FAILURE MAP
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FA-49591 / PCM sample encoding / Open access

Pcm error feedback quantizer: feedback sign · case 01

Quantization error is fed back with the opposite sign.

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

ROOT CAUSE

Quantization error is fed back with the opposite sign.

VERIFIED REPAIR

Use the stated conversion contract at feedback sign.

Unsuccessful approach: Dropping feedback loses the declared error-shaping conversion.

Case contract

Integer PCM precision reducer with first-order error feedback, even positive step, ties toward positive infinity, explicit reset positions and returned error state.

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, step, error, resets):
    out=[]
    for index,sample in enumerate(samples):
        if index in resets:
            error=0
        driven=sample-error
        code=(driven+step//2)//step
        restored=code*step
        error=driven-restored
        out.append(code)
    return [out,error]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, 1, 1, 1], 4, 0, [])), [[0, 1, 0, 0], 0])
check('oracle 2', solve(*([3, -3, 2, -2], 4, 1, [])), [[1, -1, 1, -1], 1])
check('oracle 3', solve(*([1, 2, 3, 4], 4, 2, [2])), [[1, 0, 1, 1], -1])
check('oracle 4', solve(*([], 4, 3, [])), [[], 3])
check('oracle 5', solve(*([-1, -1, -1], 2, 0, [])), [[0, -1, 0], -1])
check('oracle 6', solve(*([0, 1, 2], 2, -1, [0])), [[0, 1, 1], -1])
check('oracle 7', solve(*([7, -7, 5], 6, 1, [1])), [[1, -1, 1], -2])
if N == 1: check('variant packet 1', solve(*[[1, 1, 1, 1, 1, 1, 1, 1], 4, 0, []]), [[0, 1, 0, 0, 0, 1, 0, 0], 0])
if N == 2: check('variant packet 2', solve(*[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 4, 0, []]), [[0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], 0])
if N == 3: check('variant packet 3', solve(*[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 4, 0, []]), [[0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], 0])
if N == 4: check('variant packet 4', solve(*[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 4, 0, []]), [[0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], 0])
if N == 5: check('variant packet 5', solve(*[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 4, 0, []]), [[0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], 0])
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[[0, 0, 0, 0], 0][[0, 1, 0, 0], 0]Failed
oracle 2[[1, 0, 1, 0], -1][[1, -1, 1, -1], 1]Failed
oracle 3[[0, 1, 1, 1], 1][[1, 0, 1, 1], -1]Failed
oracle 4[[], 3][[], 3]Passed
oracle 5[[0, 0, 0], -1][[0, -1, 0], -1]Failed
oracle 6[[0, 1, 2], -1][[0, 1, 1], -1]Failed
oracle 7[[1, -1, 1], 0][[1, -1, 1], -2]Failed
variant packet 1[[0, 0, 0, 0, 0, 0, 0, 0], 0][[0, 1, 0, 0, 0, 1, 0, 0], 0]Failed

SHA-256 / eebce2b1ea153b22b138f146781652eb7f7b9abee6d41645053c8119961c597b

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(samples, step, error, resets):
    out=[]
    for index,sample in enumerate(samples):
        if index in resets:
            error=0
        driven=sample
        code=(driven+step//2)//step
        restored=code*step
        error=driven-restored
        out.append(code)
    return [out,error]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, 1, 1, 1], 4, 0, [])), [[0, 1, 0, 0], 0])
check('oracle 2', solve(*([3, -3, 2, -2], 4, 1, [])), [[1, -1, 1, -1], 1])
check('oracle 3', solve(*([1, 2, 3, 4], 4, 2, [2])), [[1, 0, 1, 1], -1])
check('oracle 4', solve(*([], 4, 3, [])), [[], 3])
check('oracle 5', solve(*([-1, -1, -1], 2, 0, [])), [[0, -1, 0], -1])
check('oracle 6', solve(*([0, 1, 2], 2, -1, [0])), [[0, 1, 1], -1])
check('oracle 7', solve(*([7, -7, 5], 6, 1, [1])), [[1, -1, 1], -2])
if N == 1: check('variant packet 1', solve(*[[1, 1, 1, 1, 1, 1, 1, 1], 4, 0, []]), [[0, 1, 0, 0, 0, 1, 0, 0], 0])
if N == 2: check('variant packet 2', solve(*[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 4, 0, []]), [[0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], 0])
if N == 3: check('variant packet 3', solve(*[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 4, 0, []]), [[0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], 0])
if N == 4: check('variant packet 4', solve(*[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 4, 0, []]), [[0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], 0])
if N == 5: check('variant packet 5', solve(*[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 4, 0, []]), [[0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], 0])
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[[0, 0, 0, 0], 1][[0, 1, 0, 0], 0]Failed
oracle 2[[1, -1, 1, 0], -2][[1, -1, 1, -1], 1]Failed
oracle 3[[0, 1, 1, 1], 0][[1, 0, 1, 1], -1]Failed
oracle 4[[], 3][[], 3]Passed
oracle 5[[0, 0, 0], -1][[0, -1, 0], -1]Failed
oracle 6[[0, 1, 1], 0][[0, 1, 1], -1]Failed
oracle 7[[1, -1, 1], -1][[1, -1, 1], -2]Failed
variant packet 1[[0, 0, 0, 0, 0, 0, 0, 0], 1][[0, 1, 0, 0, 0, 1, 0, 0], 0]Failed

SHA-256 / 612961db7704d7954f20867f9f588059ab0b51cf90c0db6c93d96cb95ed1b288

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(samples, step, error, resets):
    out=[]
    for index,sample in enumerate(samples):
        if index in resets:
            error=0
        driven=sample+error
        code=(driven+step//2)//step
        restored=code*step
        error=driven-restored
        out.append(code)
    return [out,error]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, 1, 1, 1], 4, 0, [])), [[0, 1, 0, 0], 0])
check('oracle 2', solve(*([3, -3, 2, -2], 4, 1, [])), [[1, -1, 1, -1], 1])
check('oracle 3', solve(*([1, 2, 3, 4], 4, 2, [2])), [[1, 0, 1, 1], -1])
check('oracle 4', solve(*([], 4, 3, [])), [[], 3])
check('oracle 5', solve(*([-1, -1, -1], 2, 0, [])), [[0, -1, 0], -1])
check('oracle 6', solve(*([0, 1, 2], 2, -1, [0])), [[0, 1, 1], -1])
check('oracle 7', solve(*([7, -7, 5], 6, 1, [1])), [[1, -1, 1], -2])
if N == 1: check('variant packet 1', solve(*[[1, 1, 1, 1, 1, 1, 1, 1], 4, 0, []]), [[0, 1, 0, 0, 0, 1, 0, 0], 0])
if N == 2: check('variant packet 2', solve(*[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 4, 0, []]), [[0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], 0])
if N == 3: check('variant packet 3', solve(*[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 4, 0, []]), [[0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], 0])
if N == 4: check('variant packet 4', solve(*[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 4, 0, []]), [[0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], 0])
if N == 5: check('variant packet 5', solve(*[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 4, 0, []]), [[0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], 0])
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[[0, 1, 0, 0], 0][[0, 1, 0, 0], 0]Passed
oracle 2[[1, -1, 1, -1], 1][[1, -1, 1, -1], 1]Passed
oracle 3[[1, 0, 1, 1], -1][[1, 0, 1, 1], -1]Passed
oracle 4[[], 3][[], 3]Passed
oracle 5[[0, -1, 0], -1][[0, -1, 0], -1]Passed
oracle 6[[0, 1, 1], -1][[0, 1, 1], -1]Passed
oracle 7[[1, -1, 1], -2][[1, -1, 1], -2]Passed
variant packet 1[[0, 1, 0, 0, 0, 1, 0, 0], 0][[0, 1, 0, 0, 0, 1, 0, 0], 0]Passed

SHA-256 / 29c1c1c2a97919fa6fcbe73cf6cddb859183d15ccd704f79b4bfde66d32e13b1

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 2026-09-29T14:45:01.466829+00:00.

Case digest / b556c60359d8534785a782a3ba7697dfd55fac2381df2107d7c75bb8098de661