FA-49251 / PCM sample encoding / Open access

Pcm delta generation: residual order · case 01

Residual polarity is reversed.

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

ROOT CAUSE

Residual polarity is reversed.

VERIFIED REPAIR

Use the stated conversion contract at residual order.

Unsuccessful approach: Adding predictor does not cancel the predicted level.

Case contract

Generate signed PCM residuals relative to the previous amplitude; reset at explicit sample positions and return the final amplitude continuation seed.

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, initial, reset_positions):
    previous=initial
    out=[]
    for i,sample in enumerate(samples):
        if i in reset_positions:
            previous=initial
        out.append(previous-sample)
        previous=sample
    return [out,previous]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([12, 11, 14], 10, [])), [[2, -1, 3], 14])
check('oracle 2', solve(*([3, 7, 9, 5], 2, [2])), [[1, 4, 7, -4], 5])
check('oracle 3', solve(*([], -7, [])), [[], -7])
check('oracle 4', solve(*([-3, -4], -2, [])), [[-1, -1], -4])
check('oracle 5', solve(*([0, 0], 5, [1])), [[-5, -5], 0])
check('oracle 6', solve(*([1], 0, [])), [[1], 1])
check('oracle 7', solve(*([1, 2, 3], 4, [0, 1, 2])), [[-3, -2, -1], 3])
if N == 1: check('variant packet 1', solve(*[[12, 11, 14, 12, 11, 14], 10, []]), [[2, -1, 3, -2, -1, 3], 14])
if N == 2: check('variant packet 2', solve(*[[12, 11, 14, 12, 11, 14, 12, 11, 14], 10, []]), [[2, -1, 3, -2, -1, 3, -2, -1, 3], 14])
if N == 3: check('variant packet 3', solve(*[[12, 11, 14, 12, 11, 14, 12, 11, 14, 12, 11, 14], 10, []]), [[2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 3], 14])
if N == 4: check('variant packet 4', solve(*[[12, 11, 14, 12, 11, 14, 12, 11, 14, 12, 11, 14, 12, 11, 14], 10, []]), [[2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 3], 14])
if N == 5: check('variant packet 5', solve(*[[12, 11, 14, 12, 11, 14, 12, 11, 14, 12, 11, 14, 12, 11, 14, 12, 11, 14], 10, []]), [[2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 3], 14])
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, 1, -3], 14]`	`[[2, -1, 3], 14]`	Failed
oracle 2	`[[-1, -4, -7, 4], 5]`	`[[1, 4, 7, -4], 5]`	Failed
oracle 3	`[[], -7]`	`[[], -7]`	Passed
oracle 4	`[[1, 1], -4]`	`[[-1, -1], -4]`	Failed
oracle 5	`[[5, 5], 0]`	`[[-5, -5], 0]`	Failed
oracle 6	`[[-1], 1]`	`[[1], 1]`	Failed
oracle 7	`[[3, 2, 1], 3]`	`[[-3, -2, -1], 3]`	Failed
variant packet 1	`[[-2, 1, -3, 2, 1, -3], 14]`	`[[2, -1, 3, -2, -1, 3], 14]`	Failed

SHA-256 / 8d9d80dbace61ddf22dd1b4f4a5f7ab222351dbd7fc6555aca7e4fc6588d15d5

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(samples, initial, reset_positions):
    previous=initial
    out=[]
    for i,sample in enumerate(samples):
        if i in reset_positions:
            previous=initial
        out.append(sample+previous)
        previous=sample
    return [out,previous]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([12, 11, 14], 10, [])), [[2, -1, 3], 14])
check('oracle 2', solve(*([3, 7, 9, 5], 2, [2])), [[1, 4, 7, -4], 5])
check('oracle 3', solve(*([], -7, [])), [[], -7])
check('oracle 4', solve(*([-3, -4], -2, [])), [[-1, -1], -4])
check('oracle 5', solve(*([0, 0], 5, [1])), [[-5, -5], 0])
check('oracle 6', solve(*([1], 0, [])), [[1], 1])
check('oracle 7', solve(*([1, 2, 3], 4, [0, 1, 2])), [[-3, -2, -1], 3])
if N == 1: check('variant packet 1', solve(*[[12, 11, 14, 12, 11, 14], 10, []]), [[2, -1, 3, -2, -1, 3], 14])
if N == 2: check('variant packet 2', solve(*[[12, 11, 14, 12, 11, 14, 12, 11, 14], 10, []]), [[2, -1, 3, -2, -1, 3, -2, -1, 3], 14])
if N == 3: check('variant packet 3', solve(*[[12, 11, 14, 12, 11, 14, 12, 11, 14, 12, 11, 14], 10, []]), [[2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 3], 14])
if N == 4: check('variant packet 4', solve(*[[12, 11, 14, 12, 11, 14, 12, 11, 14, 12, 11, 14, 12, 11, 14], 10, []]), [[2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 3], 14])
if N == 5: check('variant packet 5', solve(*[[12, 11, 14, 12, 11, 14, 12, 11, 14, 12, 11, 14, 12, 11, 14, 12, 11, 14], 10, []]), [[2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 3], 14])
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	`[[22, 23, 25], 14]`	`[[2, -1, 3], 14]`	Failed
oracle 2	`[[5, 10, 11, 14], 5]`	`[[1, 4, 7, -4], 5]`	Failed
oracle 3	`[[], -7]`	`[[], -7]`	Passed
oracle 4	`[[-5, -7], -4]`	`[[-1, -1], -4]`	Failed
oracle 5	`[[5, 5], 0]`	`[[-5, -5], 0]`	Failed
oracle 6	`[[1], 1]`	`[[1], 1]`	Passed
oracle 7	`[[5, 6, 7], 3]`	`[[-3, -2, -1], 3]`	Failed
variant packet 1	`[[22, 23, 25, 26, 23, 25], 14]`	`[[2, -1, 3, -2, -1, 3], 14]`	Failed

SHA-256 / 408ed6684087a33c1656a1bd13d327cf86dad70979f008ef8934293fd8abdd23

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(samples, initial, reset_positions):
    previous=initial
    out=[]
    for i,sample in enumerate(samples):
        if i in reset_positions:
            previous=initial
        out.append(sample-previous)
        previous=sample
    return [out,previous]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([12, 11, 14], 10, [])), [[2, -1, 3], 14])
check('oracle 2', solve(*([3, 7, 9, 5], 2, [2])), [[1, 4, 7, -4], 5])
check('oracle 3', solve(*([], -7, [])), [[], -7])
check('oracle 4', solve(*([-3, -4], -2, [])), [[-1, -1], -4])
check('oracle 5', solve(*([0, 0], 5, [1])), [[-5, -5], 0])
check('oracle 6', solve(*([1], 0, [])), [[1], 1])
check('oracle 7', solve(*([1, 2, 3], 4, [0, 1, 2])), [[-3, -2, -1], 3])
if N == 1: check('variant packet 1', solve(*[[12, 11, 14, 12, 11, 14], 10, []]), [[2, -1, 3, -2, -1, 3], 14])
if N == 2: check('variant packet 2', solve(*[[12, 11, 14, 12, 11, 14, 12, 11, 14], 10, []]), [[2, -1, 3, -2, -1, 3, -2, -1, 3], 14])
if N == 3: check('variant packet 3', solve(*[[12, 11, 14, 12, 11, 14, 12, 11, 14, 12, 11, 14], 10, []]), [[2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 3], 14])
if N == 4: check('variant packet 4', solve(*[[12, 11, 14, 12, 11, 14, 12, 11, 14, 12, 11, 14, 12, 11, 14], 10, []]), [[2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 3], 14])
if N == 5: check('variant packet 5', solve(*[[12, 11, 14, 12, 11, 14, 12, 11, 14, 12, 11, 14, 12, 11, 14, 12, 11, 14], 10, []]), [[2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 3], 14])
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, -1, 3], 14]`	`[[2, -1, 3], 14]`	Passed
oracle 2	`[[1, 4, 7, -4], 5]`	`[[1, 4, 7, -4], 5]`	Passed
oracle 3	`[[], -7]`	`[[], -7]`	Passed
oracle 4	`[[-1, -1], -4]`	`[[-1, -1], -4]`	Passed
oracle 5	`[[-5, -5], 0]`	`[[-5, -5], 0]`	Passed
oracle 6	`[[1], 1]`	`[[1], 1]`	Passed
oracle 7	`[[-3, -2, -1], 3]`	`[[-3, -2, -1], 3]`	Passed
variant packet 1	`[[2, -1, 3, -2, -1, 3], 14]`	`[[2, -1, 3, -2, -1, 3], 14]`	Passed

SHA-256 / 636466d6ee47e6fa42469739634988d453e56ae1440e52f5d832f00c21d4db79

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 2026-09-29T14:44:58.266587+00:00.

Case digest / 4ede106fb300c6067844ac2e9f2dfb58dd1aa5b3bbc88212e595da47602490ce