FA-49951 / PCM sample encoding / Open access
Pcm companding segment code: segment shift · case 01
Segment number is assumed to equal its declared quantization shift.
ROOT CAUSE
Segment number is assumed to equal its declared quantization shift.
VERIFIED REPAIR
Use the stated conversion contract at segment shift.
Unsuccessful approach: Using the first shift ignores nonuniform companding precision.
Case contract
Encode bounded PCM magnitude into an explicitly stipulated piecewise companding table: sign sideband, selected lower-bound segment and shifted residual mantissa.
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(samples, edges, shifts):
out=[]
for sample in samples:
negative=sample<0
magnitude=abs(sample)
segment=0
while segment+1<len(edges) and magnitude>=edges[segment+1]:
segment+=1
residual=max(0,magnitude-edges[segment])
mantissa=residual>>segment
out.append([negative,segment,mantissa])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([-15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3])), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
check('oracle 2', solve(*([0, 2, 3, 8], [0, 3, 8], [0, 2, 2])), [[False, 0, 0], [False, 0, 2], [False, 1, 0], [False, 2, 0]])
check('oracle 3', solve(*([1, 2, 3], [0], [1])), [[False, 0, 0], [False, 0, 1], [False, 0, 1]])
check('oracle 4', solve(*([], [0, 8], [1, 3])), [])
check('oracle 5', solve(*([-8, 8, 9], [0, 8], [0, 3])), [[True, 1, 0], [False, 1, 0], [False, 1, 0]])
check('oracle 6', solve(*([0, 1, 16], [0, 1, 16], [0, 0, 2])), [[False, 0, 0], [False, 1, 0], [False, 2, 0]])
check('oracle 7', solve(*([7, -7], [0, 4], [1, 0])), [[False, 1, 3], [True, 1, 3]])
if N == 1: check('variant packet 1', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 2: check('variant packet 2', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 3: check('variant packet 3', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 4: check('variant packet 4', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 5: check('variant packet 5', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| oracle 1 | [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]] | [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]] | Passed |
| oracle 2 | [[False, 0, 0], [False, 0, 2], [False, 1, 0], [False, 2, 0]] | [[False, 0, 0], [False, 0, 2], [False, 1, 0], [False, 2, 0]] | Passed |
| oracle 3 | [[False, 0, 1], [False, 0, 2], [False, 0, 3]] | [[False, 0, 0], [False, 0, 1], [False, 0, 1]] | Failed |
| oracle 4 | [] | [] | Passed |
| oracle 5 | [[True, 1, 0], [False, 1, 0], [False, 1, 0]] | [[True, 1, 0], [False, 1, 0], [False, 1, 0]] | Passed |
| oracle 6 | [[False, 0, 0], [False, 1, 0], [False, 2, 0]] | [[False, 0, 0], [False, 1, 0], [False, 2, 0]] | Passed |
| oracle 7 | [[False, 1, 1], [True, 1, 1]] | [[False, 1, 3], [True, 1, 3]] | Failed |
| variant packet 1 | [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]] | [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]] | Passed |
SHA-256 / b2e388d41f327f16c26b3dadf0dc4c8d18afe7d38418ea3b81730fbd63f9f1fa
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(samples, edges, shifts):
out=[]
for sample in samples:
negative=sample<0
magnitude=abs(sample)
segment=0
while segment+1<len(edges) and magnitude>=edges[segment+1]:
segment+=1
residual=max(0,magnitude-edges[segment])
mantissa=residual>>shifts[0]
out.append([negative,segment,mantissa])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([-15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3])), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
check('oracle 2', solve(*([0, 2, 3, 8], [0, 3, 8], [0, 2, 2])), [[False, 0, 0], [False, 0, 2], [False, 1, 0], [False, 2, 0]])
check('oracle 3', solve(*([1, 2, 3], [0], [1])), [[False, 0, 0], [False, 0, 1], [False, 0, 1]])
check('oracle 4', solve(*([], [0, 8], [1, 3])), [])
check('oracle 5', solve(*([-8, 8, 9], [0, 8], [0, 3])), [[True, 1, 0], [False, 1, 0], [False, 1, 0]])
check('oracle 6', solve(*([0, 1, 16], [0, 1, 16], [0, 0, 2])), [[False, 0, 0], [False, 1, 0], [False, 2, 0]])
check('oracle 7', solve(*([7, -7], [0, 4], [1, 0])), [[False, 1, 3], [True, 1, 3]])
if N == 1: check('variant packet 1', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 2: check('variant packet 2', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 3: check('variant packet 3', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 4: check('variant packet 4', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 5: check('variant packet 5', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| oracle 1 | [[True, 2, 3], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 3]] | [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]] | Failed |
| oracle 2 | [[False, 0, 0], [False, 0, 2], [False, 1, 0], [False, 2, 0]] | [[False, 0, 0], [False, 0, 2], [False, 1, 0], [False, 2, 0]] | Passed |
| oracle 3 | [[False, 0, 0], [False, 0, 1], [False, 0, 1]] | [[False, 0, 0], [False, 0, 1], [False, 0, 1]] | Passed |
| oracle 4 | [] | [] | Passed |
| oracle 5 | [[True, 1, 0], [False, 1, 0], [False, 1, 1]] | [[True, 1, 0], [False, 1, 0], [False, 1, 0]] | Failed |
| oracle 6 | [[False, 0, 0], [False, 1, 0], [False, 2, 0]] | [[False, 0, 0], [False, 1, 0], [False, 2, 0]] | Passed |
| oracle 7 | [[False, 1, 1], [True, 1, 1]] | [[False, 1, 3], [True, 1, 3]] | Failed |
| variant packet 1 | [[True, 2, 3], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 3], [True, 2, 3], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 3]] | [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]] | Failed |
SHA-256 / 44049234f3060e51c599d1505d67afbf6c6084a31544f17fba9fc1d030659756
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(samples, edges, shifts):
out=[]
for sample in samples:
negative=sample<0
magnitude=abs(sample)
segment=0
while segment+1<len(edges) and magnitude>=edges[segment+1]:
segment+=1
residual=max(0,magnitude-edges[segment])
mantissa=residual>>shifts[segment]
out.append([negative,segment,mantissa])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([-15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3])), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
check('oracle 2', solve(*([0, 2, 3, 8], [0, 3, 8], [0, 2, 2])), [[False, 0, 0], [False, 0, 2], [False, 1, 0], [False, 2, 0]])
check('oracle 3', solve(*([1, 2, 3], [0], [1])), [[False, 0, 0], [False, 0, 1], [False, 0, 1]])
check('oracle 4', solve(*([], [0, 8], [1, 3])), [])
check('oracle 5', solve(*([-8, 8, 9], [0, 8], [0, 3])), [[True, 1, 0], [False, 1, 0], [False, 1, 0]])
check('oracle 6', solve(*([0, 1, 16], [0, 1, 16], [0, 0, 2])), [[False, 0, 0], [False, 1, 0], [False, 2, 0]])
check('oracle 7', solve(*([7, -7], [0, 4], [1, 0])), [[False, 1, 3], [True, 1, 3]])
if N == 1: check('variant packet 1', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 2: check('variant packet 2', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 3: check('variant packet 3', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 4: check('variant packet 4', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 5: check('variant packet 5', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| oracle 1 | [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]] | [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]] | Passed |
| oracle 2 | [[False, 0, 0], [False, 0, 2], [False, 1, 0], [False, 2, 0]] | [[False, 0, 0], [False, 0, 2], [False, 1, 0], [False, 2, 0]] | Passed |
| oracle 3 | [[False, 0, 0], [False, 0, 1], [False, 0, 1]] | [[False, 0, 0], [False, 0, 1], [False, 0, 1]] | Passed |
| oracle 4 | [] | [] | Passed |
| oracle 5 | [[True, 1, 0], [False, 1, 0], [False, 1, 0]] | [[True, 1, 0], [False, 1, 0], [False, 1, 0]] | Passed |
| oracle 6 | [[False, 0, 0], [False, 1, 0], [False, 2, 0]] | [[False, 0, 0], [False, 1, 0], [False, 2, 0]] | Passed |
| oracle 7 | [[False, 1, 3], [True, 1, 3]] | [[False, 1, 3], [True, 1, 3]] | Passed |
| variant packet 1 | [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]] | [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]] | Passed |
SHA-256 / b936e90cfccecaa5f1228a45a07d89abce9fee9d748bd2a380bf8851476f5bbf
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 2026-09-29T14:45:04.716289+00:00.
Case digest / 1b21ca75753c3d1fd99db67d17e88955050b98bdecda06976320c919077308f6