FA-49911 / PCM sample encoding / Open access

Pcm nonlinear reconstruction table: lookup address · case 01

Calibration table code order is reversed.

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

ROOT CAUSE

Calibration table code order is reversed.

THE FAILURE

Calibration table code order is reversed.

Unsuccessful approach: Reversing amplitude subtraction negates every calibrated deviation.

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[len(table)-1-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	`[17, 6, 0, -7]`	`[-7, 0, 6, 17]`	Failed
oracle 2	`[None, 8, None]`	`[None, 0, None]`	Failed
oracle 3	`[0]`	`[0]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[0, -10]`	`[0, 1]`	Failed
oracle 6	`[8, 0, -8]`	`[-8, 0, 8]`	Failed
oracle 7	`[4, None, -4]`	`[-4, None, 4]`	Failed
variant packet 1	`[17, 6, 0, -7, 17, 6, 0, -7]`	`[-7, 0, 6, 17, -7, 0, 6, 17]`	Failed

SHA-256 / 158e5bd1306b011d832b7f91fc5f9e945c7803cbdb78f46bc0640c43a7a0dffb

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[zero_index]-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	`[7, 0, -6, -17]`	`[-7, 0, 6, 17]`	Failed
oracle 2	`[None, 0, None]`	`[None, 0, None]`	Passed
oracle 3	`[0]`	`[0]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[0, -1]`	`[0, 1]`	Failed
oracle 6	`[8, 0, -8]`	`[-8, 0, 8]`	Failed
oracle 7	`[4, None, -4]`	`[-4, None, 4]`	Failed
variant packet 1	`[7, 0, -6, -17, 7, 0, -6, -17]`	`[-7, 0, 6, 17, -7, 0, 6, 17]`	Failed

SHA-256 / 64e3721168d3c12bc2ad53f1c31bc2da757dd0dc2c9134c2625564985d90ed38

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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 2026-09-29T14:45:04.335912+00:00.

Case digest / c183a1e9323ebdd0c339442965dfe4b5f43fd7263528384a04020da6fb6e5a10