FA-49901 / PCM sample encoding / Open access

Pcm nonlinear reconstruction table: zero reference · case 01

Reconstruction leaves the calibration-table DC offset.

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

ROOT CAUSE

Reconstruction leaves the calibration-table DC offset.

VERIFIED REPAIR

Use the stated conversion contract at zero reference.

Unsuccessful approach: Subtracting an index instead of its amplitude uses incompatible units.

Case contract

Decode an explicitly calibrated nonlinear PCM code table relative to its designated zero entry; invalid indices return null rather than a plausible 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(codes, table, zero_index):
    out=[]
    for code in codes:
        if code<0 or code>=len(table):
            out.append(None)
            continue
        amplitude=table[code]
        out.append(amplitude)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 1, 2, 3], [-9, -2, 4, 15], 1)), [-7, 0, 6, 17])
check('oracle 2', solve(*([-1, 0, 3], [1, 3, 9], 0)), [None, 0, None])
check('oracle 3', solve(*([0], [-5], 0)), [0])
check('oracle 4', solve(*([], [-3, 2], 1)), [])
check('oracle 5', solve(*([1, 2], [0, 10, 11], 1)), [0, 1])
check('oracle 6', solve(*([0, 2, 4], [-8, -3, 0, 3, 8], 2)), [-8, 0, 8])
check('oracle 7', solve(*([0, -2, 2], [4, 8, 12], 1)), [-4, None, 4])
if N == 1: check('variant packet 1', solve(*[[0, 1, 2, 3, 0, 1, 2, 3], [-9, -2, 4, 15], 1]), [-7, 0, 6, 17, -7, 0, 6, 17])
if N == 2: check('variant packet 2', solve(*[[0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3], [-9, -2, 4, 15], 1]), [-7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17])
if N == 3: check('variant packet 3', solve(*[[0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3], [-9, -2, 4, 15], 1]), [-7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17])
if N == 4: check('variant packet 4', solve(*[[0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3], [-9, -2, 4, 15], 1]), [-7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17])
if N == 5: check('variant packet 5', solve(*[[0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3], [-9, -2, 4, 15], 1]), [-7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17])
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	`[-9, -2, 4, 15]`	`[-7, 0, 6, 17]`	Failed
oracle 2	`[None, 1, None]`	`[None, 0, None]`	Failed
oracle 3	`[-5]`	`[0]`	Failed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[10, 11]`	`[0, 1]`	Failed
oracle 6	`[-8, 0, 8]`	`[-8, 0, 8]`	Passed
oracle 7	`[4, None, 12]`	`[-4, None, 4]`	Failed
variant packet 1	`[-9, -2, 4, 15, -9, -2, 4, 15]`	`[-7, 0, 6, 17, -7, 0, 6, 17]`	Failed

SHA-256 / 90681a2735e27718695abd92604996cf4152ab6e7529688e9357f1b23d2d87b7

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(codes, table, zero_index):
    out=[]
    for code in codes:
        if code<0 or code>=len(table):
            out.append(None)
            continue
        amplitude=table[code]-zero_index
        out.append(amplitude)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 1, 2, 3], [-9, -2, 4, 15], 1)), [-7, 0, 6, 17])
check('oracle 2', solve(*([-1, 0, 3], [1, 3, 9], 0)), [None, 0, None])
check('oracle 3', solve(*([0], [-5], 0)), [0])
check('oracle 4', solve(*([], [-3, 2], 1)), [])
check('oracle 5', solve(*([1, 2], [0, 10, 11], 1)), [0, 1])
check('oracle 6', solve(*([0, 2, 4], [-8, -3, 0, 3, 8], 2)), [-8, 0, 8])
check('oracle 7', solve(*([0, -2, 2], [4, 8, 12], 1)), [-4, None, 4])
if N == 1: check('variant packet 1', solve(*[[0, 1, 2, 3, 0, 1, 2, 3], [-9, -2, 4, 15], 1]), [-7, 0, 6, 17, -7, 0, 6, 17])
if N == 2: check('variant packet 2', solve(*[[0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3], [-9, -2, 4, 15], 1]), [-7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17])
if N == 3: check('variant packet 3', solve(*[[0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3], [-9, -2, 4, 15], 1]), [-7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17])
if N == 4: check('variant packet 4', solve(*[[0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3], [-9, -2, 4, 15], 1]), [-7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17])
if N == 5: check('variant packet 5', solve(*[[0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3], [-9, -2, 4, 15], 1]), [-7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17])
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	`[-10, -3, 3, 14]`	`[-7, 0, 6, 17]`	Failed
oracle 2	`[None, 1, None]`	`[None, 0, None]`	Failed
oracle 3	`[-5]`	`[0]`	Failed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[9, 10]`	`[0, 1]`	Failed
oracle 6	`[-10, -2, 6]`	`[-8, 0, 8]`	Failed
oracle 7	`[3, None, 11]`	`[-4, None, 4]`	Failed
variant packet 1	`[-10, -3, 3, 14, -10, -3, 3, 14]`	`[-7, 0, 6, 17, -7, 0, 6, 17]`	Failed

SHA-256 / e9d768407b77a0de12b288e5aa98653c5e39aedd8002d71e079c810d68b677c4

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(codes, table, zero_index):
    out=[]
    for code in codes:
        if code<0 or code>=len(table):
            out.append(None)
            continue
        amplitude=table[code]-table[zero_index]
        out.append(amplitude)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 1, 2, 3], [-9, -2, 4, 15], 1)), [-7, 0, 6, 17])
check('oracle 2', solve(*([-1, 0, 3], [1, 3, 9], 0)), [None, 0, None])
check('oracle 3', solve(*([0], [-5], 0)), [0])
check('oracle 4', solve(*([], [-3, 2], 1)), [])
check('oracle 5', solve(*([1, 2], [0, 10, 11], 1)), [0, 1])
check('oracle 6', solve(*([0, 2, 4], [-8, -3, 0, 3, 8], 2)), [-8, 0, 8])
check('oracle 7', solve(*([0, -2, 2], [4, 8, 12], 1)), [-4, None, 4])
if N == 1: check('variant packet 1', solve(*[[0, 1, 2, 3, 0, 1, 2, 3], [-9, -2, 4, 15], 1]), [-7, 0, 6, 17, -7, 0, 6, 17])
if N == 2: check('variant packet 2', solve(*[[0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3], [-9, -2, 4, 15], 1]), [-7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17])
if N == 3: check('variant packet 3', solve(*[[0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3], [-9, -2, 4, 15], 1]), [-7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17])
if N == 4: check('variant packet 4', solve(*[[0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3], [-9, -2, 4, 15], 1]), [-7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17])
if N == 5: check('variant packet 5', solve(*[[0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3], [-9, -2, 4, 15], 1]), [-7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17, -7, 0, 6, 17])
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, 0, 6, 17]`	`[-7, 0, 6, 17]`	Passed
oracle 2	`[None, 0, None]`	`[None, 0, None]`	Passed
oracle 3	`[0]`	`[0]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[0, 1]`	`[0, 1]`	Passed
oracle 6	`[-8, 0, 8]`	`[-8, 0, 8]`	Passed
oracle 7	`[-4, None, 4]`	`[-4, None, 4]`	Passed
variant packet 1	`[-7, 0, 6, 17, -7, 0, 6, 17]`	`[-7, 0, 6, 17, -7, 0, 6, 17]`	Passed

SHA-256 / d754a48d1633122d3f5923c7b9156a14acad856ca6c136430413b61518b4994b

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 2026-09-29T14:45:04.209870+00:00.

Case digest / 83cdbf13dbaec0e2bfae2d98410c6f850c0f78da18d0f56cc4d8289486c3dcfb