FAILURE MAP
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FA-49711 / PCM sample encoding / Open access

Pcm onebit pulse density: continuation residue · case 01

Packet continuation loses the fractional density residue.

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

ROOT CAUSE

Packet continuation loses the fractional density residue.

VERIFIED REPAIR

Use the stated conversion contract at continuation residue.

Unsuccessful approach: Reducing residue modulo two ignores the actual quantizer denominator.

Case contract

Convert bounded nonnegative PCM levels no greater than denominator into a deterministic one-bit pulse-density stream, preserving fractional accumulator state.

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(samples, denominator, accumulator):
    bits=[]
    for sample in samples:
        accumulator+=sample
        pulse=accumulator>=denominator
        if pulse:
            accumulator-=denominator
        bits.append(int(pulse))
    return [bits,0]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, 2, 3, 4], 5, 0)), [[0, 0, 1, 1], 0])
check('oracle 2', solve(*([5, 0, 5], 5, 0)), [[1, 0, 1], 0])
check('oracle 3', solve(*([2, 2, 2, 2], 3, 1)), [[1, 0, 1, 1], 0])
check('oracle 4', solve(*([], 5, 2)), [[], 2])
check('oracle 5', solve(*([0, 0], 4, 3)), [[0, 0], 3])
check('oracle 6', solve(*([3, 3, 3], 4, 2)), [[1, 1, 0], 3])
check('oracle 7', solve(*([1, 1, 1], 2, 0)), [[0, 1, 0], 1])
if N == 1: check('variant packet 1', solve(*[[1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1], 0])
if N == 2: check('variant packet 2', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])
if N == 3: check('variant packet 3', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])
if N == 4: check('variant packet 4', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])
if N == 5: check('variant packet 5', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 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, 0, 1, 1], 0][[0, 0, 1, 1], 0]Passed
oracle 2[[1, 0, 1], 0][[1, 0, 1], 0]Passed
oracle 3[[1, 0, 1, 1], 0][[1, 0, 1, 1], 0]Passed
oracle 4[[], 0][[], 2]Failed
oracle 5[[0, 0], 0][[0, 0], 3]Failed
oracle 6[[1, 1, 0], 0][[1, 1, 0], 3]Failed
oracle 7[[0, 1, 0], 0][[0, 1, 0], 1]Failed
variant packet 1[[0, 0, 1, 1, 0, 0, 1, 1], 0][[0, 0, 1, 1, 0, 0, 1, 1], 0]Passed

SHA-256 / 5eefde58241f51af886a3393c56015a189326bedea939566fbbf7e660dbefed6

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(samples, denominator, accumulator):
    bits=[]
    for sample in samples:
        accumulator+=sample
        pulse=accumulator>=denominator
        if pulse:
            accumulator-=denominator
        bits.append(int(pulse))
    return [bits,accumulator%2]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, 2, 3, 4], 5, 0)), [[0, 0, 1, 1], 0])
check('oracle 2', solve(*([5, 0, 5], 5, 0)), [[1, 0, 1], 0])
check('oracle 3', solve(*([2, 2, 2, 2], 3, 1)), [[1, 0, 1, 1], 0])
check('oracle 4', solve(*([], 5, 2)), [[], 2])
check('oracle 5', solve(*([0, 0], 4, 3)), [[0, 0], 3])
check('oracle 6', solve(*([3, 3, 3], 4, 2)), [[1, 1, 0], 3])
check('oracle 7', solve(*([1, 1, 1], 2, 0)), [[0, 1, 0], 1])
if N == 1: check('variant packet 1', solve(*[[1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1], 0])
if N == 2: check('variant packet 2', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])
if N == 3: check('variant packet 3', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])
if N == 4: check('variant packet 4', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])
if N == 5: check('variant packet 5', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 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, 0, 1, 1], 0][[0, 0, 1, 1], 0]Passed
oracle 2[[1, 0, 1], 0][[1, 0, 1], 0]Passed
oracle 3[[1, 0, 1, 1], 0][[1, 0, 1, 1], 0]Passed
oracle 4[[], 0][[], 2]Failed
oracle 5[[0, 0], 1][[0, 0], 3]Failed
oracle 6[[1, 1, 0], 1][[1, 1, 0], 3]Failed
oracle 7[[0, 1, 0], 1][[0, 1, 0], 1]Passed
variant packet 1[[0, 0, 1, 1, 0, 0, 1, 1], 0][[0, 0, 1, 1, 0, 0, 1, 1], 0]Passed

SHA-256 / 14765287e3424b74e84ce04cdcf6182cfe39e99f828d244910bde9f2da099dbc

3 / The verified repair

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

N = 1
observations = []
def solve(samples, denominator, accumulator):
    bits=[]
    for sample in samples:
        accumulator+=sample
        pulse=accumulator>=denominator
        if pulse:
            accumulator-=denominator
        bits.append(int(pulse))
    return [bits,accumulator]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, 2, 3, 4], 5, 0)), [[0, 0, 1, 1], 0])
check('oracle 2', solve(*([5, 0, 5], 5, 0)), [[1, 0, 1], 0])
check('oracle 3', solve(*([2, 2, 2, 2], 3, 1)), [[1, 0, 1, 1], 0])
check('oracle 4', solve(*([], 5, 2)), [[], 2])
check('oracle 5', solve(*([0, 0], 4, 3)), [[0, 0], 3])
check('oracle 6', solve(*([3, 3, 3], 4, 2)), [[1, 1, 0], 3])
check('oracle 7', solve(*([1, 1, 1], 2, 0)), [[0, 1, 0], 1])
if N == 1: check('variant packet 1', solve(*[[1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1], 0])
if N == 2: check('variant packet 2', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])
if N == 3: check('variant packet 3', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])
if N == 4: check('variant packet 4', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])
if N == 5: check('variant packet 5', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 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, 0, 1, 1], 0][[0, 0, 1, 1], 0]Passed
oracle 2[[1, 0, 1], 0][[1, 0, 1], 0]Passed
oracle 3[[1, 0, 1, 1], 0][[1, 0, 1, 1], 0]Passed
oracle 4[[], 2][[], 2]Passed
oracle 5[[0, 0], 3][[0, 0], 3]Passed
oracle 6[[1, 1, 0], 3][[1, 1, 0], 3]Passed
oracle 7[[0, 1, 0], 1][[0, 1, 0], 1]Passed
variant packet 1[[0, 0, 1, 1, 0, 0, 1, 1], 0][[0, 0, 1, 1, 0, 0, 1, 1], 0]Passed

SHA-256 / a35e3a0b70e13f2156299bc65806267432f0c203f88fd326ca134eab6fc0641d

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 2026-09-29T14:45:02.435115+00:00.

Case digest / 578d3d0858190609d6557bb8be339ec43fbf3fd3193a72d33c5796d306c88757