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FA-49611 / PCM sample encoding / Open access

Pcm error feedback quantizer: quantizer midpoint · case 01

Error-feedback conversion uses floor instead of nearest midpoint bins.

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

ROOT CAUSE

Error-feedback conversion uses floor instead of nearest midpoint bins.

THE FAILURE

Error-feedback conversion uses floor instead of nearest midpoint bins.

Unsuccessful approach: Ceiling assigns all nonzero residues upward.

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
        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, 1], 0][[0, 1, 0, 0], 0]Failed
oracle 2[[1, -1, 0, 0], 1][[1, -1, 1, -1], 1]Failed
oracle 3[[0, 1, 0, 1], 3][[1, 0, 1, 1], -1]Failed
oracle 4[[], 3][[], 3]Passed
oracle 5[[-1, 0, -1], 1][[0, -1, 0], -1]Failed
oracle 6[[0, 0, 1], 1][[0, 1, 1], -1]Failed
oracle 7[[1, -2, 1], 4][[1, -1, 1], -2]Failed
variant packet 1[[0, 0, 0, 1, 0, 0, 0, 1], 0][[0, 1, 0, 0, 0, 1, 0, 0], 0]Failed

SHA-256 / 624cf68416fc9fe09e56798afee8eb379856249b1f682e8e37cde5ef9f197dbe

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+error
        code=(driven+step-1)//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[[1, 0, 0, 0], 0][[0, 1, 0, 0], 0]Failed
oracle 2[[1, 0, 0, 0], -3][[1, -1, 1, -1], 1]Failed
oracle 3[[1, 1, 1, 1], -1][[1, 0, 1, 1], -1]Failed
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[[2, -1, 1], -2][[1, -1, 1], -2]Failed
variant packet 1[[1, 0, 0, 0, 1, 0, 0, 0], 0][[0, 1, 0, 0, 0, 1, 0, 0], 0]Failed

SHA-256 / 61557622f15968d7edf163627a92c16b1ed11902548e7a81443ce2f70465ed35

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 2026-09-29T14:45:01.597306+00:00.

Case digest / d5abd5fd85fc349dce1632e8a7d616842d28180b44fd949bf27bd416b80a692b