[2], 1]Passed
oracle 4[[1], 1][[1], 1]Passed
oracle 5[[], 3][[], 3]Passed
oracle 6[[1, None, None, 2], 2][[1, None, None, 2], 2]Passed
oracle 7[[1, 2, 4], 2][[1, 2, 4], 2]Passed
variant packet 1[[4, 5, 6], 2][[4, 5, 6], 2]Passed

SHA-256 / 77f56d5c81666a70a87e514b0dbd130c5bbb4cd6d07d3d0c13f6f21f55c36222

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 2026-09-29T14:44:57.544018+00:00.

Case digest / bed64c91c3ef84b0ff15d48eff6ad964913fa9a7e8b20571569626ff70b94be6