FA-49451 / PCM sample encoding / Open access

Pcm progressive refinement: missing refinement · case 01

Absent refinement bits are replaced with maximum positive low bits.

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

ROOT CAUSE

Absent refinement bits are replaced with maximum positive low bits.

VERIFIED REPAIR

Use the stated conversion contract at missing refinement.

Unsuccessful approach: Holding the last refinement value fabricates low bits for later samples.

Case contract

Restore PCM from arithmetic-shift coarse samples and optional unsigned low-bit refinements; missing refinement bits are zero and out-of-field residual bits are masked.

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(coarse, residuals, missing_bits):
    scale=1<<missing_bits
    out=[]
    for index,base in enumerate(coarse):
        tail=residuals[index] if index<len(residuals) else scale-1
        tail &= scale-1
        out.append(base*scale+tail)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, -2, 3], [3, 1, 2], 2)), [7, -7, 14])
check('oracle 2', solve(*([-1, 0], [7, 4], 2)), [-1, 0])
check('oracle 3', solve(*([2, 3, 4], [1], 3)), [17, 24, 32])
check('oracle 4', solve(*([], [], 2)), [])
check('oracle 5', solve(*([1, -1], [0, 0], 0)), [1, -1])
check('oracle 6', solve(*([0, 0], [3, -1], 2)), [3, 3])
check('oracle 7', solve(*([3, -3], [2, 1], 1)), [6, -5])
if N == 1: check('variant packet 1', solve(*[[1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12])
if N == 2: check('variant packet 2', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12])
if N == 3: check('variant packet 3', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12])
if N == 4: check('variant packet 4', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12])
if N == 5: check('variant packet 5', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12])
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	`[7, -7, 14]`	`[7, -7, 14]`	Passed
oracle 2	`[-1, 0]`	`[-1, 0]`	Passed
oracle 3	`[17, 31, 39]`	`[17, 24, 32]`	Failed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[1, -1]`	`[1, -1]`	Passed
oracle 6	`[3, 3]`	`[3, 3]`	Passed
oracle 7	`[6, -5]`	`[6, -5]`	Passed
variant packet 1	`[7, -7, 14, 7, -5, 15]`	`[7, -7, 14, 4, -8, 12]`	Failed

SHA-256 / 43fffc9e1efd1f2332e9521e5be130e263540edb5830271974c958487c551205

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(coarse, residuals, missing_bits):
    scale=1<<missing_bits
    out=[]
    for index,base in enumerate(coarse):
        tail=residuals[index] if index<len(residuals) else (residuals[-1] if residuals else 0)
        tail &= scale-1
        out.append(base*scale+tail)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, -2, 3], [3, 1, 2], 2)), [7, -7, 14])
check('oracle 2', solve(*([-1, 0], [7, 4], 2)), [-1, 0])
check('oracle 3', solve(*([2, 3, 4], [1], 3)), [17, 24, 32])
check('oracle 4', solve(*([], [], 2)), [])
check('oracle 5', solve(*([1, -1], [0, 0], 0)), [1, -1])
check('oracle 6', solve(*([0, 0], [3, -1], 2)), [3, 3])
check('oracle 7', solve(*([3, -3], [2, 1], 1)), [6, -5])
if N == 1: check('variant packet 1', solve(*[[1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12])
if N == 2: check('variant packet 2', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12])
if N == 3: check('variant packet 3', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12])
if N == 4: check('variant packet 4', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12])
if N == 5: check('variant packet 5', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12])
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	`[7, -7, 14]`	`[7, -7, 14]`	Passed
oracle 2	`[-1, 0]`	`[-1, 0]`	Passed
oracle 3	`[17, 25, 33]`	`[17, 24, 32]`	Failed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[1, -1]`	`[1, -1]`	Passed
oracle 6	`[3, 3]`	`[3, 3]`	Passed
oracle 7	`[6, -5]`	`[6, -5]`	Passed
variant packet 1	`[7, -7, 14, 6, -6, 14]`	`[7, -7, 14, 4, -8, 12]`	Failed

SHA-256 / a13fb1c73d30433846a2152b89a3e6ef269fb4196526f9c5904022595bf99448

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(coarse, residuals, missing_bits):
    scale=1<<missing_bits
    out=[]
    for index,base in enumerate(coarse):
        tail=residuals[index] if index<len(residuals) else 0
        tail &= scale-1
        out.append(base*scale+tail)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, -2, 3], [3, 1, 2], 2)), [7, -7, 14])
check('oracle 2', solve(*([-1, 0], [7, 4], 2)), [-1, 0])
check('oracle 3', solve(*([2, 3, 4], [1], 3)), [17, 24, 32])
check('oracle 4', solve(*([], [], 2)), [])
check('oracle 5', solve(*([1, -1], [0, 0], 0)), [1, -1])
check('oracle 6', solve(*([0, 0], [3, -1], 2)), [3, 3])
check('oracle 7', solve(*([3, -3], [2, 1], 1)), [6, -5])
if N == 1: check('variant packet 1', solve(*[[1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12])
if N == 2: check('variant packet 2', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12])
if N == 3: check('variant packet 3', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12])
if N == 4: check('variant packet 4', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12])
if N == 5: check('variant packet 5', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12])
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	`[7, -7, 14]`	`[7, -7, 14]`	Passed
oracle 2	`[-1, 0]`	`[-1, 0]`	Passed
oracle 3	`[17, 24, 32]`	`[17, 24, 32]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[1, -1]`	`[1, -1]`	Passed
oracle 6	`[3, 3]`	`[3, 3]`	Passed
oracle 7	`[6, -5]`	`[6, -5]`	Passed
variant packet 1	`[7, -7, 14, 4, -8, 12]`	`[7, -7, 14, 4, -8, 12]`	Passed

SHA-256 / 8bea1a4700c378aff21411c9a049fc5b0a4e68405eb7934ec7cfee54df52d31f

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 2026-09-29T14:45:00.185298+00:00.

Case digest / 0d5399ec5e95fd7c54d380f046d6b0ef8fe868afcf8ac6fb78133394f138b845