FA-49216 / PCM sample encoding / Open access

Pcm delta reconstruction: initial predictor · case 01

PCM difference reconstruction discards the packet seed.

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

ROOT CAUSE

PCM difference reconstruction discards the packet seed.

VERIFIED REPAIR

Use the stated conversion contract at initial predictor.

Unsuccessful approach: Negating the seed reverses the initial DC value.

Case contract

Reconstruct bounded delta-coded PCM from a seed and explicit sample-index resets before residual application, returning the continuation predictor.

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(deltas, initial, reset_positions):
    previous=0
    out=[]
    for i,delta in enumerate(deltas):
        if i in reset_positions:
            previous=initial
        previous+=delta
        out.append(previous)
    return [out,previous]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([2, -1, 3], 10, [])), [[12, 11, 14], 14])
check('oracle 2', solve(*([1, 2, 3, 4], 5, [2])), [[6, 8, 8, 12], 12])
check('oracle 3', solve(*([], 7, [])), [[], 7])
check('oracle 4', solve(*([0, 0], -3, [0])), [[-3, -3], -3])
check('oracle 5', solve(*([-2, 4, -1], 0, [1])), [[-2, 4, 3], 3])
check('oracle 6', solve(*([3], 2, [])), [[5], 5])
check('oracle 7', solve(*([1, 1, 1], 1, [0, 1, 2])), [[2, 2, 2], 2])
if N == 1: check('variant packet 1', solve(*[[2, -1, 3, 2, -1, 3], 10, []]), [[12, 11, 14, 16, 15, 18], 18])
if N == 2: check('variant packet 2', solve(*[[2, -1, 3, 2, -1, 3, 2, -1, 3], 10, []]), [[12, 11, 14, 16, 15, 18, 20, 19, 22], 22])
if N == 3: check('variant packet 3', solve(*[[2, -1, 3, 2, -1, 3, 2, -1, 3, 2, -1, 3], 10, []]), [[12, 11, 14, 16, 15, 18, 20, 19, 22, 24, 23, 26], 26])
if N == 4: check('variant packet 4', solve(*[[2, -1, 3, 2, -1, 3, 2, -1, 3, 2, -1, 3, 2, -1, 3], 10, []]), [[12, 11, 14, 16, 15, 18, 20, 19, 22, 24, 23, 26, 28, 27, 30], 30])
if N == 5: check('variant packet 5', solve(*[[2, -1, 3, 2, -1, 3, 2, -1, 3, 2, -1, 3, 2, -1, 3, 2, -1, 3], 10, []]), [[12, 11, 14, 16, 15, 18, 20, 19, 22, 24, 23, 26, 28, 27, 30, 32, 31, 34], 34])
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, 4], 4]`	`[[12, 11, 14], 14]`	Failed
oracle 2	`[[1, 3, 8, 12], 12]`	`[[6, 8, 8, 12], 12]`	Failed
oracle 3	`[[], 0]`	`[[], 7]`	Failed
oracle 4	`[[-3, -3], -3]`	`[[-3, -3], -3]`	Passed
oracle 5	`[[-2, 4, 3], 3]`	`[[-2, 4, 3], 3]`	Passed
oracle 6	`[[3], 3]`	`[[5], 5]`	Failed
oracle 7	`[[2, 2, 2], 2]`	`[[2, 2, 2], 2]`	Passed
variant packet 1	`[[2, 1, 4, 6, 5, 8], 8]`	`[[12, 11, 14, 16, 15, 18], 18]`	Failed

SHA-256 / b10bc6f862db249f7e2c2c8e38c9a99da69b1e7bd6e1bf2e05bc3c75158628d9

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(deltas, initial, reset_positions):
    previous=-initial
    out=[]
    for i,delta in enumerate(deltas):
        if i in reset_positions:
            previous=initial
        previous+=delta
        out.append(previous)
    return [out,previous]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([2, -1, 3], 10, [])), [[12, 11, 14], 14])
check('oracle 2', solve(*([1, 2, 3, 4], 5, [2])), [[6, 8, 8, 12], 12])
check('oracle 3', solve(*([], 7, [])), [[], 7])
check('oracle 4', solve(*([0, 0], -3, [0])), [[-3, -3], -3])
check('oracle 5', solve(*([-2, 4, -1], 0, [1])), [[-2, 4, 3], 3])
check('oracle 6', solve(*([3], 2, [])), [[5], 5])
check('oracle 7', solve(*([1, 1, 1], 1, [0, 1, 2])), [[2, 2, 2], 2])
if N == 1: check('variant packet 1', solve(*[[2, -1, 3, 2, -1, 3], 10, []]), [[12, 11, 14, 16, 15, 18], 18])
if N == 2: check('variant packet 2', solve(*[[2, -1, 3, 2, -1, 3, 2, -1, 3], 10, []]), [[12, 11, 14, 16, 15, 18, 20, 19, 22], 22])
if N == 3: check('variant packet 3', solve(*[[2, -1, 3, 2, -1, 3, 2, -1, 3, 2, -1, 3], 10, []]), [[12, 11, 14, 16, 15, 18, 20, 19, 22, 24, 23, 26], 26])
if N == 4: check('variant packet 4', solve(*[[2, -1, 3, 2, -1, 3, 2, -1, 3, 2, -1, 3, 2, -1, 3], 10, []]), [[12, 11, 14, 16, 15, 18, 20, 19, 22, 24, 23, 26, 28, 27, 30], 30])
if N == 5: check('variant packet 5', solve(*[[2, -1, 3, 2, -1, 3, 2, -1, 3, 2, -1, 3, 2, -1, 3, 2, -1, 3], 10, []]), [[12, 11, 14, 16, 15, 18, 20, 19, 22, 24, 23, 26, 28, 27, 30, 32, 31, 34], 34])
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	`[[-8, -9, -6], -6]`	`[[12, 11, 14], 14]`	Failed
oracle 2	`[[-4, -2, 8, 12], 12]`	`[[6, 8, 8, 12], 12]`	Failed
oracle 3	`[[], -7]`	`[[], 7]`	Failed
oracle 4	`[[-3, -3], -3]`	`[[-3, -3], -3]`	Passed
oracle 5	`[[-2, 4, 3], 3]`	`[[-2, 4, 3], 3]`	Passed
oracle 6	`[[1], 1]`	`[[5], 5]`	Failed
oracle 7	`[[2, 2, 2], 2]`	`[[2, 2, 2], 2]`	Passed
variant packet 1	`[[-8, -9, -6, -4, -5, -2], -2]`	`[[12, 11, 14, 16, 15, 18], 18]`	Failed

SHA-256 / d725ef7cb5de754a11c69da941adde50dc523b78ddf08165fb43986b49abe4ea

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(deltas, initial, reset_positions):
    previous=initial
    out=[]
    for i,delta in enumerate(deltas):
        if i in reset_positions:
            previous=initial
        previous+=delta
        out.append(previous)
    return [out,previous]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([2, -1, 3], 10, [])), [[12, 11, 14], 14])
check('oracle 2', solve(*([1, 2, 3, 4], 5, [2])), [[6, 8, 8, 12], 12])
check('oracle 3', solve(*([], 7, [])), [[], 7])
check('oracle 4', solve(*([0, 0], -3, [0])), [[-3, -3], -3])
check('oracle 5', solve(*([-2, 4, -1], 0, [1])), [[-2, 4, 3], 3])
check('oracle 6', solve(*([3], 2, [])), [[5], 5])
check('oracle 7', solve(*([1, 1, 1], 1, [0, 1, 2])), [[2, 2, 2], 2])
if N == 1: check('variant packet 1', solve(*[[2, -1, 3, 2, -1, 3], 10, []]), [[12, 11, 14, 16, 15, 18], 18])
if N == 2: check('variant packet 2', solve(*[[2, -1, 3, 2, -1, 3, 2, -1, 3], 10, []]), [[12, 11, 14, 16, 15, 18, 20, 19, 22], 22])
if N == 3: check('variant packet 3', solve(*[[2, -1, 3, 2, -1, 3, 2, -1, 3, 2, -1, 3], 10, []]), [[12, 11, 14, 16, 15, 18, 20, 19, 22, 24, 23, 26], 26])
if N == 4: check('variant packet 4', solve(*[[2, -1, 3, 2, -1, 3, 2, -1, 3, 2, -1, 3, 2, -1, 3], 10, []]), [[12, 11, 14, 16, 15, 18, 20, 19, 22, 24, 23, 26, 28, 27, 30], 30])
if N == 5: check('variant packet 5', solve(*[[2, -1, 3, 2, -1, 3, 2, -1, 3, 2, -1, 3, 2, -1, 3, 2, -1, 3], 10, []]), [[12, 11, 14, 16, 15, 18, 20, 19, 22, 24, 23, 26, 28, 27, 30, 32, 31, 34], 34])
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	`[[12, 11, 14], 14]`	`[[12, 11, 14], 14]`	Passed
oracle 2	`[[6, 8, 8, 12], 12]`	`[[6, 8, 8, 12], 12]`	Passed
oracle 3	`[[], 7]`	`[[], 7]`	Passed
oracle 4	`[[-3, -3], -3]`	`[[-3, -3], -3]`	Passed
oracle 5	`[[-2, 4, 3], 3]`	`[[-2, 4, 3], 3]`	Passed
oracle 6	`[[5], 5]`	`[[5], 5]`	Passed
oracle 7	`[[2, 2, 2], 2]`	`[[2, 2, 2], 2]`	Passed
variant packet 1	`[[12, 11, 14, 16, 15, 18], 18]`	`[[12, 11, 14, 16, 15, 18], 18]`	Passed

SHA-256 / 7a2542fc018856e5d2479ea2204d465ae6c94048c48d0793d6c34727392a72b4

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 2026-09-29T14:44:57.906505+00:00.

Case digest / e82bd281951948374547b5886b74eb52c1f0dce3f55492b6c97dad669a573a25