FA-10931 / Audio channel mixing / Open access
Pan linear complement · case 01
The pan law doubles total amplitude by omitting normalization.
ROOT CAUSE
The pan law doubles total amplitude by omitting normalization.
VERIFIED REPAIR
Apply the explicit PCM/playback contract: Pan mono into stereo using a linear constant-sum law with pan in [-1,1], negative left and positive right; this is not an equal-power law.
Unsuccessful approach: Swapping the complement factors reverses pan direction.
Case contract
Pan mono into stereo using a linear constant-sum law with pan in [-1,1], negative left and positive right; this is not an equal-power law.
Why this case matters
A pure Python local audio pipeline stage with explicit sample formats and frame conventions; no real-time device or signal-spectrum claims.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(samples, pan):
return [[x*(1-pan),x*(1+pan)] for x in samples]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1',solve(*([1], 0)),[[0.5, 0.5]])
check('fixture 2',solve(*([1], -1)),[[1, 0]])
check('fixture 3',solve(*([1], 1)),[[0, 1]])
check('fixture 4',solve(*([], 0.5)),[])
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 |
|---|---|---|---|
| fixture 1 | [[1, 1]] | [[0.5, 0.5]] | Failed |
| fixture 2 | [[2, 0]] | [[1, 0]] | Failed |
| fixture 3 | [[0, 2]] | [[0, 1]] | Failed |
| fixture 4 | [] | [] | Passed |
SHA-256 / 6c237396f91a18525b7ee9b83b14e152f0803cf470d89327882d95b31cad7f6d
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(samples, pan):
return [[x*(1+pan)/2,x*(1-pan)/2] for x in samples]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1',solve(*([1], 0)),[[0.5, 0.5]])
check('fixture 2',solve(*([1], -1)),[[1, 0]])
check('fixture 3',solve(*([1], 1)),[[0, 1]])
check('fixture 4',solve(*([], 0.5)),[])
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 |
|---|---|---|---|
| fixture 1 | [[0.5, 0.5]] | [[0.5, 0.5]] | Passed |
| fixture 2 | [[0.0, 1.0]] | [[1, 0]] | Failed |
| fixture 3 | [[1.0, 0.0]] | [[0, 1]] | Failed |
| fixture 4 | [] | [] | Passed |
SHA-256 / 1b2f419c81564d89301696fecef65bf1cb355eddad3b56f1a05e9ffef8aab61c
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(samples, pan):
return [[x*(1-pan)/2,x*(1+pan)/2] for x in samples]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1',solve(*([1], 0)),[[0.5, 0.5]])
check('fixture 2',solve(*([1], -1)),[[1, 0]])
check('fixture 3',solve(*([1], 1)),[[0, 1]])
check('fixture 4',solve(*([], 0.5)),[])
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 |
|---|---|---|---|
| fixture 1 | [[0.5, 0.5]] | [[0.5, 0.5]] | Passed |
| fixture 2 | [[1.0, 0.0]] | [[1, 0]] | Passed |
| fixture 3 | [[0.0, 1.0]] | [[0, 1]] | Passed |
| fixture 4 | [] | [] | Passed |
SHA-256 / 2b94835c03489dc15352069c9b596c1a7fd20bcf54ab29df045a4f64d55c2575
Verification & scope
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 2026-09-29T14:38:43.512015+00:00.
Case digest / 7f77ef54cf39d2252f808429daf23c5b6479341dea030acbcd5d979c3a36bca8