FA-49091 / PCM sample encoding / Open access

Pcm bitplane restore: plane significance · case 01

Bit planes are assigned reversed amplitude significance.

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

ROOT CAUSE

Bit planes are assigned reversed amplitude significance.

THE FAILURE

Bit planes are assigned reversed amplitude significance.

Unsuccessful approach: Collapsing all planes into the low bit loses sample precision.

Case contract

Restore signed PCM sample integers from least-significant-bit-first bitplanes; sample index selects a bit inside each plane, and extra planes are ignored.

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, samples, width):
    out=[0]*samples
    for bit,plane in enumerate(planes[:width]):
        for i in range(samples):
            value=(plane>>i)&1
            out[i]|=value<<(width-1-bit)
    sign=1<<(width-1)
    return [x-(1<<width) if x&sign else x for x in out]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([5, 6, 3], 3, 3)), [-3, -2, 3])
check('oracle 2', solve(*([1, 2, 4, 7], 3, 3)), [1, 2, -4])
check('oracle 3', solve(*([0, 0, 7], 3, 3)), [-4, -4, -4])
check('oracle 4', solve(*([3, 0], 2, 2)), [1, 1])
check('oracle 5', solve(*([], 0, 4)), [])
check('oracle 6', solve(*([1], 1, 1)), [-1])
check('oracle 7', solve(*([0, 1, 0, 0], 1, 3)), [2])
if N == 1: check('variant packet 1', solve(*[[5, 6, 3], 4, 3]), [-3, -2, 3, 0])
if N == 2: check('variant packet 2', solve(*[[5, 6, 3], 5, 3]), [-3, -2, 3, 0, 0])
if N == 3: check('variant packet 3', solve(*[[5, 6, 3], 6, 3]), [-3, -2, 3, 0, 0, 0])
if N == 4: check('variant packet 4', solve(*[[5, 6, 3], 7, 3]), [-3, -2, 3, 0, 0, 0, 0])
if N == 5: check('variant packet 5', solve(*[[5, 6, 3], 8, 3]), [-3, -2, 3, 0, 0, 0, 0, 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 fixture	Actual	Expected	Outcome
oracle 1	`[-3, 3, -2]`	`[-3, -2, 3]`	Failed
oracle 2	`[-4, 2, 1]`	`[1, 2, -4]`	Failed
oracle 3	`[1, 1, 1]`	`[-4, -4, -4]`	Failed
oracle 4	`[-2, -2]`	`[1, 1]`	Failed
oracle 5	`[]`	`[]`	Passed
oracle 6	`[-1]`	`[-1]`	Passed
oracle 7	`[2]`	`[2]`	Passed
variant packet 1	`[-3, 3, -2, 0]`	`[-3, -2, 3, 0]`	Failed

SHA-256 / a549c5a878329311eb86698e2b8041fbf990a82d37350fc8159fb84a977063c9

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(planes, samples, width):
    out=[0]*samples
    for bit,plane in enumerate(planes[:width]):
        for i in range(samples):
            value=(plane>>i)&1
            out[i]|=value
    sign=1<<(width-1)
    return [x-(1<<width) if x&sign else x for x in out]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([5, 6, 3], 3, 3)), [-3, -2, 3])
check('oracle 2', solve(*([1, 2, 4, 7], 3, 3)), [1, 2, -4])
check('oracle 3', solve(*([0, 0, 7], 3, 3)), [-4, -4, -4])
check('oracle 4', solve(*([3, 0], 2, 2)), [1, 1])
check('oracle 5', solve(*([], 0, 4)), [])
check('oracle 6', solve(*([1], 1, 1)), [-1])
check('oracle 7', solve(*([0, 1, 0, 0], 1, 3)), [2])
if N == 1: check('variant packet 1', solve(*[[5, 6, 3], 4, 3]), [-3, -2, 3, 0])
if N == 2: check('variant packet 2', solve(*[[5, 6, 3], 5, 3]), [-3, -2, 3, 0, 0])
if N == 3: check('variant packet 3', solve(*[[5, 6, 3], 6, 3]), [-3, -2, 3, 0, 0, 0])
if N == 4: check('variant packet 4', solve(*[[5, 6, 3], 7, 3]), [-3, -2, 3, 0, 0, 0, 0])
if N == 5: check('variant packet 5', solve(*[[5, 6, 3], 8, 3]), [-3, -2, 3, 0, 0, 0, 0, 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 fixture	Actual	Expected	Outcome
oracle 1	`[1, 1, 1]`	`[-3, -2, 3]`	Failed
oracle 2	`[1, 1, 1]`	`[1, 2, -4]`	Failed
oracle 3	`[1, 1, 1]`	`[-4, -4, -4]`	Failed
oracle 4	`[1, 1]`	`[1, 1]`	Passed
oracle 5	`[]`	`[]`	Passed
oracle 6	`[-1]`	`[-1]`	Passed
oracle 7	`[1]`	`[2]`	Failed
variant packet 1	`[1, 1, 1, 0]`	`[-3, -2, 3, 0]`	Failed

SHA-256 / 922c278395ef8dedb1d8b20cd33ee657a7c417e37d9e87e36df548f41511a6ce

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.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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 2026-09-29T14:44:56.938680+00:00.

Case digest / 6d7c6950b4f5d1dd5fa274a24d56e926a7d0e98a06ab970d1b64dfc0827c68ef