Fault diagnosis

TASK: Fault diagnosis.

Each case is a separate 12 V circuit. BAT is the battery positive (12 V); CH is chassis ground (0 V).
Segments are wires (F1 is the fuse, treated as a segment). Loads are resistive devices between two nodes.
Wires have negligible resistance; every switch is closed. In each case EXACTLY ONE element is open circuit:
one segment (including the fuse) or one load. Symptoms say which loads operate. Readings are DC voltage at a node, measured to chassis.
Identify the open element in each case.

CASE1:
segments: [
  {"id":"F1","a":"BAT","b":"P0"},
  {"id":"S1","a":"P0","b":"P1"},
  {"id":"S2","a":"P1","b":"P2"},
  {"id":"S3","a":"P0","b":"P3"},
  {"id":"S4","a":"G1","b":"GS1"},
  {"id":"S5","a":"G2","b":"GS1"},
  {"id":"S6","a":"G3","b":"GS1"},
  {"id":"S7","a":"GS1","b":"CH"}
]
loads: [
  {"id":"L1","a":"P2","b":"G1"},
  {"id":"L2","a":"P1","b":"G2"},
  {"id":"L3","a":"P3","b":"G3"}
]
symptoms: [{"load":"L1","state":"OFF"},{"load":"L2","state":"ON"},{"load":"L3","state":"ON"}]
readings: [{"node":"P2","reading":"12V"},{"node":"P3","reading":"12V"},{"node":"GS1","reading":"0V"},{"node":"G1","reading":"0V"}]

CASE2:
segments: [
  {"id":"F1","a":"BAT","b":"P0"},
  {"id":"S1","a":"P0","b":"P1"},
  {"id":"S2","a":"P1","b":"P2"},
  {"id":"S3","a":"P2","b":"P3"},
  {"id":"S4","a":"P2","b":"P4"},
  {"id":"S5","a":"P4","b":"P5"},
  {"id":"S6","a":"G1","b":"GS1"},
  {"id":"S7","a":"G2","b":"GS1"},
  {"id":"S8","a":"G3","b":"GS1"},
  {"id":"S9","a":"G4","b":"GS1"},
  {"id":"S10","a":"GS1","b":"CH"}
]
loads: [
  {"id":"L1","a":"P4","b":"G1"},
  {"id":"L2","a":"P5","b":"G2"},
  {"id":"L3","a":"P2","b":"G3"},
  {"id":"L4","a":"P3","b":"G4"}
]
symptoms: [{"load":"L1","state":"ON"},{"load":"L2","state":"OFF"},{"load":"L3","state":"ON"},{"load":"L4","state":"ON"}]
readings: [{"node":"P5","reading":"12V"},{"node":"G3","reading":"0V"},{"node":"G2","reading":"0V"}]

CASE3:
segments: [
  {"id":"F1","a":"BAT","b":"P0"},
  {"id":"S1","a":"P0","b":"P1"},
  {"id":"S2","a":"P0","b":"P2"},
  {"id":"S3","a":"P1","b":"P3"},
  {"id":"S4","a":"P1","b":"P4"},
  {"id":"S5","a":"G1","b":"GS1"},
  {"id":"S6","a":"G2","b":"GS1"},
  {"id":"S7","a":"G3","b":"GS1"},
  {"id":"S8","a":"G4","b":"GS1"},
  {"id":"S9","a":"GS1","b":"CH"}
]
loads: [
  {"id":"L1","a":"P2","b":"G1"},
  {"id":"L2","a":"P4","b":"G2"},
  {"id":"L3","a":"P1","b":"G3"},
  {"id":"L4","a":"P3","b":"G4"}
]
symptoms: [{"load":"L1","state":"ON"},{"load":"L2","state":"ON"},{"load":"L3","state":"OFF"},{"load":"L4","state":"ON"}]
readings: [{"node":"P3","reading":"12V"},{"node":"G2","reading":"0V"},{"node":"G3","reading":"0V"}]

Output format (JSON, exactly these keys):
```json
{
 "cases": [
  {
   "case": "CASE1",
   "fault": "S4"
  }
 ]
}
```