FA-49916 / PCM sample encoding / Open access

Pcm calibrated nearest code: distance absolute · case 01

Signed distance always favors one end of the PCM reconstruction table.

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

ROOT CAUSE

Signed distance always favors one end of the PCM reconstruction table.

VERIFIED REPAIR

Use the stated conversion contract at distance absolute.

Unsuccessful approach: Comparing magnitudes loses sample polarity.

Case contract

Encode PCM amplitudes to nearest entries of an explicit possibly repeated calibration table, with a declared lowest/highest code-index tie policy.

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(samples, table, tie_high):
    out=[]
    for sample in samples:
        distances=[value-sample for value in table]
        best=min(distances)
        candidates=[i for i,d in enumerate(distances) if d==best]
        out.append(candidates[-1] if tie_high else candidates[0])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([-8, -2, 0, 5, 12], [-10, 0, 10], False)), [0, 1, 1, 1, 2])
check('oracle 2', solve(*([5, -5], [-10, 0, 10], True)), [2, 1])
check('oracle 3', solve(*([2, 3], [0, 4, 4, 8], True)), [2, 2])
check('oracle 4', solve(*([], [-1, 1], False)), [])
check('oracle 5', solve(*([0, 4], [2], False)), [0, 0])
check('oracle 6', solve(*([1, 4, 8], [0, 3, 10], False)), [0, 1, 2])
check('oracle 7', solve(*([-3, 3], [-6, 0, 6], True)), [1, 2])
if N == 1: check('variant packet 1', solve(*[[-8, -2, 0, 5, 12, -8, -2, 0, 5, 12], [-10, 0, 10], False]), [0, 1, 1, 1, 2, 0, 1, 1, 1, 2])
if N == 2: check('variant packet 2', solve(*[[-8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12], [-10, 0, 10], False]), [0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2])
if N == 3: check('variant packet 3', solve(*[[-8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12], [-10, 0, 10], False]), [0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2])
if N == 4: check('variant packet 4', solve(*[[-8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12], [-10, 0, 10], False]), [0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2])
if N == 5: check('variant packet 5', solve(*[[-8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12], [-10, 0, 10], False]), [0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2])
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	`[0, 0, 0, 0, 0]`	`[0, 1, 1, 1, 2]`	Failed
oracle 2	`[0, 0]`	`[2, 1]`	Failed
oracle 3	`[0, 0]`	`[2, 2]`	Failed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[0, 0]`	`[0, 0]`	Passed
oracle 6	`[0, 0, 0]`	`[0, 1, 2]`	Failed
oracle 7	`[0, 0]`	`[1, 2]`	Failed
variant packet 1	`[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]`	`[0, 1, 1, 1, 2, 0, 1, 1, 1, 2]`	Failed

SHA-256 / 3f9b1f450c9e21d67f427d1bf161d632d2380a45466861362140472b36b72d7a

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(samples, table, tie_high):
    out=[]
    for sample in samples:
        distances=[abs(value)-abs(sample) for value in table]
        best=min(distances)
        candidates=[i for i,d in enumerate(distances) if d==best]
        out.append(candidates[-1] if tie_high else candidates[0])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([-8, -2, 0, 5, 12], [-10, 0, 10], False)), [0, 1, 1, 1, 2])
check('oracle 2', solve(*([5, -5], [-10, 0, 10], True)), [2, 1])
check('oracle 3', solve(*([2, 3], [0, 4, 4, 8], True)), [2, 2])
check('oracle 4', solve(*([], [-1, 1], False)), [])
check('oracle 5', solve(*([0, 4], [2], False)), [0, 0])
check('oracle 6', solve(*([1, 4, 8], [0, 3, 10], False)), [0, 1, 2])
check('oracle 7', solve(*([-3, 3], [-6, 0, 6], True)), [1, 2])
if N == 1: check('variant packet 1', solve(*[[-8, -2, 0, 5, 12, -8, -2, 0, 5, 12], [-10, 0, 10], False]), [0, 1, 1, 1, 2, 0, 1, 1, 1, 2])
if N == 2: check('variant packet 2', solve(*[[-8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12], [-10, 0, 10], False]), [0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2])
if N == 3: check('variant packet 3', solve(*[[-8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12], [-10, 0, 10], False]), [0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2])
if N == 4: check('variant packet 4', solve(*[[-8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12], [-10, 0, 10], False]), [0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2])
if N == 5: check('variant packet 5', solve(*[[-8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12], [-10, 0, 10], False]), [0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2])
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	`[1, 1, 1, 1, 1]`	`[0, 1, 1, 1, 2]`	Failed
oracle 2	`[1, 1]`	`[2, 1]`	Failed
oracle 3	`[0, 0]`	`[2, 2]`	Failed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[0, 0]`	`[0, 0]`	Passed
oracle 6	`[0, 0, 0]`	`[0, 1, 2]`	Failed
oracle 7	`[1, 1]`	`[1, 2]`	Failed
variant packet 1	`[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]`	`[0, 1, 1, 1, 2, 0, 1, 1, 1, 2]`	Failed

SHA-256 / 57e88857ccfd31ee54678ad7dff9942e36625bd587d49b401632cde38c12e4b3

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(samples, table, tie_high):
    out=[]
    for sample in samples:
        distances=[abs(value-sample) for value in table]
        best=min(distances)
        candidates=[i for i,d in enumerate(distances) if d==best]
        out.append(candidates[-1] if tie_high else candidates[0])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([-8, -2, 0, 5, 12], [-10, 0, 10], False)), [0, 1, 1, 1, 2])
check('oracle 2', solve(*([5, -5], [-10, 0, 10], True)), [2, 1])
check('oracle 3', solve(*([2, 3], [0, 4, 4, 8], True)), [2, 2])
check('oracle 4', solve(*([], [-1, 1], False)), [])
check('oracle 5', solve(*([0, 4], [2], False)), [0, 0])
check('oracle 6', solve(*([1, 4, 8], [0, 3, 10], False)), [0, 1, 2])
check('oracle 7', solve(*([-3, 3], [-6, 0, 6], True)), [1, 2])
if N == 1: check('variant packet 1', solve(*[[-8, -2, 0, 5, 12, -8, -2, 0, 5, 12], [-10, 0, 10], False]), [0, 1, 1, 1, 2, 0, 1, 1, 1, 2])
if N == 2: check('variant packet 2', solve(*[[-8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12], [-10, 0, 10], False]), [0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2])
if N == 3: check('variant packet 3', solve(*[[-8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12], [-10, 0, 10], False]), [0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2])
if N == 4: check('variant packet 4', solve(*[[-8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12], [-10, 0, 10], False]), [0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2])
if N == 5: check('variant packet 5', solve(*[[-8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12, -8, -2, 0, 5, 12], [-10, 0, 10], False]), [0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2])
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	`[0, 1, 1, 1, 2]`	`[0, 1, 1, 1, 2]`	Passed
oracle 2	`[2, 1]`	`[2, 1]`	Passed
oracle 3	`[2, 2]`	`[2, 2]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[0, 0]`	`[0, 0]`	Passed
oracle 6	`[0, 1, 2]`	`[0, 1, 2]`	Passed
oracle 7	`[1, 2]`	`[1, 2]`	Passed
variant packet 1	`[0, 1, 1, 1, 2, 0, 1, 1, 1, 2]`	`[0, 1, 1, 1, 2, 0, 1, 1, 1, 2]`	Passed

SHA-256 / 81757ee4aaa3ddfa7604faabfc9967e7902d7e0fc892a5b707f5184ea769f1eb

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 2026-09-29T14:45:04.376242+00:00.

Case digest / 0798d732478f0b5960a60d681e5700ae5e42420f226d9b64a8b7965018cbf9f9