FAILURE MAP
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FA-49461 / PCM sample encoding / Open access

Pcm progressive refinement: signed coarse compose · case 01

Negative coarse PCM loses its sign before refinement.

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

ROOT CAUSE

Negative coarse PCM loses its sign before refinement.

THE FAILURE

Negative coarse PCM loses its sign before refinement.

Unsuccessful approach: Subtracting low bits uses the wrong residue representation for negative bins.

Case contract

Restore PCM from arithmetic-shift coarse samples and optional unsigned low-bit refinements; missing refinement bits are zero and out-of-field residual bits are masked.

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(coarse, residuals, missing_bits):
    scale=1<<missing_bits
    out=[]
    for index,base in enumerate(coarse):
        tail=residuals[index] if index<len(residuals) else 0
        tail &= scale-1
        out.append((abs(base)*scale+tail))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, -2, 3], [3, 1, 2], 2)), [7, -7, 14])
check('oracle 2', solve(*([-1, 0], [7, 4], 2)), [-1, 0])
check('oracle 3', solve(*([2, 3, 4], [1], 3)), [17, 24, 32])
check('oracle 4', solve(*([], [], 2)), [])
check('oracle 5', solve(*([1, -1], [0, 0], 0)), [1, -1])
check('oracle 6', solve(*([0, 0], [3, -1], 2)), [3, 3])
check('oracle 7', solve(*([3, -3], [2, 1], 1)), [6, -5])
if N == 1: check('variant packet 1', solve(*[[1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12])
if N == 2: check('variant packet 2', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12])
if N == 3: check('variant packet 3', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12])
if N == 4: check('variant packet 4', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12])
if N == 5: check('variant packet 5', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12])
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[7, 9, 14][7, -7, 14]Failed
oracle 2[7, 0][-1, 0]Failed
oracle 3[17, 24, 32][17, 24, 32]Passed
oracle 4[][]Passed
oracle 5[1, 1][1, -1]Failed
oracle 6[3, 3][3, 3]Passed
oracle 7[6, 7][6, -5]Failed
variant packet 1[7, 9, 14, 4, 8, 12][7, -7, 14, 4, -8, 12]Failed

SHA-256 / c384bcc5ecad2f1e1a32d989b4f29a8b2f770be349f571eba432e825bad356fd

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(coarse, residuals, missing_bits):
    scale=1<<missing_bits
    out=[]
    for index,base in enumerate(coarse):
        tail=residuals[index] if index<len(residuals) else 0
        tail &= scale-1
        out.append(base*scale-tail)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, -2, 3], [3, 1, 2], 2)), [7, -7, 14])
check('oracle 2', solve(*([-1, 0], [7, 4], 2)), [-1, 0])
check('oracle 3', solve(*([2, 3, 4], [1], 3)), [17, 24, 32])
check('oracle 4', solve(*([], [], 2)), [])
check('oracle 5', solve(*([1, -1], [0, 0], 0)), [1, -1])
check('oracle 6', solve(*([0, 0], [3, -1], 2)), [3, 3])
check('oracle 7', solve(*([3, -3], [2, 1], 1)), [6, -5])
if N == 1: check('variant packet 1', solve(*[[1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12])
if N == 2: check('variant packet 2', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12])
if N == 3: check('variant packet 3', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12])
if N == 4: check('variant packet 4', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12])
if N == 5: check('variant packet 5', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12])
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[1, -9, 10][7, -7, 14]Failed
oracle 2[-7, 0][-1, 0]Failed
oracle 3[15, 24, 32][17, 24, 32]Failed
oracle 4[][]Passed
oracle 5[1, -1][1, -1]Passed
oracle 6[-3, -3][3, 3]Failed
oracle 7[6, -7][6, -5]Failed
variant packet 1[1, -9, 10, 4, -8, 12][7, -7, 14, 4, -8, 12]Failed

SHA-256 / 301bc02d4e96e5b1b1a83dbbb87cabef32783dc41fb89ccf59ac789c5ba85991

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 2026-09-29T14:45:00.230349+00:00.

Case digest / 87affc0ebb66b5084e5f48a4dd5974259d82f7825a950235b9dfd95cac064bb9