FA-49291 / PCM sample encoding / Open access
Pcm mid side unlifting: parity validation · case 01
PCM side parity is checked against midpoint bits.
ROOT CAUSE
PCM side parity is checked against midpoint bits.
VERIFIED REPAIR
Use the stated conversion contract at parity validation.
Unsuccessful approach: Skipping sideband validation accepts corrupted channel residuals.
Case contract
Invert the stipulated reversible PCM midpoint/side code, rejecting parity-mismatched triples and preserving L,R destination order.
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(triples):
out=[]
for mid,side,parity in triples:
if parity!=(mid&1):
out.append(None)
continue
right=mid-side//2
left=side+right
out.append([left,right])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[3, 3, 1], [3, -3, 1]],)), [[5, 2], [2, 5]])
check('oracle 2', solve(*([[0, 0, 0], [1, 0, 0]],)), [[0, 0], [1, 1]])
check('oracle 3', solve(*([[0, -5, 1]],)), [[-2, 3]])
check('oracle 4', solve(*([],)), [])
check('oracle 5', solve(*([[3, 2, 1], [3, 2, 0]],)), [None, [4, 2]])
check('oracle 6', solve(*([[-2, -1, 1], [4, 1, 1]],)), [[-2, -1], [5, 4]])
check('oracle 7', solve(*([[3, 0, 1]],)), [None])
if N == 1: check('variant packet 1', solve(*[[[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]]]), [[5, 2], [2, 5], [5, 2], [2, 5]])
if N == 2: check('variant packet 2', solve(*[[[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]]]), [[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]])
if N == 3: check('variant packet 3', solve(*[[[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]]]), [[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]])
if N == 4: check('variant packet 4', solve(*[[[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]]]), [[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]])
if N == 5: check('variant packet 5', solve(*[[[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]]]), [[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]])
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 | [[5, 2], [2, 5]] | [[5, 2], [2, 5]] | Passed |
| oracle 2 | [[0, 0], None] | [[0, 0], [1, 1]] | Failed |
| oracle 3 | [None] | [[-2, 3]] | Failed |
| oracle 4 | [] | [] | Passed |
| oracle 5 | [[4, 2], None] | [None, [4, 2]] | Failed |
| oracle 6 | [None, None] | [[-2, -1], [5, 4]] | Failed |
| oracle 7 | [[3, 3]] | [None] | Failed |
| variant packet 1 | [[5, 2], [2, 5], [5, 2], [2, 5]] | [[5, 2], [2, 5], [5, 2], [2, 5]] | Passed |
SHA-256 / 4f1f48ea58fc4bf54604eb54725a2c311a70a4d2003a006faeb443870560931e
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(triples):
out=[]
for mid,side,parity in triples:
if False:
out.append(None)
continue
right=mid-side//2
left=side+right
out.append([left,right])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[3, 3, 1], [3, -3, 1]],)), [[5, 2], [2, 5]])
check('oracle 2', solve(*([[0, 0, 0], [1, 0, 0]],)), [[0, 0], [1, 1]])
check('oracle 3', solve(*([[0, -5, 1]],)), [[-2, 3]])
check('oracle 4', solve(*([],)), [])
check('oracle 5', solve(*([[3, 2, 1], [3, 2, 0]],)), [None, [4, 2]])
check('oracle 6', solve(*([[-2, -1, 1], [4, 1, 1]],)), [[-2, -1], [5, 4]])
check('oracle 7', solve(*([[3, 0, 1]],)), [None])
if N == 1: check('variant packet 1', solve(*[[[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]]]), [[5, 2], [2, 5], [5, 2], [2, 5]])
if N == 2: check('variant packet 2', solve(*[[[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]]]), [[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]])
if N == 3: check('variant packet 3', solve(*[[[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]]]), [[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]])
if N == 4: check('variant packet 4', solve(*[[[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]]]), [[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]])
if N == 5: check('variant packet 5', solve(*[[[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]]]), [[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]])
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 | [[5, 2], [2, 5]] | [[5, 2], [2, 5]] | Passed |
| oracle 2 | [[0, 0], [1, 1]] | [[0, 0], [1, 1]] | Passed |
| oracle 3 | [[-2, 3]] | [[-2, 3]] | Passed |
| oracle 4 | [] | [] | Passed |
| oracle 5 | [[4, 2], [4, 2]] | [None, [4, 2]] | Failed |
| oracle 6 | [[-2, -1], [5, 4]] | [[-2, -1], [5, 4]] | Passed |
| oracle 7 | [[3, 3]] | [None] | Failed |
| variant packet 1 | [[5, 2], [2, 5], [5, 2], [2, 5]] | [[5, 2], [2, 5], [5, 2], [2, 5]] | Passed |
SHA-256 / 2f12e573d70072bf1dbdfbd4a0c0765688a25677ad70e1500e8672f88ac646fd
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(triples):
out=[]
for mid,side,parity in triples:
if parity!=(side&1):
out.append(None)
continue
right=mid-side//2
left=side+right
out.append([left,right])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([[3, 3, 1], [3, -3, 1]],)), [[5, 2], [2, 5]])
check('oracle 2', solve(*([[0, 0, 0], [1, 0, 0]],)), [[0, 0], [1, 1]])
check('oracle 3', solve(*([[0, -5, 1]],)), [[-2, 3]])
check('oracle 4', solve(*([],)), [])
check('oracle 5', solve(*([[3, 2, 1], [3, 2, 0]],)), [None, [4, 2]])
check('oracle 6', solve(*([[-2, -1, 1], [4, 1, 1]],)), [[-2, -1], [5, 4]])
check('oracle 7', solve(*([[3, 0, 1]],)), [None])
if N == 1: check('variant packet 1', solve(*[[[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]]]), [[5, 2], [2, 5], [5, 2], [2, 5]])
if N == 2: check('variant packet 2', solve(*[[[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]]]), [[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]])
if N == 3: check('variant packet 3', solve(*[[[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]]]), [[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]])
if N == 4: check('variant packet 4', solve(*[[[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]]]), [[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]])
if N == 5: check('variant packet 5', solve(*[[[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]]]), [[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]])
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 | [[5, 2], [2, 5]] | [[5, 2], [2, 5]] | Passed |
| oracle 2 | [[0, 0], [1, 1]] | [[0, 0], [1, 1]] | Passed |
| oracle 3 | [[-2, 3]] | [[-2, 3]] | Passed |
| oracle 4 | [] | [] | Passed |
| oracle 5 | [None, [4, 2]] | [None, [4, 2]] | Passed |
| oracle 6 | [[-2, -1], [5, 4]] | [[-2, -1], [5, 4]] | Passed |
| oracle 7 | [None] | [None] | Passed |
| variant packet 1 | [[5, 2], [2, 5], [5, 2], [2, 5]] | [[5, 2], [2, 5], [5, 2], [2, 5]] | Passed |
SHA-256 / dcd1da4deb9bf58e5fb35568551230cfeecabdfc0b0d635dbf866d27d82da225
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 2026-09-29T14:44:58.587104+00:00.
Case digest / c7837a77b93ac986bcc57b13a3d8dbcf3baa2125c3832d9db5b48d780b79a357