FAILURE MAP
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FA-49976 / PCM sample encoding / Open access

Pcm i2s delayed capture: serial bit significance · case 01

Serial PCM field bits are reconstructed least-significant-first.

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

ROOT CAUSE

Serial PCM field bits are reconstructed least-significant-first.

THE FAILURE

Serial PCM field bits are reconstructed least-significant-first.

Unsuccessful approach: Weighting against slot width includes non-sample padding positions.

Case contract

Capture a stipulated I2S-like slot with one delay clock, MSB-first signed PCM payload and explicit trailing slot bits; reject incomplete slots.

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(slots, payload_bits, slot_bits):
    out=[]
    for bits in slots:
        field=bits[1:1+payload_bits]
        if len(bits)<slot_bits or len(field)!=payload_bits:
            out.append(None)
            continue
        code=sum(bit<<i for i,bit in enumerate(field))
        sample=code-(1<<payload_bits) if field[0] else code
        tail=bits[1+payload_bits:slot_bits]
        out.append([sample,tail])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0]], 4, 6)), [[-6, [0]], [7, [0]]])
check('oracle 2', solve(*([[0, 0, 0, 1, 1]], 3, 5)), [[1, [1]]])
check('oracle 3', solve(*([[1, 1, 1, 1]], 3, 5)), [None])
check('oracle 4', solve(*([], 4, 6)), [])
check('oracle 5', solve(*([[1, 0, 0, 0, 1, 1, 1]], 4, 6)), [[1, [1]]])
check('oracle 6', solve(*([[0, 1, 0]], 1, 3)), [[-1, [0]]])
check('oracle 7', solve(*([[0, 0, 1, 0, 0, 1]], 3, 5)), [[2, [0]]])
if N == 1: check('variant packet 1', solve(*[[[0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0]], 4, 6]), [[-6, [0]], [7, [0]], [-6, [0]], [7, [0]]])
if N == 2: check('variant packet 2', solve(*[[[0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0]], 4, 6]), [[-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]]])
if N == 3: check('variant packet 3', solve(*[[[0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0]], 4, 6]), [[-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]]])
if N == 4: check('variant packet 4', solve(*[[[0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0]], 4, 6]), [[-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]]])
if N == 5: check('variant packet 5', solve(*[[[0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0]], 4, 6]), [[-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]]])
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, [0]], [14, [0]]][[-6, [0]], [7, [0]]]Failed
oracle 2[[4, [1]]][[1, [1]]]Failed
oracle 3[None][None]Passed
oracle 4[][]Passed
oracle 5[[8, [1]]][[1, [1]]]Failed
oracle 6[[-1, [0]]][[-1, [0]]]Passed
oracle 7[[2, [0]]][[2, [0]]]Passed
variant packet 1[[-11, [0]], [14, [0]], [-11, [0]], [14, [0]]][[-6, [0]], [7, [0]], [-6, [0]], [7, [0]]]Failed

SHA-256 / 47a6d77f0b9eb2fbeff11ad722300640cf5247ee2e94c4bce66a7aa87eba271c

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(slots, payload_bits, slot_bits):
    out=[]
    for bits in slots:
        field=bits[1:1+payload_bits]
        if len(bits)<slot_bits or len(field)!=payload_bits:
            out.append(None)
            continue
        code=sum(bit<<(slot_bits-1-i) for i,bit in enumerate(field))
        sample=code-(1<<payload_bits) if field[0] else code
        tail=bits[1+payload_bits:slot_bits]
        out.append([sample,tail])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0]], 4, 6)), [[-6, [0]], [7, [0]]])
check('oracle 2', solve(*([[0, 0, 0, 1, 1]], 3, 5)), [[1, [1]]])
check('oracle 3', solve(*([[1, 1, 1, 1]], 3, 5)), [None])
check('oracle 4', solve(*([], 4, 6)), [])
check('oracle 5', solve(*([[1, 0, 0, 0, 1, 1, 1]], 4, 6)), [[1, [1]]])
check('oracle 6', solve(*([[0, 1, 0]], 1, 3)), [[-1, [0]]])
check('oracle 7', solve(*([[0, 0, 1, 0, 0, 1]], 3, 5)), [[2, [0]]])
if N == 1: check('variant packet 1', solve(*[[[0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0]], 4, 6]), [[-6, [0]], [7, [0]], [-6, [0]], [7, [0]]])
if N == 2: check('variant packet 2', solve(*[[[0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0]], 4, 6]), [[-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]]])
if N == 3: check('variant packet 3', solve(*[[[0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0]], 4, 6]), [[-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]]])
if N == 4: check('variant packet 4', solve(*[[[0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0]], 4, 6]), [[-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]]])
if N == 5: check('variant packet 5', solve(*[[[0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0]], 4, 6]), [[-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]], [-6, [0]], [7, [0]]])
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[[24, [0]], [28, [0]]][[-6, [0]], [7, [0]]]Failed
oracle 2[[4, [1]]][[1, [1]]]Failed
oracle 3[None][None]Passed
oracle 4[][]Passed
oracle 5[[4, [1]]][[1, [1]]]Failed
oracle 6[[2, [0]]][[-1, [0]]]Failed
oracle 7[[8, [0]]][[2, [0]]]Failed
variant packet 1[[24, [0]], [28, [0]], [24, [0]], [28, [0]]][[-6, [0]], [7, [0]], [-6, [0]], [7, [0]]]Failed

SHA-256 / 94bccc81bb79890405c02a611b2535d2a63f9e4d6463baf011c388934ca61776

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 2026-09-29T14:45:05.008563+00:00.

Case digest / 875b918c594e485e1fff64be874c94b0910d8809754bb2f53b43ec258ab0d354