FAILURE MAP
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FA-49176 / PCM sample encoding / Open access

Pcm frame sequence: gap placeholder · case 01

Missing packet units become valid digital-silence samples.

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

ROOT CAUSE

Missing packet units become valid digital-silence samples.

VERIFIED REPAIR

Use the stated conversion contract at gap placeholder.

Unsuccessful approach: Adding the received packet to the gap count inserts an extra loss marker.

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([0]*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, 0, 3, 4], 4][[1, None, 3, 4], 4]Failed
oracle 3[[2], 1][[2], 1]Passed
oracle 4[[1], 1][[1], 1]Passed
oracle 5[[], 3][[], 3]Passed
oracle 6[[1, 0, 0, 2], 2][[1, None, None, 2], 2]Failed
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 / b50fdbab194dc5a224f57d6c2612c86482fdad4091a8eecdf1640c6e05e32e83

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//2:
            out.extend([None]*(delta+1))
            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, None, 3, 4], 4][[1, None, 3, 4], 4]Failed
oracle 3[[2], 1][[2], 1]Passed
oracle 4[[1], 1][[1], 1]Passed
oracle 5[[], 3][[], 3]Passed
oracle 6[[1, None, None, None, 2], 2][[1, None, None, 2], 2]Failed
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 / 8ad5f32b781003c3e447d01d08b058470ddffb22fd7ec762d3716bf4b4428e6d

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 2026-09-29T14:44:57.575844+00:00.

Case digest / a0f5268f06a61c62ed1df7a15d23ddeb97893ae9b80a5c12f53a09ea51cbbbef