knapsack derived

{
  "input": {
    "body": {
      "items": [
        {
          "id": "camera",
          "value": 4,
          "weight": 3
        },
        {
          "id": "battery",
          "value": 5,
          "weight": 4
        },
        {
          "id": "tripod",
          "value": 6,
          "weight": 5
        }
      ],
      "capacity": 7
    },
    "type": "http",
    "method": "POST",
    "bodyType": "json"
  },
  "output": {
    "type": "json",
    "example": {
      "optimal": true,
      "evidence": {
        "dp_items": 3,
        "dp_capacity": 7,
        "verification": "recompute the bounded dynamic program; the digest detects transcript drift but is not an optimality proof",
        "optimality_proof": false,
        "transcript_sha256": "ec9c54475ee83fff14d13c4bc4728d2d22b27125fcf88ed76782a0425e758ecf",
        "transcript_encoding": "dpValue[0..capacity] as signed int64 two's-complement, 8-byte big-endian, no prefix"
      },
      "solution": {
        "selected": [
          {
            "id": "camera",
            "value": 4,
            "weight": 3,
            "original_index": 0
          },
          {
            "id": "battery",
            "value": 5,
            "weight": 4,
            "original_index": 1
          }
        ],
        "used_capacity": 7,
        "remaining_capacity": 0
      },
      "warnings": [],
      "objective": "maximum_total_value",
      "operation": "knapsack",
      "work_units": 24,
      "objective_value": 9,
      "algorithm_version": "knapsack-01-dp-v1"
    }
  }
}