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FA-50146 / PCM sample encoding / Open access

Pcm lpc residual reconstruction: sum before division · case 01

Per-tap rounding changes the integer LPC prediction.

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

ROOT CAUSE

Per-tap rounding changes the integer LPC prediction.

THE FAILURE

Per-tap rounding changes the integer LPC prediction.

Unsuccessful approach: Truncation toward zero differs from the declared floor for negative predictions.

Case contract

Reconstruct bounded integer PCM LPC residuals using newest-first history, floor-divided complete dot products and reconstructed-sample history feedback.

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(residuals, history, coefficients, divisor):
    state=list(history)
    out=[]
    for residual in residuals:
        prediction=sum(c*x//divisor for c,x in zip(coefficients,state))
        sample=prediction+residual
        out.append(sample)
        state=[sample]+state[:-1]
    return [out,state]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, 2, -1], [3, 1], [2, -1], 1)), [[6, 11, 15], [15, 11]])
check('oracle 2', solve(*([0, 1, -2], [-3, 2], [1, 1], 3)), [[-1, -1, -3], [-3, -1]])
check('oracle 3', solve(*([], [2, 1], [2, -1], 1)), [[], [2, 1]])
check('oracle 4', solve(*([2, 0, 1], [0, 0, 0], [3, -2, 1], 2)), [[2, 3, 3], [3, 3, 2]])
check('oracle 5', solve(*([-1, 3], [5], [1], 2)), [[1, 3], [3]])
check('oracle 6', solve(*([1, 1], [1, 2, 3], [1, 2, 3], 4)), [[4, 4], [4, 4, 1]])
check('oracle 7', solve(*([0, -1], [4, -2], [3, 1], 3)), [[3, 3], [3, 3]])
if N == 1: check('variant packet 1', solve(*[[1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33], [33, 27]])
if N == 2: check('variant packet 2', solve(*[[1, 2, -1, 1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33, 40, 49, 57], [57, 49]])
if N == 3: check('variant packet 3', solve(*[[1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33, 40, 49, 57, 66, 77, 87], [87, 77]])
if N == 4: check('variant packet 4', solve(*[[1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33, 40, 49, 57, 66, 77, 87, 98, 111, 123], [123, 111]])
if N == 5: check('variant packet 5', solve(*[[1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33, 40, 49, 57, 66, 77, 87, 98, 111, 123, 136, 151, 165], [165, 151]])
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 fixtureActualExpectedOutcome
oracle 1[[6, 11, 15], [15, 11]][[6, 11, 15], [15, 11]]Passed
oracle 2[[-1, -1, -4], [-4, -1]][[-1, -1, -3], [-3, -1]]Failed
oracle 3[[], [2, 1]][[], [2, 1]]Passed
oracle 4[[2, 3, 3], [3, 3, 2]][[2, 3, 3], [3, 3, 2]]Passed
oracle 5[[1, 3], [3]][[1, 3], [3]]Passed
oracle 6[[4, 3], [3, 4, 1]][[4, 4], [4, 4, 1]]Failed
oracle 7[[3, 3], [3, 3]][[3, 3], [3, 3]]Passed
variant packet 1[[6, 11, 15, 20, 27, 33], [33, 27]][[6, 11, 15, 20, 27, 33], [33, 27]]Passed

SHA-256 / e402789626a928e9ccc149af5c9909fcfe99576ec78ea7650eb98e57c388b161

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(residuals, history, coefficients, divisor):
    state=list(history)
    out=[]
    for residual in residuals:
        prediction=int(sum(c*x for c,x in zip(coefficients,state))/divisor)
        sample=prediction+residual
        out.append(sample)
        state=[sample]+state[:-1]
    return [out,state]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, 2, -1], [3, 1], [2, -1], 1)), [[6, 11, 15], [15, 11]])
check('oracle 2', solve(*([0, 1, -2], [-3, 2], [1, 1], 3)), [[-1, -1, -3], [-3, -1]])
check('oracle 3', solve(*([], [2, 1], [2, -1], 1)), [[], [2, 1]])
check('oracle 4', solve(*([2, 0, 1], [0, 0, 0], [3, -2, 1], 2)), [[2, 3, 3], [3, 3, 2]])
check('oracle 5', solve(*([-1, 3], [5], [1], 2)), [[1, 3], [3]])
check('oracle 6', solve(*([1, 1], [1, 2, 3], [1, 2, 3], 4)), [[4, 4], [4, 4, 1]])
check('oracle 7', solve(*([0, -1], [4, -2], [3, 1], 3)), [[3, 3], [3, 3]])
if N == 1: check('variant packet 1', solve(*[[1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33], [33, 27]])
if N == 2: check('variant packet 2', solve(*[[1, 2, -1, 1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33, 40, 49, 57], [57, 49]])
if N == 3: check('variant packet 3', solve(*[[1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33, 40, 49, 57, 66, 77, 87], [87, 77]])
if N == 4: check('variant packet 4', solve(*[[1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33, 40, 49, 57, 66, 77, 87, 98, 111, 123], [123, 111]])
if N == 5: check('variant packet 5', solve(*[[1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33, 40, 49, 57, 66, 77, 87, 98, 111, 123, 136, 151, 165], [165, 151]])
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 fixtureActualExpectedOutcome
oracle 1[[6, 11, 15], [15, 11]][[6, 11, 15], [15, 11]]Passed
oracle 2[[0, 0, -2], [-2, 0]][[-1, -1, -3], [-3, -1]]Failed
oracle 3[[], [2, 1]][[], [2, 1]]Passed
oracle 4[[2, 3, 3], [3, 3, 2]][[2, 3, 3], [3, 3, 2]]Passed
oracle 5[[1, 3], [3]][[1, 3], [3]]Passed
oracle 6[[4, 4], [4, 4, 1]][[4, 4], [4, 4, 1]]Passed
oracle 7[[3, 3], [3, 3]][[3, 3], [3, 3]]Passed
variant packet 1[[6, 11, 15, 20, 27, 33], [33, 27]][[6, 11, 15, 20, 27, 33], [33, 27]]Passed

SHA-256 / 00cc992912e1faf4f1c6c55561bbd30677b50bb787d035adde3f689e559b36a1

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 2026-09-29T14:45:06.619573+00:00.

Case digest / 784ab7351907c6b828fba32b657a26a19ebd57d27ad6656fd110e1504cc1ea4d