FA-49441 / PCM sample encoding / Open access

Pcm progressive refinement: coarse scale · case 01

Progressive PCM scales coarse samples by bit count instead of bit weight.

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

ROOT CAUSE

Progressive PCM scales coarse samples by bit count instead of bit weight.

VERIFIED REPAIR

Use the stated conversion contract at coarse scale.

Unsuccessful approach: One extra shift doubles the coarse contribution.

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=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	`[3, -3, 6]`	`[7, -7, 14]`	Failed
oracle 2	`[-1, 0]`	`[-1, 0]`	Passed
oracle 3	`[6, 9, 12]`	`[17, 24, 32]`	Failed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[0, 0]`	`[1, -1]`	Failed
oracle 6	`[1, 1]`	`[3, 3]`	Failed
oracle 7	`[3, -3]`	`[6, -5]`	Failed
variant packet 1	`[3, -3, 6, 2, -4, 6]`	`[7, -7, 14, 4, -8, 12]`	Failed

SHA-256 / 47fab77a56664105839b1a1bafb6ca3e9382ddb2cc0dc94fddb5ef93b4e1a2b0

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+1)
    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	`[11, -15, 26]`	`[7, -7, 14]`	Failed
oracle 2	`[-1, 4]`	`[-1, 0]`	Failed
oracle 3	`[33, 48, 64]`	`[17, 24, 32]`	Failed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[2, -2]`	`[1, -1]`	Failed
oracle 6	`[3, 7]`	`[3, 3]`	Failed
oracle 7	`[14, -11]`	`[6, -5]`	Failed
variant packet 1	`[11, -15, 26, 8, -16, 24]`	`[7, -7, 14, 4, -8, 12]`	Failed

SHA-256 / 360024baf5e9a9e92450ff98cb89493e4ff513c13542502cba53120512b645c1

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 2026-09-29T14:44:59.951721+00:00.

Case digest / dcda0f3072a7bab51802c3db10a3cd1c9cddaf220ae45572b4efd8f5ada3adad