FAILURE MAP
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FA-49026 / PCM sample encoding / Open access

Excess code recenter: negative headroom · case 01

Negative available amplitude is inferred from positive headroom.

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

ROOT CAUSE

Negative available amplitude is inferred from positive headroom.

VERIFIED REPAIR

Use the stated conversion contract at negative headroom.

Unsuccessful approach: Assuming a symmetric midpoint ignores zero calibration.

Case contract

Recenter bounded unsigned PCM around an explicitly calibrated zero code and report asymmetric representable headroom; clamp invalid code inputs before recentering.

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, width, zero_code):
    limit=(1<<width)-1
    out=[]
    for code in codes:
        bounded=max(0,min(limit,code))
        delta=bounded-zero_code
        low=zero_code-limit
        high=limit-zero_code
        out.append([delta,low,high])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 3, 7, 8], 3, 3)), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])
check('oracle 2', solve(*([-1, 0, 10], 3, 2)), [[-2, -2, 5], [-2, -2, 5], [5, -2, 5]])
check('oracle 3', solve(*([1, 2, 3], 2, 1)), [[0, -1, 2], [1, -1, 2], [2, -1, 2]])
check('oracle 4', solve(*([], 4, 5)), [])
check('oracle 5', solve(*([0, 15, 16], 4, 6)), [[-6, -6, 9], [9, -6, 9], [9, -6, 9]])
check('oracle 6', solve(*([0, 1], 1, 0)), [[0, 0, 1], [1, 0, 1]])
check('oracle 7', solve(*([2, 4, 7], 3, 5)), [[-3, -5, 2], [-1, -5, 2], [2, -5, 2]])
if N == 1: check('variant packet 1', solve(*[[0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])
if N == 2: check('variant packet 2', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])
if N == 3: check('variant packet 3', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])
if N == 4: check('variant packet 4', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])
if N == 5: check('variant packet 5', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 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 fixtureActualExpectedOutcome
oracle 1[[-3, -4, 4], [0, -4, 4], [4, -4, 4], [4, -4, 4]][[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]]Failed
oracle 2[[-2, -5, 5], [-2, -5, 5], [5, -5, 5]][[-2, -2, 5], [-2, -2, 5], [5, -2, 5]]Failed
oracle 3[[0, -2, 2], [1, -2, 2], [2, -2, 2]][[0, -1, 2], [1, -1, 2], [2, -1, 2]]Failed
oracle 4[][]Passed
oracle 5[[-6, -9, 9], [9, -9, 9], [9, -9, 9]][[-6, -6, 9], [9, -6, 9], [9, -6, 9]]Failed
oracle 6[[0, -1, 1], [1, -1, 1]][[0, 0, 1], [1, 0, 1]]Failed
oracle 7[[-3, -2, 2], [-1, -2, 2], [2, -2, 2]][[-3, -5, 2], [-1, -5, 2], [2, -5, 2]]Failed
variant packet 1[[-3, -4, 4], [0, -4, 4], [4, -4, 4], [4, -4, 4], [-3, -4, 4], [0, -4, 4], [4, -4, 4], [4, -4, 4]][[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]]Failed

SHA-256 / 086dfb83e61541056b6ae7ecfd2962ee68dd225f18214d78cae8e539afc0eef1

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(codes, width, zero_code):
    limit=(1<<width)-1
    out=[]
    for code in codes:
        bounded=max(0,min(limit,code))
        delta=bounded-zero_code
        low=-(1<<(width-1))
        high=limit-zero_code
        out.append([delta,low,high])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 3, 7, 8], 3, 3)), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])
check('oracle 2', solve(*([-1, 0, 10], 3, 2)), [[-2, -2, 5], [-2, -2, 5], [5, -2, 5]])
check('oracle 3', solve(*([1, 2, 3], 2, 1)), [[0, -1, 2], [1, -1, 2], [2, -1, 2]])
check('oracle 4', solve(*([], 4, 5)), [])
check('oracle 5', solve(*([0, 15, 16], 4, 6)), [[-6, -6, 9], [9, -6, 9], [9, -6, 9]])
check('oracle 6', solve(*([0, 1], 1, 0)), [[0, 0, 1], [1, 0, 1]])
check('oracle 7', solve(*([2, 4, 7], 3, 5)), [[-3, -5, 2], [-1, -5, 2], [2, -5, 2]])
if N == 1: check('variant packet 1', solve(*[[0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])
if N == 2: check('variant packet 2', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])
if N == 3: check('variant packet 3', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])
if N == 4: check('variant packet 4', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])
if N == 5: check('variant packet 5', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 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 fixtureActualExpectedOutcome
oracle 1[[-3, -4, 4], [0, -4, 4], [4, -4, 4], [4, -4, 4]][[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]]Failed
oracle 2[[-2, -4, 5], [-2, -4, 5], [5, -4, 5]][[-2, -2, 5], [-2, -2, 5], [5, -2, 5]]Failed
oracle 3[[0, -2, 2], [1, -2, 2], [2, -2, 2]][[0, -1, 2], [1, -1, 2], [2, -1, 2]]Failed
oracle 4[][]Passed
oracle 5[[-6, -8, 9], [9, -8, 9], [9, -8, 9]][[-6, -6, 9], [9, -6, 9], [9, -6, 9]]Failed
oracle 6[[0, -1, 1], [1, -1, 1]][[0, 0, 1], [1, 0, 1]]Failed
oracle 7[[-3, -4, 2], [-1, -4, 2], [2, -4, 2]][[-3, -5, 2], [-1, -5, 2], [2, -5, 2]]Failed
variant packet 1[[-3, -4, 4], [0, -4, 4], [4, -4, 4], [4, -4, 4], [-3, -4, 4], [0, -4, 4], [4, -4, 4], [4, -4, 4]][[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]]Failed

SHA-256 / ab0cad2fe89454a1dee83ddc3d80624d1241811fafd38b43f80f2702b905eb0b

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(codes, width, zero_code):
    limit=(1<<width)-1
    out=[]
    for code in codes:
        bounded=max(0,min(limit,code))
        delta=bounded-zero_code
        low=-zero_code
        high=limit-zero_code
        out.append([delta,low,high])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 3, 7, 8], 3, 3)), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])
check('oracle 2', solve(*([-1, 0, 10], 3, 2)), [[-2, -2, 5], [-2, -2, 5], [5, -2, 5]])
check('oracle 3', solve(*([1, 2, 3], 2, 1)), [[0, -1, 2], [1, -1, 2], [2, -1, 2]])
check('oracle 4', solve(*([], 4, 5)), [])
check('oracle 5', solve(*([0, 15, 16], 4, 6)), [[-6, -6, 9], [9, -6, 9], [9, -6, 9]])
check('oracle 6', solve(*([0, 1], 1, 0)), [[0, 0, 1], [1, 0, 1]])
check('oracle 7', solve(*([2, 4, 7], 3, 5)), [[-3, -5, 2], [-1, -5, 2], [2, -5, 2]])
if N == 1: check('variant packet 1', solve(*[[0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])
if N == 2: check('variant packet 2', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])
if N == 3: check('variant packet 3', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])
if N == 4: check('variant packet 4', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])
if N == 5: check('variant packet 5', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 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 fixtureActualExpectedOutcome
oracle 1[[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]][[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]]Passed
oracle 2[[-2, -2, 5], [-2, -2, 5], [5, -2, 5]][[-2, -2, 5], [-2, -2, 5], [5, -2, 5]]Passed
oracle 3[[0, -1, 2], [1, -1, 2], [2, -1, 2]][[0, -1, 2], [1, -1, 2], [2, -1, 2]]Passed
oracle 4[][]Passed
oracle 5[[-6, -6, 9], [9, -6, 9], [9, -6, 9]][[-6, -6, 9], [9, -6, 9], [9, -6, 9]]Passed
oracle 6[[0, 0, 1], [1, 0, 1]][[0, 0, 1], [1, 0, 1]]Passed
oracle 7[[-3, -5, 2], [-1, -5, 2], [2, -5, 2]][[-3, -5, 2], [-1, -5, 2], [2, -5, 2]]Passed
variant packet 1[[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]][[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]]Passed

SHA-256 / 4bee2d113c8af57521233324d4c110375fb668889d8937d131525b924361fd69

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 2026-09-29T14:44:56.043681+00:00.

Case digest / 85434f2445bb8c2403b6b84392f8a2e6d8ad8ddb46020b0b8e015a8820ecd348