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FA-49121 / PCM sample encoding / Open access

Pcm byteplane restore: octet weight · case 01

Byte planes are weighted as single-bit planes.

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

ROOT CAUSE

Byte planes are weighted as single-bit planes.

THE FAILURE

Byte planes are weighted as single-bit planes.

Unsuccessful approach: Reversing plane weights changes the stipulated planar layout.

Case contract

Reassemble signed integer PCM from per-byte-significance planes, preserving sample order and the declared number of octets per sample.

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(planes, count, octets):
    out=[]
    for i in range(count):
        value=sum(planes[b][i]<<b for b in range(octets))
        sign=1<<(8*octets-1)
        if value&sign:
            value-=1<<(8*octets)
        out.append(value)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[1, 255, 0], [0, 255, 128]], 3, 2)), [1, -1, -32768])
check('oracle 2', solve(*([[1, 2, 3, 4]], 4, 1)), [1, 2, 3, 4])
check('oracle 3', solve(*([[0], [128]], 1, 2)), [-32768])
check('oracle 4', solve(*([[], []], 0, 2)), [])
check('oracle 5', solve(*([[255, 0], [127, 0]], 2, 2)), [32767, 0])
check('oracle 6', solve(*([[1, 2], [3, 4], [5, 6]], 2, 3)), [328449, 394242])
check('oracle 7', solve(*([[255], [255], [255]], 1, 3)), [-1])
if N == 1: check('variant packet 1', solve(*[[[1, 255, 0, 1, 255, 0], [0, 255, 128, 0, 255, 128]], 6, 2]), [1, -1, -32768, 1, -1, -32768])
if N == 2: check('variant packet 2', solve(*[[[1, 255, 0, 1, 255, 0, 1, 255, 0], [0, 255, 128, 0, 255, 128, 0, 255, 128]], 9, 2]), [1, -1, -32768, 1, -1, -32768, 1, -1, -32768])
if N == 3: check('variant packet 3', solve(*[[[1, 255, 0, 1, 255, 0, 1, 255, 0, 1, 255, 0], [0, 255, 128, 0, 255, 128, 0, 255, 128, 0, 255, 128]], 12, 2]), [1, -1, -32768, 1, -1, -32768, 1, -1, -32768, 1, -1, -32768])
if N == 4: check('variant packet 4', solve(*[[[1, 255, 0, 1, 255, 0, 1, 255, 0, 1, 255, 0, 1, 255, 0], [0, 255, 128, 0, 255, 128, 0, 255, 128, 0, 255, 128, 0, 255, 128]], 15, 2]), [1, -1, -32768, 1, -1, -32768, 1, -1, -32768, 1, -1, -32768, 1, -1, -32768])
if N == 5: check('variant packet 5', solve(*[[[1, 255, 0, 1, 255, 0, 1, 255, 0, 1, 255, 0, 1, 255, 0, 1, 255, 0], [0, 255, 128, 0, 255, 128, 0, 255, 128, 0, 255, 128, 0, 255, 128, 0, 255, 128]], 18, 2]), [1, -1, -32768, 1, -1, -32768, 1, -1, -32768, 1, -1, -32768, 1, -1, -32768, 1, -1, -32768])
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, 765, 256][1, -1, -32768]Failed
oracle 2[1, 2, 3, 4][1, 2, 3, 4]Passed
oracle 3[256][-32768]Failed
oracle 4[][]Passed
oracle 5[509, 0][32767, 0]Failed
oracle 6[27, 34][328449, 394242]Failed
oracle 7[1785][-1]Failed
variant packet 1[1, 765, 256, 1, 765, 256][1, -1, -32768, 1, -1, -32768]Failed

SHA-256 / 561c9ec453dd5127fb3a498d4fa3224b167eddd705917b3ec4359496c537c673

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(planes, count, octets):
    out=[]
    for i in range(count):
        value=sum(planes[b][i]<<(8*(octets-1-b)) for b in range(octets))
        sign=1<<(8*octets-1)
        if value&sign:
            value-=1<<(8*octets)
        out.append(value)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[1, 255, 0], [0, 255, 128]], 3, 2)), [1, -1, -32768])
check('oracle 2', solve(*([[1, 2, 3, 4]], 4, 1)), [1, 2, 3, 4])
check('oracle 3', solve(*([[0], [128]], 1, 2)), [-32768])
check('oracle 4', solve(*([[], []], 0, 2)), [])
check('oracle 5', solve(*([[255, 0], [127, 0]], 2, 2)), [32767, 0])
check('oracle 6', solve(*([[1, 2], [3, 4], [5, 6]], 2, 3)), [328449, 394242])
check('oracle 7', solve(*([[255], [255], [255]], 1, 3)), [-1])
if N == 1: check('variant packet 1', solve(*[[[1, 255, 0, 1, 255, 0], [0, 255, 128, 0, 255, 128]], 6, 2]), [1, -1, -32768, 1, -1, -32768])
if N == 2: check('variant packet 2', solve(*[[[1, 255, 0, 1, 255, 0, 1, 255, 0], [0, 255, 128, 0, 255, 128, 0, 255, 128]], 9, 2]), [1, -1, -32768, 1, -1, -32768, 1, -1, -32768])
if N == 3: check('variant packet 3', solve(*[[[1, 255, 0, 1, 255, 0, 1, 255, 0, 1, 255, 0], [0, 255, 128, 0, 255, 128, 0, 255, 128, 0, 255, 128]], 12, 2]), [1, -1, -32768, 1, -1, -32768, 1, -1, -32768, 1, -1, -32768])
if N == 4: check('variant packet 4', solve(*[[[1, 255, 0, 1, 255, 0, 1, 255, 0, 1, 255, 0, 1, 255, 0], [0, 255, 128, 0, 255, 128, 0, 255, 128, 0, 255, 128, 0, 255, 128]], 15, 2]), [1, -1, -32768, 1, -1, -32768, 1, -1, -32768, 1, -1, -32768, 1, -1, -32768])
if N == 5: check('variant packet 5', solve(*[[[1, 255, 0, 1, 255, 0, 1, 255, 0, 1, 255, 0, 1, 255, 0, 1, 255, 0], [0, 255, 128, 0, 255, 128, 0, 255, 128, 0, 255, 128, 0, 255, 128, 0, 255, 128]], 18, 2]), [1, -1, -32768, 1, -1, -32768, 1, -1, -32768, 1, -1, -32768, 1, -1, -32768, 1, -1, -32768])
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[256, -1, 128][1, -1, -32768]Failed
oracle 2[1, 2, 3, 4][1, 2, 3, 4]Passed
oracle 3[128][-32768]Failed
oracle 4[][]Passed
oracle 5[-129, 0][32767, 0]Failed
oracle 6[66309, 132102][328449, 394242]Failed
oracle 7[-1][-1]Passed
variant packet 1[256, -1, 128, 256, -1, 128][1, -1, -32768, 1, -1, -32768]Failed

SHA-256 / 1b375f9a74e714012e13b7f3a747f6c9dd91ea332637ea3c3cba8696af387153

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 2026-09-29T14:44:57.114879+00:00.

Case digest / 69b4930ae7727724895395f0c4ea13e9e3fd30beb563cfa2e29bca655c7db1af