FA-50101 / PCM sample encoding / Open access

Pcm seeded adaptive block: residual reconstruction · case 01

Every residual is anchored directly to block seed.

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

ROOT CAUSE

Every residual is anchored directly to block seed.

VERIFIED REPAIR

Use the stated conversion contract at residual reconstruction.

Unsuccessful approach: Subtracting signed residuals reverses the differential convention.

Case contract

Decode independent seeded differential PCM blocks; seed is the first presented sample and declared sample count includes it, excluding padded residuals.

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(blocks):
    out=[]
    for seed,deltas,declared in blocks:
        decoded=[seed]
        previous=seed
        for delta in deltas:
            previous=seed+delta
            decoded.append(previous)
        out.extend(decoded[:max(0,declared)])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[10, [1, 2], 3], [2, [-1, 3], 3]],)), [10, 11, 13, 2, 1, 4])
check('oracle 2', solve(*([[7, [1, 1], 1]],)), [7])
check('oracle 3', solve(*([[4, [], 0], [5, [], 1]],)), [5])
check('oracle 4', solve(*([],)), [])
check('oracle 5', solve(*([[-3, [2, -2], 2]],)), [-3, -1])
check('oracle 6', solve(*([[1, [1, 1, 1], 8]],)), [1, 2, 3, 4])
check('oracle 7', solve(*([[9, [1], 0], [3, [2], 2]],)), [3, 5])
if N == 1: check('variant packet 1', solve(*[[[10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3]]]), [10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4])
if N == 2: check('variant packet 2', solve(*[[[10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3]]]), [10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4])
if N == 3: check('variant packet 3', solve(*[[[10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3]]]), [10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4])
if N == 4: check('variant packet 4', solve(*[[[10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3]]]), [10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4])
if N == 5: check('variant packet 5', solve(*[[[10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3]]]), [10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4])
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	`[10, 11, 12, 2, 1, 5]`	`[10, 11, 13, 2, 1, 4]`	Failed
oracle 2	`[7]`	`[7]`	Passed
oracle 3	`[5]`	`[5]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[-3, -1]`	`[-3, -1]`	Passed
oracle 6	`[1, 2, 2, 2]`	`[1, 2, 3, 4]`	Failed
oracle 7	`[3, 5]`	`[3, 5]`	Passed
variant packet 1	`[10, 11, 12, 2, 1, 5, 10, 11, 12, 2, 1, 5]`	`[10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4]`	Failed

SHA-256 / 2136efedb7b29bf11595cfaeb8ddecc3b957c35efffc8345f988fd1476313843

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(blocks):
    out=[]
    for seed,deltas,declared in blocks:
        decoded=[seed]
        previous=seed
        for delta in deltas:
            previous-=delta
            decoded.append(previous)
        out.extend(decoded[:max(0,declared)])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[10, [1, 2], 3], [2, [-1, 3], 3]],)), [10, 11, 13, 2, 1, 4])
check('oracle 2', solve(*([[7, [1, 1], 1]],)), [7])
check('oracle 3', solve(*([[4, [], 0], [5, [], 1]],)), [5])
check('oracle 4', solve(*([],)), [])
check('oracle 5', solve(*([[-3, [2, -2], 2]],)), [-3, -1])
check('oracle 6', solve(*([[1, [1, 1, 1], 8]],)), [1, 2, 3, 4])
check('oracle 7', solve(*([[9, [1], 0], [3, [2], 2]],)), [3, 5])
if N == 1: check('variant packet 1', solve(*[[[10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3]]]), [10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4])
if N == 2: check('variant packet 2', solve(*[[[10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3]]]), [10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4])
if N == 3: check('variant packet 3', solve(*[[[10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3]]]), [10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4])
if N == 4: check('variant packet 4', solve(*[[[10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3]]]), [10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4])
if N == 5: check('variant packet 5', solve(*[[[10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3]]]), [10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4])
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	`[10, 9, 7, 2, 3, 0]`	`[10, 11, 13, 2, 1, 4]`	Failed
oracle 2	`[7]`	`[7]`	Passed
oracle 3	`[5]`	`[5]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[-3, -5]`	`[-3, -1]`	Failed
oracle 6	`[1, 0, -1, -2]`	`[1, 2, 3, 4]`	Failed
oracle 7	`[3, 1]`	`[3, 5]`	Failed
variant packet 1	`[10, 9, 7, 2, 3, 0, 10, 9, 7, 2, 3, 0]`	`[10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4]`	Failed

SHA-256 / 53f818dd94dcd43409bce8471f615fad0c69dd6e54b0e0988ca3bb603aa9b058

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(blocks):
    out=[]
    for seed,deltas,declared in blocks:
        decoded=[seed]
        previous=seed
        for delta in deltas:
            previous+=delta
            decoded.append(previous)
        out.extend(decoded[:max(0,declared)])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[10, [1, 2], 3], [2, [-1, 3], 3]],)), [10, 11, 13, 2, 1, 4])
check('oracle 2', solve(*([[7, [1, 1], 1]],)), [7])
check('oracle 3', solve(*([[4, [], 0], [5, [], 1]],)), [5])
check('oracle 4', solve(*([],)), [])
check('oracle 5', solve(*([[-3, [2, -2], 2]],)), [-3, -1])
check('oracle 6', solve(*([[1, [1, 1, 1], 8]],)), [1, 2, 3, 4])
check('oracle 7', solve(*([[9, [1], 0], [3, [2], 2]],)), [3, 5])
if N == 1: check('variant packet 1', solve(*[[[10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3]]]), [10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4])
if N == 2: check('variant packet 2', solve(*[[[10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3]]]), [10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4])
if N == 3: check('variant packet 3', solve(*[[[10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3]]]), [10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4])
if N == 4: check('variant packet 4', solve(*[[[10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3]]]), [10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4])
if N == 5: check('variant packet 5', solve(*[[[10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3], [10, [1, 2], 3], [2, [-1, 3], 3]]]), [10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4])
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	`[10, 11, 13, 2, 1, 4]`	`[10, 11, 13, 2, 1, 4]`	Passed
oracle 2	`[7]`	`[7]`	Passed
oracle 3	`[5]`	`[5]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[-3, -1]`	`[-3, -1]`	Passed
oracle 6	`[1, 2, 3, 4]`	`[1, 2, 3, 4]`	Passed
oracle 7	`[3, 5]`	`[3, 5]`	Passed
variant packet 1	`[10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4]`	`[10, 11, 13, 2, 1, 4, 10, 11, 13, 2, 1, 4]`	Passed

SHA-256 / 21fba3d870c926d5c6de9acd94c7a94592f15e69fbd460b8b605c9c21a6da86c

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 2026-09-29T14:45:06.068473+00:00.

Case digest / a739227e0716311871b5f3b22024d53ae9273cd11dd953e2c18206ef8838851e