FAILURE MAP
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FA-50031 / PCM sample encoding / Open access

Pcm pdm box decimation: trailing bits · case 01

Carry starts at output-count rather than consumed bit count.

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

ROOT CAUSE

Carry starts at output-count rather than consumed bit count.

THE FAILURE

Carry starts at output-count rather than consumed bit count.

Unsuccessful approach: Dropping the first trailing bit permanently changes sample phase.

Case contract

Bounded one-bit-density to PCM adapter using nonoverlapping box windows; zero/one map to -1/+1 and incomplete input bits carry 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(bits, factor, carry):
    combined=list(carry)+list(bits)
    complete=len(combined)//factor
    samples=[]
    for group in range(complete):
        window=combined[group*factor:(group+1)*factor]
        amplitude=2*sum(window)-factor
        samples.append(amplitude)
    return [samples,combined[complete:]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, 0, 1, 1, 0, 0], 3, [])), [[1, -1], []])
check('oracle 2', solve(*([1, 0, 0], 4, [1, 1])), [[2], [0]])
check('oracle 3', solve(*([1, 1, 1, 1], 2, [])), [[2, 2], []])
check('oracle 4', solve(*([], 4, [1])), [[], [1]])
check('oracle 5', solve(*([0, 0, 0, 0], 4, [])), [[-4], []])
check('oracle 6', solve(*([1], 1, [])), [[1], []])
check('oracle 7', solve(*([0, 1, 0, 1, 1], 3, [0])), [[-1, 1], []])
if N == 1: check('variant packet 1', solve(*[[1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0], 3, []]), [[1, -1, 1, -1], []])
if N == 2: check('variant packet 2', solve(*[[1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0], 3, []]), [[1, -1, 1, -1, 1, -1], []])
if N == 3: check('variant packet 3', solve(*[[1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0], 3, []]), [[1, -1, 1, -1, 1, -1, 1, -1], []])
if N == 4: check('variant packet 4', solve(*[[1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0], 3, []]), [[1, -1, 1, -1, 1, -1, 1, -1, 1, -1], []])
if N == 5: check('variant packet 5', solve(*[[1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0], 3, []]), [[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], []])
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[[1, -1], [1, 1, 0, 0]][[1, -1], []]Failed
oracle 2[[2], [1, 1, 0, 0]][[2], [0]]Failed
oracle 3[[2, 2], [1, 1]][[2, 2], []]Failed
oracle 4[[], [1]][[], [1]]Passed
oracle 5[[-4], [0, 0, 0]][[-4], []]Failed
oracle 6[[1], []][[1], []]Passed
oracle 7[[-1, 1], [1, 0, 1, 1]][[-1, 1], []]Failed
variant packet 1[[1, -1, 1, -1], [0, 0, 1, 0, 1, 1, 0, 0]][[1, -1, 1, -1], []]Failed

SHA-256 / 4e2a78b5c47fc851bb4cdc390da154d28b36e0bffb856b465b62208927586507

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(bits, factor, carry):
    combined=list(carry)+list(bits)
    complete=len(combined)//factor
    samples=[]
    for group in range(complete):
        window=combined[group*factor:(group+1)*factor]
        amplitude=2*sum(window)-factor
        samples.append(amplitude)
    return [samples,combined[complete*factor+1:]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, 0, 1, 1, 0, 0], 3, [])), [[1, -1], []])
check('oracle 2', solve(*([1, 0, 0], 4, [1, 1])), [[2], [0]])
check('oracle 3', solve(*([1, 1, 1, 1], 2, [])), [[2, 2], []])
check('oracle 4', solve(*([], 4, [1])), [[], [1]])
check('oracle 5', solve(*([0, 0, 0, 0], 4, [])), [[-4], []])
check('oracle 6', solve(*([1], 1, [])), [[1], []])
check('oracle 7', solve(*([0, 1, 0, 1, 1], 3, [0])), [[-1, 1], []])
if N == 1: check('variant packet 1', solve(*[[1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0], 3, []]), [[1, -1, 1, -1], []])
if N == 2: check('variant packet 2', solve(*[[1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0], 3, []]), [[1, -1, 1, -1, 1, -1], []])
if N == 3: check('variant packet 3', solve(*[[1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0], 3, []]), [[1, -1, 1, -1, 1, -1, 1, -1], []])
if N == 4: check('variant packet 4', solve(*[[1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0], 3, []]), [[1, -1, 1, -1, 1, -1, 1, -1, 1, -1], []])
if N == 5: check('variant packet 5', solve(*[[1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0], 3, []]), [[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], []])
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[[1, -1], []][[1, -1], []]Passed
oracle 2[[2], []][[2], [0]]Failed
oracle 3[[2, 2], []][[2, 2], []]Passed
oracle 4[[], []][[], [1]]Failed
oracle 5[[-4], []][[-4], []]Passed
oracle 6[[1], []][[1], []]Passed
oracle 7[[-1, 1], []][[-1, 1], []]Passed
variant packet 1[[1, -1, 1, -1], []][[1, -1, 1, -1], []]Passed

SHA-256 / 1edf1fb8c2f9db3f0f5bec1cd1543e8a82937fda6ad4759d56a0cbeda72ab36e

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:45:05.461064+00:00.

Case digest / f58adacdb6d95f6fe995dcb3df74b620db8e25c454095be3b687a50c7af2be85