FA-49736 / PCM sample encoding / Open access

Pcm adaptive nibble reconstruction: feedback index · case 01

Each nibble replaces the step index rather than adapting prior state.

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

ROOT CAUSE

Each nibble replaces the step index rather than adapting prior state.

VERIFIED REPAIR

Use the stated conversion contract at feedback index.

Unsuccessful approach: Reversing the adaptation direction decreases precision for quiet codes.

Case contract

Stipulated bounded adaptive differential PCM nibble model with a 16-entry step table, magnitude adaptation, signed predictor saturation and exported predictor/index state.

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(codes, predictor, step_index):
    steps=[7,8,9,10,11,12,13,14,16,17,19,21,23,25,28,31]
    adjust=[-1,-1,-1,-1,2,4,6,8]
    out=[]
    for code in codes:
        step=steps[step_index]
        delta=step//8
        if code&1: delta+=step//4
        if code&2: delta+=step//2
        if code&4: delta+=step
        predictor+=-delta if code&8 else delta
        predictor=max(-128,min(127,predictor))
        step_index=max(0,min(len(steps)-1,adjust[code&7]))
        out.append(predictor)
    return [out,predictor,step_index]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 1, 2, 3, 4, 7, 8, 15], 0, 4)), [[1, 4, 9, 16, 23, 39, 37, 6], 6, 15])
check('oracle 2', solve(*([7, 7, 7], 120, 14)), [[127, 127, 127], 127, 15])
check('oracle 3', solve(*([15, 15], -120, 15)), [[-128, -128], -128, 15])
check('oracle 4', solve(*([], 4, 2)), [[], 4, 2])
check('oracle 5', solve(*([0, 0, 0], 0, 1)), [[1, 1, 1], 1, 0])
check('oracle 6', solve(*([4, 12, 6, 14], 3, 8)), [[21, 0, 36, -13], -13, 15])
check('oracle 7', solve(*([1, 9, 2, 10], -4, 5)), [[0, -3, 3, -2], -2, 1])
if N == 1: check('variant packet 1', solve(*[[0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15], 0, 4]), [[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66], 66, 15])
if N == 2: check('variant packet 2', solve(*[[0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15], 0, 4]), [[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66, 69, 79, 94, 112, 127, 127, 124, 72], 72, 15])
if N == 3: check('variant packet 3', solve(*[[0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15], 0, 4]), [[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66, 69, 79, 94, 112, 127, 127, 124, 72, 75, 85, 100, 118, 127, 127, 124, 72], 72, 15])
if N == 4: check('variant packet 4', solve(*[[0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15], 0, 4]), [[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66, 69, 79, 94, 112, 127, 127, 124, 72, 75, 85, 100, 118, 127, 127, 124, 72, 75, 85, 100, 118, 127, 127, 124, 72], 72, 15])
if N == 5: check('variant packet 5', solve(*[[0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15], 0, 4]), [[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66, 69, 79, 94, 112, 127, 127, 124, 72, 75, 85, 100, 118, 127, 127, 124, 72, 75, 85, 100, 118, 127, 127, 124, 72, 75, 85, 100, 118, 127, 127, 124, 72], 72, 15])
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, 5, 9, 16, 32, 30, 19], 19, 8]`	`[[1, 4, 9, 16, 23, 39, 37, 6], 6, 15]`	Failed
oracle 2	`[[127, 127, 127], 127, 8]`	`[[127, 127, 127], 127, 15]`	Failed
oracle 3	`[[-128, -128], -128, 8]`	`[[-128, -128], -128, 15]`	Failed
oracle 4	`[[], 4, 2]`	`[[], 4, 2]`	Passed
oracle 5	`[[1, 1, 1], 1, 0]`	`[[1, 1, 1], 1, 0]`	Passed
oracle 6	`[[21, 11, 25, 5], 5, 6]`	`[[21, 0, 36, -13], -13, 15]`	Failed
oracle 7	`[[0, -1, 2, -1], -1, 0]`	`[[0, -3, 3, -2], -2, 1]`	Failed
variant packet 1	`[[1, 2, 5, 9, 16, 32, 30, 19, 21, 22, 25, 29, 36, 52, 50, 39], 39, 8]`	`[[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66], 66, 15]`	Failed

SHA-256 / 74181a70bc350bd8c01bec9fe695ebcf8fcf5ab832ce1070989e7e9e059e7b2b

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(codes, predictor, step_index):
    steps=[7,8,9,10,11,12,13,14,16,17,19,21,23,25,28,31]
    adjust=[-1,-1,-1,-1,2,4,6,8]
    out=[]
    for code in codes:
        step=steps[step_index]
        delta=step//8
        if code&1: delta+=step//4
        if code&2: delta+=step//2
        if code&4: delta+=step
        predictor+=-delta if code&8 else delta
        predictor=max(-128,min(127,predictor))
        step_index=max(0,min(len(steps)-1,step_index-adjust[code&7]))
        out.append(predictor)
    return [out,predictor,step_index]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 1, 2, 3, 4, 7, 8, 15], 0, 4)), [[1, 4, 9, 16, 23, 39, 37, 6], 6, 15])
check('oracle 2', solve(*([7, 7, 7], 120, 14)), [[127, 127, 127], 127, 15])
check('oracle 3', solve(*([15, 15], -120, 15)), [[-128, -128], -128, 15])
check('oracle 4', solve(*([], 4, 2)), [[], 4, 2])
check('oracle 5', solve(*([0, 0, 0], 0, 1)), [[1, 1, 1], 1, 0])
check('oracle 6', solve(*([4, 12, 6, 14], 3, 8)), [[21, 0, 36, -13], -13, 15])
check('oracle 7', solve(*([1, 9, 2, 10], -4, 5)), [[0, -3, 3, -2], -2, 1])
if N == 1: check('variant packet 1', solve(*[[0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15], 0, 4]), [[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66], 66, 15])
if N == 2: check('variant packet 2', solve(*[[0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15], 0, 4]), [[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66, 69, 79, 94, 112, 127, 127, 124, 72], 72, 15])
if N == 3: check('variant packet 3', solve(*[[0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15], 0, 4]), [[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66, 69, 79, 94, 112, 127, 127, 124, 72, 75, 85, 100, 118, 127, 127, 124, 72], 72, 15])
if N == 4: check('variant packet 4', solve(*[[0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15], 0, 4]), [[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66, 69, 79, 94, 112, 127, 127, 124, 72, 75, 85, 100, 118, 127, 127, 124, 72, 75, 85, 100, 118, 127, 127, 124, 72], 72, 15])
if N == 5: check('variant packet 5', solve(*[[0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15], 0, 4]), [[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66, 69, 79, 94, 112, 127, 127, 124, 72, 75, 85, 100, 118, 127, 127, 124, 72, 75, 85, 100, 118, 127, 127, 124, 72, 75, 85, 100, 118, 127, 127, 124, 72], 72, 15])
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, 5, 12, 23, 41, 64, 64, 49], 49, 0]`	`[[1, 4, 9, 16, 23, 39, 37, 6], 6, 15]`	Failed
oracle 2	`[[127, 127, 127], 127, 0]`	`[[127, 127, 127], 127, 15]`	Failed
oracle 3	`[[-128, -128], -128, 0]`	`[[-128, -128], -128, 15]`	Failed
oracle 4	`[[], 4, 2]`	`[[], 4, 2]`	Passed
oracle 5	`[[1, 2, 3], 3, 4]`	`[[1, 1, 1], 1, 0]`	Failed
oracle 6	`[[21, 7, 24, 14], 14, 0]`	`[[21, 0, 36, -13], -13, 15]`	Failed
oracle 7	`[[0, -4, 4, -6], -6, 9]`	`[[0, -3, 3, -2], -2, 1]`	Failed
variant packet 1	`[[1, 5, 12, 23, 41, 64, 64, 49, 49, 52, 57, 65, 77, 93, 93, 78], 78, 0]`	`[[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66], 66, 15]`	Failed

SHA-256 / 96f6c2e4f6ba0dac9c7ec67b07985d081751e1898f2b0cd2ba6536e810e738ae

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(codes, predictor, step_index):
    steps=[7,8,9,10,11,12,13,14,16,17,19,21,23,25,28,31]
    adjust=[-1,-1,-1,-1,2,4,6,8]
    out=[]
    for code in codes:
        step=steps[step_index]
        delta=step//8
        if code&1: delta+=step//4
        if code&2: delta+=step//2
        if code&4: delta+=step
        predictor+=-delta if code&8 else delta
        predictor=max(-128,min(127,predictor))
        step_index=max(0,min(len(steps)-1,step_index+adjust[code&7]))
        out.append(predictor)
    return [out,predictor,step_index]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 1, 2, 3, 4, 7, 8, 15], 0, 4)), [[1, 4, 9, 16, 23, 39, 37, 6], 6, 15])
check('oracle 2', solve(*([7, 7, 7], 120, 14)), [[127, 127, 127], 127, 15])
check('oracle 3', solve(*([15, 15], -120, 15)), [[-128, -128], -128, 15])
check('oracle 4', solve(*([], 4, 2)), [[], 4, 2])
check('oracle 5', solve(*([0, 0, 0], 0, 1)), [[1, 1, 1], 1, 0])
check('oracle 6', solve(*([4, 12, 6, 14], 3, 8)), [[21, 0, 36, -13], -13, 15])
check('oracle 7', solve(*([1, 9, 2, 10], -4, 5)), [[0, -3, 3, -2], -2, 1])
if N == 1: check('variant packet 1', solve(*[[0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15], 0, 4]), [[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66], 66, 15])
if N == 2: check('variant packet 2', solve(*[[0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15], 0, 4]), [[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66, 69, 79, 94, 112, 127, 127, 124, 72], 72, 15])
if N == 3: check('variant packet 3', solve(*[[0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15], 0, 4]), [[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66, 69, 79, 94, 112, 127, 127, 124, 72, 75, 85, 100, 118, 127, 127, 124, 72], 72, 15])
if N == 4: check('variant packet 4', solve(*[[0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15], 0, 4]), [[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66, 69, 79, 94, 112, 127, 127, 124, 72, 75, 85, 100, 118, 127, 127, 124, 72, 75, 85, 100, 118, 127, 127, 124, 72], 72, 15])
if N == 5: check('variant packet 5', solve(*[[0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15, 0, 1, 2, 3, 4, 7, 8, 15], 0, 4]), [[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66, 69, 79, 94, 112, 127, 127, 124, 72, 75, 85, 100, 118, 127, 127, 124, 72, 75, 85, 100, 118, 127, 127, 124, 72, 75, 85, 100, 118, 127, 127, 124, 72], 72, 15])
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, 4, 9, 16, 23, 39, 37, 6], 6, 15]`	`[[1, 4, 9, 16, 23, 39, 37, 6], 6, 15]`	Passed
oracle 2	`[[127, 127, 127], 127, 15]`	`[[127, 127, 127], 127, 15]`	Passed
oracle 3	`[[-128, -128], -128, 15]`	`[[-128, -128], -128, 15]`	Passed
oracle 4	`[[], 4, 2]`	`[[], 4, 2]`	Passed
oracle 5	`[[1, 1, 1], 1, 0]`	`[[1, 1, 1], 1, 0]`	Passed
oracle 6	`[[21, 0, 36, -13], -13, 15]`	`[[21, 0, 36, -13], -13, 15]`	Passed
oracle 7	`[[0, -3, 3, -2], -2, 1]`	`[[0, -3, 3, -2], -2, 1]`	Passed
variant packet 1	`[[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66], 66, 15]`	`[[1, 4, 9, 16, 23, 39, 37, 6, 9, 19, 34, 52, 75, 121, 118, 66], 66, 15]`	Passed

SHA-256 / 2a132c685144716a4dd75f0dc0256939536edea1d2b830a2fdf440014140e03c

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 2026-09-29T14:45:02.746337+00:00.

Case digest / 4fdb9b257635fe282d40a44a7970b6334c77537f01e51b144089b65e4c236ad8