FA-49896 / PCM sample encoding / Open access

Pcm nonlinear reconstruction table: last code valid · case 01

The final reconstruction code is rejected as if the table endpoint were exclusive.

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

ROOT CAUSE

The final reconstruction code is rejected as if the table endpoint were exclusive.

THE FAILURE

The final reconstruction code is rejected as if the table endpoint were exclusive.

Unsuccessful approach: Rejecting an extra endpoint further shrinks the valid calibrated range.

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

SHA-256 / f9602431740a497ad040adcc3444b5f138a33e665d66bd5c41b1d1096d1d500e

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

SHA-256 / 4bcba688c0bf4a281b49f7b63d8f7a0030d46048a7ca0afbc0995e48055f3b93

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.

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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 / dbbc7266b729d806d3804bcce785dba5734f6190d4b3aa8fd508213878ad0c87