FA-49641 / PCM sample encoding / Open access

Pcm triangular dither: independent difference · case 01

Two supplied uniform draws are added rather than differenced for centered dither.

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

ROOT CAUSE

Two supplied uniform draws are added rather than differenced for centered dither.

VERIFIED REPAIR

Use the stated conversion contract at independent difference.

Unsuccessful approach: Reusing the same draw cancels all dither.

Case contract

Construct a bounded deterministic highpass triangular PCM dither sequence from paired supplied draws; return raw-noise delay for packet continuation.

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(pairs, amplitude, previous):
    out=[]
    for a,b in pairs:
        difference=a+b
        noise=difference*amplitude
        shaped=noise-previous
        previous=noise
        out.append(shaped)
    return [out,previous]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[1, 3], [4, 0], [2, 2]], 2, 1)), [[-5, 12, -8], 0])
check('oracle 2', solve(*([[0, 0], [1, 0]], 1, -2)), [[2, 1], 1])
check('oracle 3', solve(*([], 3, 4)), [[], 4])
check('oracle 4', solve(*([[4, 1], [1, 4]], 3, 0)), [[9, -18], -9])
check('oracle 5', solve(*([[1, 2], [2, 1], [0, 0]], 0, 3)), [[-3, 0, 0], 0])
check('oracle 6', solve(*([[3, 3]], 2, 0)), [[0], 0])
check('oracle 7', solve(*([[0, 2], [2, 0], [1, 1]], 4, -4)), [[-4, 16, -8], 0])
if N == 1: check('variant packet 1', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8], 0])
if N == 2: check('variant packet 2', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8], 0])
if N == 3: check('variant packet 3', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8], 0])
if N == 4: check('variant packet 4', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8], 0])
if N == 5: check('variant packet 5', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8], 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 fixture	Actual	Expected	Outcome
oracle 1	`[[7, 0, 0], 8]`	`[[-5, 12, -8], 0]`	Failed
oracle 2	`[[2, 1], 1]`	`[[2, 1], 1]`	Passed
oracle 3	`[[], 4]`	`[[], 4]`	Passed
oracle 4	`[[15, 0], 15]`	`[[9, -18], -9]`	Failed
oracle 5	`[[-3, 0, 0], 0]`	`[[-3, 0, 0], 0]`	Passed
oracle 6	`[[12], 12]`	`[[0], 0]`	Failed
oracle 7	`[[12, 0, 0], 8]`	`[[-4, 16, -8], 0]`	Failed
variant packet 1	`[[7, 0, 0, 0, 0, 0], 8]`	`[[-5, 12, -8, -4, 12, -8], 0]`	Failed

SHA-256 / 828f944a1f4b9ed76b871dc884b9be2b6998a3fb877e9a2b74ab9212669eaad4

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(pairs, amplitude, previous):
    out=[]
    for a,b in pairs:
        difference=a-a
        noise=difference*amplitude
        shaped=noise-previous
        previous=noise
        out.append(shaped)
    return [out,previous]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[1, 3], [4, 0], [2, 2]], 2, 1)), [[-5, 12, -8], 0])
check('oracle 2', solve(*([[0, 0], [1, 0]], 1, -2)), [[2, 1], 1])
check('oracle 3', solve(*([], 3, 4)), [[], 4])
check('oracle 4', solve(*([[4, 1], [1, 4]], 3, 0)), [[9, -18], -9])
check('oracle 5', solve(*([[1, 2], [2, 1], [0, 0]], 0, 3)), [[-3, 0, 0], 0])
check('oracle 6', solve(*([[3, 3]], 2, 0)), [[0], 0])
check('oracle 7', solve(*([[0, 2], [2, 0], [1, 1]], 4, -4)), [[-4, 16, -8], 0])
if N == 1: check('variant packet 1', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8], 0])
if N == 2: check('variant packet 2', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8], 0])
if N == 3: check('variant packet 3', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8], 0])
if N == 4: check('variant packet 4', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8], 0])
if N == 5: check('variant packet 5', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8], 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 fixture	Actual	Expected	Outcome
oracle 1	`[[-1, 0, 0], 0]`	`[[-5, 12, -8], 0]`	Failed
oracle 2	`[[2, 0], 0]`	`[[2, 1], 1]`	Failed
oracle 3	`[[], 4]`	`[[], 4]`	Passed
oracle 4	`[[0, 0], 0]`	`[[9, -18], -9]`	Failed
oracle 5	`[[-3, 0, 0], 0]`	`[[-3, 0, 0], 0]`	Passed
oracle 6	`[[0], 0]`	`[[0], 0]`	Passed
oracle 7	`[[4, 0, 0], 0]`	`[[-4, 16, -8], 0]`	Failed
variant packet 1	`[[-1, 0, 0, 0, 0, 0], 0]`	`[[-5, 12, -8, -4, 12, -8], 0]`	Failed

SHA-256 / fee78a3126f6d04ea71b66b33e5189cd1ece1cccce1d5a74d55d2dc15a0c65ea

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(pairs, amplitude, previous):
    out=[]
    for a,b in pairs:
        difference=a-b
        noise=difference*amplitude
        shaped=noise-previous
        previous=noise
        out.append(shaped)
    return [out,previous]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[1, 3], [4, 0], [2, 2]], 2, 1)), [[-5, 12, -8], 0])
check('oracle 2', solve(*([[0, 0], [1, 0]], 1, -2)), [[2, 1], 1])
check('oracle 3', solve(*([], 3, 4)), [[], 4])
check('oracle 4', solve(*([[4, 1], [1, 4]], 3, 0)), [[9, -18], -9])
check('oracle 5', solve(*([[1, 2], [2, 1], [0, 0]], 0, 3)), [[-3, 0, 0], 0])
check('oracle 6', solve(*([[3, 3]], 2, 0)), [[0], 0])
check('oracle 7', solve(*([[0, 2], [2, 0], [1, 1]], 4, -4)), [[-4, 16, -8], 0])
if N == 1: check('variant packet 1', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8], 0])
if N == 2: check('variant packet 2', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8], 0])
if N == 3: check('variant packet 3', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8], 0])
if N == 4: check('variant packet 4', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8], 0])
if N == 5: check('variant packet 5', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8], 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 fixture	Actual	Expected	Outcome
oracle 1	`[[-5, 12, -8], 0]`	`[[-5, 12, -8], 0]`	Passed
oracle 2	`[[2, 1], 1]`	`[[2, 1], 1]`	Passed
oracle 3	`[[], 4]`	`[[], 4]`	Passed
oracle 4	`[[9, -18], -9]`	`[[9, -18], -9]`	Passed
oracle 5	`[[-3, 0, 0], 0]`	`[[-3, 0, 0], 0]`	Passed
oracle 6	`[[0], 0]`	`[[0], 0]`	Passed
oracle 7	`[[-4, 16, -8], 0]`	`[[-4, 16, -8], 0]`	Passed
variant packet 1	`[[-5, 12, -8, -4, 12, -8], 0]`	`[[-5, 12, -8, -4, 12, -8], 0]`	Passed

SHA-256 / 16582d6aa6e87885df33a4775af5112e3d2053ba8627eca5cc05527757520dbf

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 2026-09-29T14:45:01.806947+00:00.

Case digest / 9912bba7ac2071dd2e810d5ad5862b3639dc79e4fd2e60345aac194421784a9d