FA-49226 / PCM sample encoding / Open access

Pcm delta reconstruction: delta accumulate · case 01

Every PCM residual is added to the seed rather than prior reconstructed sample.

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

ROOT CAUSE

Every PCM residual is added to the seed rather than prior reconstructed sample.

THE FAILURE

Every PCM residual is added to the seed rather than prior reconstructed sample.

Unsuccessful approach: Subtracting residuals reverses the differential convention.

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=initial
    out=[]
    for i,delta in enumerate(deltas):
        if i in reset_positions:
            previous=initial
        previous=initial+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, 9, 13], 13]`	`[[12, 11, 14], 14]`	Failed
oracle 2	`[[6, 7, 8, 9], 9]`	`[[6, 8, 8, 12], 12]`	Failed
oracle 3	`[[], 7]`	`[[], 7]`	Passed
oracle 4	`[[-3, -3], -3]`	`[[-3, -3], -3]`	Passed
oracle 5	`[[-2, 4, -1], -1]`	`[[-2, 4, 3], 3]`	Failed
oracle 6	`[[5], 5]`	`[[5], 5]`	Passed
oracle 7	`[[2, 2, 2], 2]`	`[[2, 2, 2], 2]`	Passed
variant packet 1	`[[12, 9, 13, 12, 9, 13], 13]`	`[[12, 11, 14, 16, 15, 18], 18]`	Failed

SHA-256 / e3843bd62bcd73f412a2f943fe3c5bc273a62037d6ba7d68bdf5bf5aff37a78b

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, 2, -2], -2]`	`[[6, 8, 8, 12], 12]`	Failed
oracle 3	`[[], 7]`	`[[], 7]`	Passed
oracle 4	`[[-3, -3], -3]`	`[[-3, -3], -3]`	Passed
oracle 5	`[[2, -4, -3], -3]`	`[[-2, 4, 3], 3]`	Failed
oracle 6	`[[-1], -1]`	`[[5], 5]`	Failed
oracle 7	`[[0, 0, 0], 0]`	`[[2, 2, 2], 2]`	Failed
variant packet 1	`[[8, 9, 6, 4, 5, 2], 2]`	`[[12, 11, 14, 16, 15, 18], 18]`	Failed

SHA-256 / b05083a660b472b0af2f2ff0f7cf296246b4300228a7d3d41b7c5e16d4aa5541

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:44:58.040035+00:00.

Case digest / de9632a5d5000e60020a6c668bf7b37e6ffadea1006dee19f14f0c4e2a592a9b