FA-49926 / PCM sample encoding / Open access

Pcm calibrated nearest code: candidate index · case 01

Encoder emits distance values instead of codeword indices.

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

ROOT CAUSE

Encoder emits distance values instead of codeword indices.

THE FAILURE

Encoder emits distance values instead of codeword indices.

Unsuccessful approach: Emitting reconstruction amplitudes bypasses the code table representation.

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=[abs(value-sample) for value in table]
        best=min(distances)
        candidates=[d 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	`[2, 2, 0, 5, 2]`	`[0, 1, 1, 1, 2]`	Failed
oracle 2	`[5, 5]`	`[2, 1]`	Failed
oracle 3	`[2, 1]`	`[2, 2]`	Failed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[2, 2]`	`[0, 0]`	Failed
oracle 6	`[1, 1, 2]`	`[0, 1, 2]`	Failed
oracle 7	`[3, 3]`	`[1, 2]`	Failed
variant packet 1	`[2, 2, 0, 5, 2, 2, 2, 0, 5, 2]`	`[0, 1, 1, 1, 2, 0, 1, 1, 1, 2]`	Failed

SHA-256 / 4452619e9c9cb282e7d3abd608da9e6c6c053cae5d6a6b62fe688a64eb210a12

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-sample) for value in table]
        best=min(distances)
        candidates=[table[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	`[-10, 0, 0, 0, 10]`	`[0, 1, 1, 1, 2]`	Failed
oracle 2	`[10, 0]`	`[2, 1]`	Failed
oracle 3	`[4, 4]`	`[2, 2]`	Failed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[2, 2]`	`[0, 0]`	Failed
oracle 6	`[0, 3, 10]`	`[0, 1, 2]`	Failed
oracle 7	`[0, 6]`	`[1, 2]`	Failed
variant packet 1	`[-10, 0, 0, 0, 10, -10, 0, 0, 0, 10]`	`[0, 1, 1, 1, 2, 0, 1, 1, 1, 2]`	Failed

SHA-256 / d90f78bcd0a3e6c8df3e1070c1d9db5756b99ada34300c64a1bead22c105f98a

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 2026-09-29T14:45:04.501573+00:00.

Case digest / 4813df7932d36c68093f70566fc4b47cb678b5cdbc46f9ec6c4d2a66ef679cbb