FA-49136 / PCM sample encoding / Open access

Pcm byteplane restore: signed conversion · case 01

Negative plane-assembled words use half the complement modulus.

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

ROOT CAUSE

Negative plane-assembled words use half the complement modulus.

VERIFIED REPAIR

Use the stated conversion contract at signed conversion.

Unsuccessful approach: Negating a stored complement code fails to restore its amplitude.

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]<<(8*b) for b in range(octets))
        sign=1<<(8*octets-1)
        if value&sign:
            value-=1<<(8*octets-1)
        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 fixture	Actual	Expected	Outcome
oracle 1	`[1, 32767, 0]`	`[1, -1, -32768]`	Failed
oracle 2	`[1, 2, 3, 4]`	`[1, 2, 3, 4]`	Passed
oracle 3	`[0]`	`[-32768]`	Failed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[32767, 0]`	`[32767, 0]`	Passed
oracle 6	`[328449, 394242]`	`[328449, 394242]`	Passed
oracle 7	`[8388607]`	`[-1]`	Failed
variant packet 1	`[1, 32767, 0, 1, 32767, 0]`	`[1, -1, -32768, 1, -1, -32768]`	Failed

SHA-256 / 3e4d5329ac1d632e01f0978f04cdff36c23b0ebf818301e87fb558ca41552632

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*b) for b in range(octets))
        sign=1<<(8*octets-1)
        if value&sign:
            value=-value
        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 fixture	Actual	Expected	Outcome
oracle 1	`[1, -65535, -32768]`	`[1, -1, -32768]`	Failed
oracle 2	`[1, 2, 3, 4]`	`[1, 2, 3, 4]`	Passed
oracle 3	`[-32768]`	`[-32768]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[32767, 0]`	`[32767, 0]`	Passed
oracle 6	`[328449, 394242]`	`[328449, 394242]`	Passed
oracle 7	`[-16777215]`	`[-1]`	Failed
variant packet 1	`[1, -65535, -32768, 1, -65535, -32768]`	`[1, -1, -32768, 1, -1, -32768]`	Failed

SHA-256 / ba15f86d045fab5a05b738966ebc585c88a10d4fe12d5751b9af6dbcea308279

3 / The verified repair

Exit 0

"""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*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 fixture	Actual	Expected	Outcome
oracle 1	`[1, -1, -32768]`	`[1, -1, -32768]`	Passed
oracle 2	`[1, 2, 3, 4]`	`[1, 2, 3, 4]`	Passed
oracle 3	`[-32768]`	`[-32768]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[32767, 0]`	`[32767, 0]`	Passed
oracle 6	`[328449, 394242]`	`[328449, 394242]`	Passed
oracle 7	`[-1]`	`[-1]`	Passed
variant packet 1	`[1, -1, -32768, 1, -1, -32768]`	`[1, -1, -32768, 1, -1, -32768]`	Passed

SHA-256 / 777900c6fa2000271d1a5580a45eca7da8578683cf67427d54fde4dc73b9f709

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 / 7883af4bae9edd0aa5a09b0ca15e41efed3963975166539325713c541f9a2794