FA-50181 / PCM sample encoding / Open access

Pcm residual partition seeds: residual direction · case 01

Residual sign is reversed inside PCM partitions.

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

ROOT CAUSE

Residual sign is reversed inside PCM partitions.

VERIFIED REPAIR

Use the stated conversion contract at residual direction.

Unsuccessful approach: Replacing state with residual skips integration.

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)
    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 fixture	Actual	Expected	Outcome
oracle 1	`[[[9, 7], [8]], 8]`	`[[[11, 13], [12]], 12]`	Failed
oracle 2	`[[[-2], [-3]], -3]`	`[[[2], [3]], 3]`	Failed
oracle 3	`[[[], [3]], 3]`	`[[[], [5]], 5]`	Failed
oracle 4	`[[], 3]`	`[[], 3]`	Passed
oracle 5	`[[[1, 0]], 0]`	`[[[3, 4]], 4]`	Failed
oracle 6	`[[[-2, -4]], -4]`	`[[[-4, -2]], -2]`	Failed
oracle 7	`[[[]], 4]`	`[[[]], 4]`	Passed
variant packet 1	`[[[9, 7], [8], [9, 7], [8]], 8]`	`[[[11, 13], [12], [11, 13], [12]], 12]`	Failed

SHA-256 / 986cb893853ea313919698390ff53c854c8e5368c61a120b8926a6454137872c

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.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 fixture	Actual	Expected	Outcome
oracle 1	`[[[1, 2], [-1]], -1]`	`[[[11, 13], [12]], 12]`	Failed
oracle 2	`[[[2], [1]], 1]`	`[[[2], [3]], 3]`	Failed
oracle 3	`[[[], [1]], 1]`	`[[[], [5]], 5]`	Failed
oracle 4	`[[], 3]`	`[[], 3]`	Passed
oracle 5	`[[[1, 1]], 1]`	`[[[3, 4]], 4]`	Failed
oracle 6	`[[[-1, 2]], 2]`	`[[[-4, -2]], -2]`	Failed
oracle 7	`[[[]], 4]`	`[[[]], 4]`	Passed
variant packet 1	`[[[1, 2], [-1], [1, 2], [-1]], -1]`	`[[[11, 13], [12], [11, 13], [12]], 12]`	Failed

SHA-256 / 34f6322b2d57a98733cd458ba665c81afabf143f6da73ef689c6499b77445875

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 fixture	Actual	Expected	Outcome
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 2026-09-29T14:45:06.742066+00:00.

Case digest / 6a16d1d6db95eca022879688cbc03dd081f63ac1ef647099fe8c0334969f2b0d