FAILURE MAP
← Case archive

FA-50176 / PCM sample encoding / Open access

Pcm residual partition seeds: empty partition state · case 01

Empty seeded partitions fabricate an audible sample.

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

ROOT CAUSE

Empty seeded partitions fabricate an audible sample.

VERIFIED REPAIR

Use the stated conversion contract at empty partition state.

Unsuccessful approach: Dropping empty partitions loses explicit partition boundaries.

Case contract

PCM residual partitions optionally replace predictor with an absolute seed; continuation partitions ignore their seed field and empty partitions retain state transitions.

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(partitions, initial):
    state=initial
    out=[]
    for reset,seed,residuals in partitions:
        if reset:
            state=seed
        section=[]
        for residual in residuals:
            state+=residual
            section.append(state)
        out.append(section if section else [state])
    return [out,state]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[True, 10, [1, 2]], [False, 99, [-1]]], 0)), [[[11, 13], [12]], 12])
check('oracle 2', solve(*([[True, 0, [2]], [False, 5, [1]]], 7)), [[[2], [3]], 3])
check('oracle 3', solve(*([[True, 4, []], [False, 0, [1]]], 0)), [[[], [5]], 5])
check('oracle 4', solve(*([], 3)), [[], 3])
check('oracle 5', solve(*([[False, 99, [1, 1]]], 2)), [[[3, 4]], 4])
check('oracle 6', solve(*([[True, -3, [-1, 2]]], 5)), [[[-4, -2]], -2])
check('oracle 7', solve(*([[False, 0, []]], 4)), [[[]], 4])
if N == 1: check('variant packet 1', solve(*[[[True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]]], 0]), [[[11, 13], [12], [11, 13], [12]], 12])
if N == 2: check('variant packet 2', solve(*[[[True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]]], 0]), [[[11, 13], [12], [11, 13], [12], [11, 13], [12]], 12])
if N == 3: check('variant packet 3', solve(*[[[True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]]], 0]), [[[11, 13], [12], [11, 13], [12], [11, 13], [12], [11, 13], [12]], 12])
if N == 4: check('variant packet 4', solve(*[[[True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]]], 0]), [[[11, 13], [12], [11, 13], [12], [11, 13], [12], [11, 13], [12], [11, 13], [12]], 12])
if N == 5: check('variant packet 5', solve(*[[[True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]]], 0]), [[[11, 13], [12], [11, 13], [12], [11, 13], [12], [11, 13], [12], [11, 13], [12], [11, 13], [12]], 12])
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[[[11, 13], [12]], 12][[[11, 13], [12]], 12]Passed
oracle 2[[[2], [3]], 3][[[2], [3]], 3]Passed
oracle 3[[[4], [5]], 5][[[], [5]], 5]Failed
oracle 4[[], 3][[], 3]Passed
oracle 5[[[3, 4]], 4][[[3, 4]], 4]Passed
oracle 6[[[-4, -2]], -2][[[-4, -2]], -2]Passed
oracle 7[[[4]], 4][[[]], 4]Failed
variant packet 1[[[11, 13], [12], [11, 13], [12]], 12][[[11, 13], [12], [11, 13], [12]], 12]Passed

SHA-256 / f130c15f55b1c6026324397321e41d00398b145f4c0c4e2ac995293035cc97a1

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(partitions, initial):
    state=initial
    out=[]
    for reset,seed,residuals in partitions:
        if reset:
            state=seed
        section=[]
        for residual in residuals:
            state+=residual
            section.append(state)
        out.extend([section] if section else [])
    return [out,state]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[True, 10, [1, 2]], [False, 99, [-1]]], 0)), [[[11, 13], [12]], 12])
check('oracle 2', solve(*([[True, 0, [2]], [False, 5, [1]]], 7)), [[[2], [3]], 3])
check('oracle 3', solve(*([[True, 4, []], [False, 0, [1]]], 0)), [[[], [5]], 5])
check('oracle 4', solve(*([], 3)), [[], 3])
check('oracle 5', solve(*([[False, 99, [1, 1]]], 2)), [[[3, 4]], 4])
check('oracle 6', solve(*([[True, -3, [-1, 2]]], 5)), [[[-4, -2]], -2])
check('oracle 7', solve(*([[False, 0, []]], 4)), [[[]], 4])
if N == 1: check('variant packet 1', solve(*[[[True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]]], 0]), [[[11, 13], [12], [11, 13], [12]], 12])
if N == 2: check('variant packet 2', solve(*[[[True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]]], 0]), [[[11, 13], [12], [11, 13], [12], [11, 13], [12]], 12])
if N == 3: check('variant packet 3', solve(*[[[True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]]], 0]), [[[11, 13], [12], [11, 13], [12], [11, 13], [12], [11, 13], [12]], 12])
if N == 4: check('variant packet 4', solve(*[[[True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]]], 0]), [[[11, 13], [12], [11, 13], [12], [11, 13], [12], [11, 13], [12], [11, 13], [12]], 12])
if N == 5: check('variant packet 5', solve(*[[[True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]]], 0]), [[[11, 13], [12], [11, 13], [12], [11, 13], [12], [11, 13], [12], [11, 13], [12], [11, 13], [12]], 12])
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[[[11, 13], [12]], 12][[[11, 13], [12]], 12]Passed
oracle 2[[[2], [3]], 3][[[2], [3]], 3]Passed
oracle 3[[[5]], 5][[[], [5]], 5]Failed
oracle 4[[], 3][[], 3]Passed
oracle 5[[[3, 4]], 4][[[3, 4]], 4]Passed
oracle 6[[[-4, -2]], -2][[[-4, -2]], -2]Passed
oracle 7[[], 4][[[]], 4]Failed
variant packet 1[[[11, 13], [12], [11, 13], [12]], 12][[[11, 13], [12], [11, 13], [12]], 12]Passed

SHA-256 / 01f19a908a0cec9cb7c517f5f59428c19494cc359e25340896773d6cf62b51c6

3 / The verified repair

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

N = 1
observations = []
def solve(partitions, initial):
    state=initial
    out=[]
    for reset,seed,residuals in partitions:
        if reset:
            state=seed
        section=[]
        for residual in residuals:
            state+=residual
            section.append(state)
        out.append(section)
    return [out,state]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[True, 10, [1, 2]], [False, 99, [-1]]], 0)), [[[11, 13], [12]], 12])
check('oracle 2', solve(*([[True, 0, [2]], [False, 5, [1]]], 7)), [[[2], [3]], 3])
check('oracle 3', solve(*([[True, 4, []], [False, 0, [1]]], 0)), [[[], [5]], 5])
check('oracle 4', solve(*([], 3)), [[], 3])
check('oracle 5', solve(*([[False, 99, [1, 1]]], 2)), [[[3, 4]], 4])
check('oracle 6', solve(*([[True, -3, [-1, 2]]], 5)), [[[-4, -2]], -2])
check('oracle 7', solve(*([[False, 0, []]], 4)), [[[]], 4])
if N == 1: check('variant packet 1', solve(*[[[True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]]], 0]), [[[11, 13], [12], [11, 13], [12]], 12])
if N == 2: check('variant packet 2', solve(*[[[True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]]], 0]), [[[11, 13], [12], [11, 13], [12], [11, 13], [12]], 12])
if N == 3: check('variant packet 3', solve(*[[[True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]]], 0]), [[[11, 13], [12], [11, 13], [12], [11, 13], [12], [11, 13], [12]], 12])
if N == 4: check('variant packet 4', solve(*[[[True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]]], 0]), [[[11, 13], [12], [11, 13], [12], [11, 13], [12], [11, 13], [12], [11, 13], [12]], 12])
if N == 5: check('variant packet 5', solve(*[[[True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]], [True, 10, [1, 2]], [False, 99, [-1]]], 0]), [[[11, 13], [12], [11, 13], [12], [11, 13], [12], [11, 13], [12], [11, 13], [12], [11, 13], [12]], 12])
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[[[11, 13], [12]], 12][[[11, 13], [12]], 12]Passed
oracle 2[[[2], [3]], 3][[[2], [3]], 3]Passed
oracle 3[[[], [5]], 5][[[], [5]], 5]Passed
oracle 4[[], 3][[], 3]Passed
oracle 5[[[3, 4]], 4][[[3, 4]], 4]Passed
oracle 6[[[-4, -2]], -2][[[-4, -2]], -2]Passed
oracle 7[[[]], 4][[[]], 4]Passed
variant packet 1[[[11, 13], [12], [11, 13], [12]], 12][[[11, 13], [12], [11, 13], [12]], 12]Passed

SHA-256 / 9db0e32dd0a9f4b2466e8b228582dfc277b2739ac65d890b0d6b6e869ad85988

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 2026-09-29T14:45:06.707020+00:00.

Case digest / 76ce69e5da463795ba32fa058fde05faa8d98f685e83d20eefe1ff7552866d21