FA-50281 / PCM sample encoding / Open access

Pcm common trailing zero shift: signed coarse · case 01

Removing common zero bits drops PCM polarity.

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

ROOT CAUSE

Removing common zero bits drops PCM polarity.

VERIFIED REPAIR

Use the stated conversion contract at signed coarse.

Unsuccessful approach: Shifting left increases precision instead of factoring common low zeros.

Case contract

Losslessly factor the largest capped common trailing-zero count from signed PCM samples; zero samples do not constrain the count and all-silence blocks canonically use zero.

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, maximum):
    shift=0
    nonzero=[abs(x) for x in samples if x!=0]
    if nonzero:
        while shift<maximum and all((x&((1<<(shift+1))-1))==0 for x in nonzero):
            shift+=1
    coarse=[abs(x)>>shift for x in samples]
    return [shift,coarse]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([8, -12, 0], 5)), [2, [2, -3, 0]])
check('oracle 2', solve(*([0, 0], 4)), [0, [0, 0]])
check('oracle 3', solve(*([8, 6], 4)), [1, [4, 3]])
check('oracle 4', solve(*([], 3)), [0, []])
check('oracle 5', solve(*([-8, -4], 5)), [2, [-2, -1]])
check('oracle 6', solve(*([16, 32], 2)), [2, [4, 8]])
check('oracle 7', solve(*([3, -8], 4)), [0, [3, -8]])
if N == 1: check('variant packet 1', solve(*[[8, -12, 0, 8, -12, 0], 5]), [2, [2, -3, 0, 2, -3, 0]])
if N == 2: check('variant packet 2', solve(*[[8, -12, 0, 8, -12, 0, 8, -12, 0], 5]), [2, [2, -3, 0, 2, -3, 0, 2, -3, 0]])
if N == 3: check('variant packet 3', solve(*[[8, -12, 0, 8, -12, 0, 8, -12, 0, 8, -12, 0], 5]), [2, [2, -3, 0, 2, -3, 0, 2, -3, 0, 2, -3, 0]])
if N == 4: check('variant packet 4', solve(*[[8, -12, 0, 8, -12, 0, 8, -12, 0, 8, -12, 0, 8, -12, 0], 5]), [2, [2, -3, 0, 2, -3, 0, 2, -3, 0, 2, -3, 0, 2, -3, 0]])
if N == 5: check('variant packet 5', solve(*[[8, -12, 0, 8, -12, 0, 8, -12, 0, 8, -12, 0, 8, -12, 0, 8, -12, 0], 5]), [2, [2, -3, 0, 2, -3, 0, 2, -3, 0, 2, -3, 0, 2, -3, 0, 2, -3, 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	`[2, [2, 3, 0]]`	`[2, [2, -3, 0]]`	Failed
oracle 2	`[0, [0, 0]]`	`[0, [0, 0]]`	Passed
oracle 3	`[1, [4, 3]]`	`[1, [4, 3]]`	Passed
oracle 4	`[0, []]`	`[0, []]`	Passed
oracle 5	`[2, [2, 1]]`	`[2, [-2, -1]]`	Failed
oracle 6	`[2, [4, 8]]`	`[2, [4, 8]]`	Passed
oracle 7	`[0, [3, 8]]`	`[0, [3, -8]]`	Failed
variant packet 1	`[2, [2, 3, 0, 2, 3, 0]]`	`[2, [2, -3, 0, 2, -3, 0]]`	Failed

SHA-256 / 34b8a868150500a4814a11c8f3fc90f5583168c40333a94c4df0de141d87db80

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(samples, maximum):
    shift=0
    nonzero=[abs(x) for x in samples if x!=0]
    if nonzero:
        while shift<maximum and all((x&((1<<(shift+1))-1))==0 for x in nonzero):
            shift+=1
    coarse=[x<<shift for x in samples]
    return [shift,coarse]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([8, -12, 0], 5)), [2, [2, -3, 0]])
check('oracle 2', solve(*([0, 0], 4)), [0, [0, 0]])
check('oracle 3', solve(*([8, 6], 4)), [1, [4, 3]])
check('oracle 4', solve(*([], 3)), [0, []])
check('oracle 5', solve(*([-8, -4], 5)), [2, [-2, -1]])
check('oracle 6', solve(*([16, 32], 2)), [2, [4, 8]])
check('oracle 7', solve(*([3, -8], 4)), [0, [3, -8]])
if N == 1: check('variant packet 1', solve(*[[8, -12, 0, 8, -12, 0], 5]), [2, [2, -3, 0, 2, -3, 0]])
if N == 2: check('variant packet 2', solve(*[[8, -12, 0, 8, -12, 0, 8, -12, 0], 5]), [2, [2, -3, 0, 2, -3, 0, 2, -3, 0]])
if N == 3: check('variant packet 3', solve(*[[8, -12, 0, 8, -12, 0, 8, -12, 0, 8, -12, 0], 5]), [2, [2, -3, 0, 2, -3, 0, 2, -3, 0, 2, -3, 0]])
if N == 4: check('variant packet 4', solve(*[[8, -12, 0, 8, -12, 0, 8, -12, 0, 8, -12, 0, 8, -12, 0], 5]), [2, [2, -3, 0, 2, -3, 0, 2, -3, 0, 2, -3, 0, 2, -3, 0]])
if N == 5: check('variant packet 5', solve(*[[8, -12, 0, 8, -12, 0, 8, -12, 0, 8, -12, 0, 8, -12, 0, 8, -12, 0], 5]), [2, [2, -3, 0, 2, -3, 0, 2, -3, 0, 2, -3, 0, 2, -3, 0, 2, -3, 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	`[2, [32, -48, 0]]`	`[2, [2, -3, 0]]`	Failed
oracle 2	`[0, [0, 0]]`	`[0, [0, 0]]`	Passed
oracle 3	`[1, [16, 12]]`	`[1, [4, 3]]`	Failed
oracle 4	`[0, []]`	`[0, []]`	Passed
oracle 5	`[2, [-32, -16]]`	`[2, [-2, -1]]`	Failed
oracle 6	`[2, [64, 128]]`	`[2, [4, 8]]`	Failed
oracle 7	`[0, [3, -8]]`	`[0, [3, -8]]`	Passed
variant packet 1	`[2, [32, -48, 0, 32, -48, 0]]`	`[2, [2, -3, 0, 2, -3, 0]]`	Failed

SHA-256 / c872ff99a2f5ea451d2fc700262c23b91738bac6b42ebcd68ec42de1e7fe4327

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(samples, maximum):
    shift=0
    nonzero=[abs(x) for x in samples if x!=0]
    if nonzero:
        while shift<maximum and all((x&((1<<(shift+1))-1))==0 for x in nonzero):
            shift+=1
    coarse=[x>>shift for x in samples]
    return [shift,coarse]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([8, -12, 0], 5)), [2, [2, -3, 0]])
check('oracle 2', solve(*([0, 0], 4)), [0, [0, 0]])
check('oracle 3', solve(*([8, 6], 4)), [1, [4, 3]])
check('oracle 4', solve(*([], 3)), [0, []])
check('oracle 5', solve(*([-8, -4], 5)), [2, [-2, -1]])
check('oracle 6', solve(*([16, 32], 2)), [2, [4, 8]])
check('oracle 7', solve(*([3, -8], 4)), [0, [3, -8]])
if N == 1: check('variant packet 1', solve(*[[8, -12, 0, 8, -12, 0], 5]), [2, [2, -3, 0, 2, -3, 0]])
if N == 2: check('variant packet 2', solve(*[[8, -12, 0, 8, -12, 0, 8, -12, 0], 5]), [2, [2, -3, 0, 2, -3, 0, 2, -3, 0]])
if N == 3: check('variant packet 3', solve(*[[8, -12, 0, 8, -12, 0, 8, -12, 0, 8, -12, 0], 5]), [2, [2, -3, 0, 2, -3, 0, 2, -3, 0, 2, -3, 0]])
if N == 4: check('variant packet 4', solve(*[[8, -12, 0, 8, -12, 0, 8, -12, 0, 8, -12, 0, 8, -12, 0], 5]), [2, [2, -3, 0, 2, -3, 0, 2, -3, 0, 2, -3, 0, 2, -3, 0]])
if N == 5: check('variant packet 5', solve(*[[8, -12, 0, 8, -12, 0, 8, -12, 0, 8, -12, 0, 8, -12, 0, 8, -12, 0], 5]), [2, [2, -3, 0, 2, -3, 0, 2, -3, 0, 2, -3, 0, 2, -3, 0, 2, -3, 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	`[2, [2, -3, 0]]`	`[2, [2, -3, 0]]`	Passed
oracle 2	`[0, [0, 0]]`	`[0, [0, 0]]`	Passed
oracle 3	`[1, [4, 3]]`	`[1, [4, 3]]`	Passed
oracle 4	`[0, []]`	`[0, []]`	Passed
oracle 5	`[2, [-2, -1]]`	`[2, [-2, -1]]`	Passed
oracle 6	`[2, [4, 8]]`	`[2, [4, 8]]`	Passed
oracle 7	`[0, [3, -8]]`	`[0, [3, -8]]`	Passed
variant packet 1	`[2, [2, -3, 0, 2, -3, 0]]`	`[2, [2, -3, 0, 2, -3, 0]]`	Passed

SHA-256 / 6685802ff7a99ffcc55132b69825144bf3bc94edfbe08b4d6e15a53c618d2c9d

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 2026-09-29T14:45:07.545623+00:00.

Case digest / addd17d5ee1155bfa02edf4ff073073c37cd4c48f1c1504c7079009534597bde