{
  "x402Version": 2,
  "id": 28627,
  "slug": "28627",
  "resource": "https://decision-solver.use.x402atlas.com/knapsack",
  "description": "0/1 knapsack solver — exact work-bounded capacity planning and portfolio selection for maximum value, with deterministic ties and reproducible DP evidence.",
  "type": "http",
  "serviceName": "Bounded Decision Solver",
  "resourceType": "Blockchain Data",
  "accepts": [
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      "scheme": "exact",
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      "scheme": "exact",
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      "amount": "5000",
      "amountUsd": 0.005,
      "maxTimeoutSeconds": 300
    }
  ],
  "outputSchema": {
    "properties": {
      "example": {
        "additionalProperties": false,
        "properties": {
          "_atlas": {
            "additionalProperties": false,
            "description": "Atlas documentation and related-route metadata added after deployment",
            "properties": {
              "docs": {
                "description": "Documentation URL for this bridge",
                "format": "uri",
                "maxLength": 512,
                "type": "string"
              },
              "related": {
                "description": "Bounded related Atlas routes",
                "items": {
                  "additionalProperties": false,
                  "description": "One related Atlas route",
                  "properties": {
                    "bridge": {
                      "description": "Related bridge name",
                      "maxLength": 64,
                      "type": "string"
                    },
                    "docs": {
                      "description": "Related bridge documentation URL",
                      "format": "uri",
                      "maxLength": 512,
                      "type": "string"
                    },
                    "summary": {
                      "description": "Short capability summary",
                      "maxLength": 256,
                      "type": "string"
                    },
                    "url": {
                      "description": "Related route URL",
                      "format": "uri",
                      "maxLength": 512,
                      "type": "string"
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                    "bridge",
                    "url",
                    "docs",
                    "summary"
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                  "type": "object"
                },
                "maxItems": 3,
                "type": "array"
              }
            },
            "required": [
              "docs"
            ],
            "type": "object"
          },
          "algorithm_version": {
            "const": "knapsack-01-dp-v1",
            "description": "Pinned deterministic algorithm and transcript contract",
            "type": "string"
          },
          "evidence": {
            "additionalProperties": false,
            "description": "Reproducible transcript evidence that detects final-DP drift but does not prove optimality",
            "properties": {
              "dp_capacity": {
                "description": "Maximum capacity index in the final DP transcript",
                "maximum": 100000,
                "minimum": 0,
                "type": "integer"
              },
              "dp_items": {
                "description": "Number of item rows incorporated into the final dynamic program",
                "maximum": 512,
                "minimum": 0,
                "type": "integer"
              },
              "optimality_proof": {
                "const": false,
                "description": "Always false: the digest alone is not an optimality proof",
                "type": "boolean"
              },
              "transcript_encoding": {
                "const": "dpValue[0..capacity] as signed int64 two's-complement, 8-byte big-endian, no prefix",
                "description": "Exact byte encoding hashed; dimensions are carried separately and are not part of the digest",
                "type": "string"
              },
              "transcript_sha256": {
                "description": "Lowercase SHA-256 digest of the encoded final DP values; this is non-proof evidence",
                "maxLength": 64,
                "minLength": 64,
                "pattern": "^[0-9a-f]{64}$",
                "type": "string"
              },
              "verification": {
                "const": "recompute the bounded dynamic program; the digest detects transcript drift but is not an optimality proof",
                "description": "Independent verification instruction; recomputation is required to verify optimality",
                "type": "string"
              }
            },
            "required": [
              "dp_items",
              "dp_capacity",
              "transcript_encoding",
              "transcript_sha256",
              "optimality_proof",
              "verification"
            ],
            "type": "object"
          },
          "objective": {
            "const": "maximum_total_value",
            "description": "The solver maximizes total selected value within capacity",
            "type": "string"
          },
          "objective_value": {
            "description": "Proven maximum total value",
            "maximum": 512000000000,
            "minimum": 0,
            "type": "integer"
          },
          "operation": {
            "const": "knapsack",
            "description": "Stable route operation name",
            "type": "string"
          },
          "optimal": {
            "const": true,
            "description": "True because the bounded dynamic program computes the exact optimum",
            "type": "boolean"
          },
          "solution": {
            "additionalProperties": false,
            "description": "Selected item set and capacity accounting",
            "properties": {
              "remaining_capacity": {
                "description": "Capacity minus selected weight",
                "maximum": 100000,
                "minimum": 0,
                "type": "integer"
              },
              "selected": {
                "description": "Selected items in input order; [] is valid when no positive-value item fits",
                "items": {
                  "additionalProperties": false,
                  "description": "One selected item",
                  "properties": {
                    "id": {
                      "description": "Input item identifier",
                      "maxLength": 64,
                      "minLength": 1,
                      "pattern": "^[ -~]+$",
                      "type": "string"
                    },
                    "original_index": {
                      "description": "Zero-based input index",
                      "maximum": 511,
                      "minimum": 0,
                      "type": "integer"
                    },
                    "value": {
                      "description": "Input item value",
                      "maximum": 1000000000,
                      "minimum": 0,
                      "type": "integer"
                    },
                    "weight": {
                      "description": "Input item weight",
                      "maximum": 1000000000,
                      "minimum": 0,
                      "type": "integer"
                    }
                  },
                  "required": [
                    "id",
                    "original_index",
                    "weight",
                    "value"
                  ],
                  "type": "object"
                },
                "maxItems": 512,
                "type": "array"
              },
              "used_capacity": {
                "description": "Total selected weight",
                "maximum": 100000,
                "minimum": 0,
                "type": "integer"
              }
            },
            "required": [
              "selected",
              "used_capacity",
              "remaining_capacity"
            ],
            "type": "object"
          },
          "warnings": {
            "description": "Always empty for this exact solver; non-proof semantics are carried in evidence",
            "items": {
              "description": "Human-readable warning",
              "type": "string"
            },
            "maxItems": 0,
            "type": "array"
          },
          "work_units": {
            "description": "Item count times (capacity+1), the declared dynamic-program work units",
            "maximum": 2000000,
            "minimum": 0,
            "type": "integer"
          }
        },
        "required": [
          "operation",
          "algorithm_version",
          "objective",
          "objective_value",
          "optimal",
          "solution",
          "work_units",
          "evidence",
          "warnings"
        ],
        "type": "object"
      },
      "type": {
        "type": "string"
      }
    },
    "required": [
      "type"
    ],
    "type": "object"
  },
  "extensions": {
    "bazaar": {
      "category": "utilities",
      "info": {
        "input": {
          "body": {
            "capacity": 7,
            "items": [
              {
                "id": "camera",
                "value": 4,
                "weight": 3
              },
              {
                "id": "battery",
                "value": 5,
                "weight": 4
              },
              {
                "id": "tripod",
                "value": 6,
                "weight": 5
              }
            ]
          },
          "bodyType": "json",
          "method": "POST",
          "type": "http"
        },
        "output": {
          "example": {
            "algorithm_version": "knapsack-01-dp-v1",
            "evidence": {
              "dp_capacity": 7,
              "dp_items": 3,
              "optimality_proof": false,
              "transcript_encoding": "dpValue[0..capacity] as signed int64 two's-complement, 8-byte big-endian, no prefix",
              "transcript_sha256": "ec9c54475ee83fff14d13c4bc4728d2d22b27125fcf88ed76782a0425e758ecf",
              "verification": "recompute the bounded dynamic program; the digest detects transcript drift but is not an optimality proof"
            },
            "objective": "maximum_total_value",
            "objective_value": 9,
            "operation": "knapsack",
            "optimal": true,
            "solution": {
              "remaining_capacity": 0,
              "selected": [
                {
                  "id": "camera",
                  "original_index": 0,
                  "value": 4,
                  "weight": 3
                },
                {
                  "id": "battery",
                  "original_index": 1,
                  "value": 5,
                  "weight": 4
                }
              ],
              "used_capacity": 7
            },
            "warnings": [],
            "work_units": 24
          },
          "type": "json"
        }
      },
      "schema": {
        "$schema": "https://json-schema.org/draft/2020-12/schema",
        "properties": {
          "input": {
            "additionalProperties": false,
            "properties": {
              "body": {
                "additionalProperties": false,
                "properties": {
                  "capacity": {
                    "description": "Maximum total selected weight; item count times (capacity+1) must not exceed 2,000,000 work units",
                    "maximum": 100000,
                    "minimum": 1,
                    "type": "integer"
                  },
                  "items": {
                    "description": "Unique-ID 0/1 items; each item is considered at most once",
                    "items": {
                      "additionalProperties": false,
                      "description": "One 0/1 item selectable at most once",
                      "properties": {
                        "id": {
                          "description": "Unique printable-ASCII item identifier",
                          "maxLength": 64,
                          "minLength": 1,
                          "pattern": "^[ -~]+$",
                          "type": "string"
                        },
                        "value": {
                          "description": "Non-negative objective value",
                          "maximum": 1000000000,
                          "minimum": 0,
                          "type": "integer"
                        },
                        "weight": {
                          "description": "Positive item weight; items heavier than capacity remain valid but cannot be selected",
                          "maximum": 1000000000,
                          "minimum": 1,
                          "type": "integer"
                        }
                      },
                      "required": [
                        "id",
                        "weight",
                        "value"
                      ],
                      "type": "object"
                    },
                    "maxItems": 512,
                    "minItems": 1,
                    "type": "array"
                  }
                },
                "required": [
                  "capacity",
                  "items"
                ],
                "type": "object"
              },
              "bodyType": {
                "enum": [
                  "json",
                  "form-data",
                  "text"
                ],
                "type": "string"
              },
              "method": {
                "enum": [
                  "POST"
                ],
                "type": "string"
              },
              "type": {
                "const": "http",
                "type": "string"
              }
            },
            "required": [
              "type",
              "method",
              "bodyType",
              "body"
            ],
            "type": "object"
          },
          "output": {
            "properties": {
              "example": {
                "additionalProperties": false,
                "properties": {
                  "_atlas": {
                    "additionalProperties": false,
                    "description": "Atlas documentation and related-route metadata added after deployment",
                    "properties": {
                      "docs": {
                        "description": "Documentation URL for this bridge",
                        "format": "uri",
                        "maxLength": 512,
                        "type": "string"
                      },
                      "related": {
                        "description": "Bounded related Atlas routes",
                        "items": {
                          "additionalProperties": false,
                          "description": "One related Atlas route",
                          "properties": {
                            "bridge": {
                              "description": "Related bridge name",
                              "maxLength": 64,
                              "type": "string"
                            },
                            "docs": {
                              "description": "Related bridge documentation URL",
                              "format": "uri",
                              "maxLength": 512,
                              "type": "string"
                            },
                            "summary": {
                              "description": "Short capability summary",
                              "maxLength": 256,
                              "type": "string"
                            },
                            "url": {
                              "description": "Related route URL",
                              "format": "uri",
                              "maxLength": 512,
                              "type": "string"
                            }
                          },
                          "required": [
                            "bridge",
                            "url",
                            "docs",
                            "summary"
                          ],
                          "type": "object"
                        },
                        "maxItems": 3,
                        "type": "array"
                      }
                    },
                    "required": [
                      "docs"
                    ],
                    "type": "object"
                  },
                  "algorithm_version": {
                    "const": "knapsack-01-dp-v1",
                    "description": "Pinned deterministic algorithm and transcript contract",
                    "type": "string"
                  },
                  "evidence": {
                    "additionalProperties": false,
                    "description": "Reproducible transcript evidence that detects final-DP drift but does not prove optimality",
                    "properties": {
                      "dp_capacity": {
                        "description": "Maximum capacity index in the final DP transcript",
                        "maximum": 100000,
                        "minimum": 0,
                        "type": "integer"
                      },
                      "dp_items": {
                        "description": "Number of item rows incorporated into the final dynamic program",
                        "maximum": 512,
                        "minimum": 0,
                        "type": "integer"
                      },
                      "optimality_proof": {
                        "const": false,
                        "description": "Always false: the digest alone is not an optimality proof",
                        "type": "boolean"
                      },
                      "transcript_encoding": {
                        "const": "dpValue[0..capacity] as signed int64 two's-complement, 8-byte big-endian, no prefix",
                        "description": "Exact byte encoding hashed; dimensions are carried separately and are not part of the digest",
                        "type": "string"
                      },
                      "transcript_sha256": {
                        "description": "Lowercase SHA-256 digest of the encoded final DP values; this is non-proof evidence",
                        "maxLength": 64,
                        "minLength": 64,
                        "pattern": "^[0-9a-f]{64}$",
                        "type": "string"
                      },
                      "verification": {
                        "const": "recompute the bounded dynamic program; the digest detects transcript drift but is not an optimality proof",
                        "description": "Independent verification instruction; recomputation is required to verify optimality",
                        "type": "string"
                      }
                    },
                    "required": [
                      "dp_items",
                      "dp_capacity",
                      "transcript_encoding",
                      "transcript_sha256",
                      "optimality_proof",
                      "verification"
                    ],
                    "type": "object"
                  },
                  "objective": {
                    "const": "maximum_total_value",
                    "description": "The solver maximizes total selected value within capacity",
                    "type": "string"
                  },
                  "objective_value": {
                    "description": "Proven maximum total value",
                    "maximum": 512000000000,
                    "minimum": 0,
                    "type": "integer"
                  },
                  "operation": {
                    "const": "knapsack",
                    "description": "Stable route operation name",
                    "type": "string"
                  },
                  "optimal": {
                    "const": true,
                    "description": "True because the bounded dynamic program computes the exact optimum",
                    "type": "boolean"
                  },
                  "solution": {
                    "additionalProperties": false,
                    "description": "Selected item set and capacity accounting",
                    "properties": {
                      "remaining_capacity": {
                        "description": "Capacity minus selected weight",
                        "maximum": 100000,
                        "minimum": 0,
                        "type": "integer"
                      },
                      "selected": {
                        "description": "Selected items in input order; [] is valid when no positive-value item fits",
                        "items": {
                          "additionalProperties": false,
                          "description": "One selected item",
                          "properties": {
                            "id": {
                              "description": "Input item identifier",
                              "maxLength": 64,
                              "minLength": 1,
                              "pattern": "^[ -~]+$",
                              "type": "string"
                            },
                            "original_index": {
                              "description": "Zero-based input index",
                              "maximum": 511,
                              "minimum": 0,
                              "type": "integer"
                            },
                            "value": {
                              "description": "Input item value",
                              "maximum": 1000000000,
                              "minimum": 0,
                              "type": "integer"
                            },
                            "weight": {
                              "description": "Input item weight",
                              "maximum": 1000000000,
                              "minimum": 0,
                              "type": "integer"
                            }
                          },
                          "required": [
                            "id",
                            "original_index",
                            "weight",
                            "value"
                          ],
                          "type": "object"
                        },
                        "maxItems": 512,
                        "type": "array"
                      },
                      "used_capacity": {
                        "description": "Total selected weight",
                        "maximum": 100000,
                        "minimum": 0,
                        "type": "integer"
                      }
                    },
                    "required": [
                      "selected",
                      "used_capacity",
                      "remaining_capacity"
                    ],
                    "type": "object"
                  },
                  "warnings": {
                    "description": "Always empty for this exact solver; non-proof semantics are carried in evidence",
                    "items": {
                      "description": "Human-readable warning",
                      "type": "string"
                    },
                    "maxItems": 0,
                    "type": "array"
                  },
                  "work_units": {
                    "description": "Item count times (capacity+1), the declared dynamic-program work units",
                    "maximum": 2000000,
                    "minimum": 0,
                    "type": "integer"
                  }
                },
                "required": [
                  "operation",
                  "algorithm_version",
                  "objective",
                  "objective_value",
                  "optimal",
                  "solution",
                  "work_units",
                  "evidence",
                  "warnings"
                ],
                "type": "object"
              },
              "type": {
                "type": "string"
              }
            },
            "required": [
              "type"
            ],
            "type": "object"
          }
        },
        "required": [
          "input"
        ],
        "type": "object"
      },
      "tags": [
        "0-1-knapsack-solver",
        "optimization",
        "operations-research",
        "bounded-computation",
        "deterministic"
      ]
    }
  },
  "tags": [
    "0-1-knapsack-solver",
    "optimization",
    "operations-research",
    "bounded-computation",
    "deterministic",
    "bazaar"
  ],
  "sourceHost": "decision-solver.use.x402atlas.com",
  "lastUpdated": "2026-10-08T05:33:14.68Z",
  "quality": {
    "calls30d": 5,
    "uniquePayers30d": 4,
    "lastCalledAt": "2026-10-08T05:33:14.556Z"
  },
  "metadata": {
    "serviceName": "Bounded Decision Solver",
    "extensions": {
      "bazaar": {
        "category": "utilities",
        "info": {
          "input": {
            "body": {
              "capacity": 7,
              "items": [
                {
                  "id": "camera",
                  "value": 4,
                  "weight": 3
                },
                {
                  "id": "battery",
                  "value": 5,
                  "weight": 4
                },
                {
                  "id": "tripod",
                  "value": 6,
                  "weight": 5
                }
              ]
            },
            "bodyType": "json",
            "method": "POST",
            "type": "http"
          },
          "output": {
            "example": {
              "algorithm_version": "knapsack-01-dp-v1",
              "evidence": {
                "dp_capacity": 7,
                "dp_items": 3,
                "optimality_proof": false,
                "transcript_encoding": "dpValue[0..capacity] as signed int64 two's-complement, 8-byte big-endian, no prefix",
                "transcript_sha256": "ec9c54475ee83fff14d13c4bc4728d2d22b27125fcf88ed76782a0425e758ecf",
                "verification": "recompute the bounded dynamic program; the digest detects transcript drift but is not an optimality proof"
              },
              "objective": "maximum_total_value",
              "objective_value": 9,
              "operation": "knapsack",
              "optimal": true,
              "solution": {
                "remaining_capacity": 0,
                "selected": [
                  {
                    "id": "camera",
                    "original_index": 0,
                    "value": 4,
                    "weight": 3
                  },
                  {
                    "id": "battery",
                    "original_index": 1,
                    "value": 5,
                    "weight": 4
                  }
                ],
                "used_capacity": 7
              },
              "warnings": [],
              "work_units": 24
            },
            "type": "json"
          }
        },
        "schema": {
          "$schema": "https://json-schema.org/draft/2020-12/schema",
          "properties": {
            "input": {
              "additionalProperties": false,
              "properties": {
                "body": {
                  "additionalProperties": false,
                  "properties": {
                    "capacity": {
                      "description": "Maximum total selected weight; item count times (capacity+1) must not exceed 2,000,000 work units",
                      "maximum": 100000,
                      "minimum": 1,
                      "type": "integer"
                    },
                    "items": {
                      "description": "Unique-ID 0/1 items; each item is considered at most once",
                      "items": {
                        "additionalProperties": false,
                        "description": "One 0/1 item selectable at most once",
                        "properties": {
                          "id": {
                            "description": "Unique printable-ASCII item identifier",
                            "maxLength": 64,
                            "minLength": 1,
                            "pattern": "^[ -~]+$",
                            "type": "string"
                          },
                          "value": {
                            "description": "Non-negative objective value",
                            "maximum": 1000000000,
                            "minimum": 0,
                            "type": "integer"
                          },
                          "weight": {
                            "description": "Positive item weight; items heavier than capacity remain valid but cannot be selected",
                            "maximum": 1000000000,
                            "minimum": 1,
                            "type": "integer"
                          }
                        },
                        "required": [
                          "id",
                          "weight",
                          "value"
                        ],
                        "type": "object"
                      },
                      "maxItems": 512,
                      "minItems": 1,
                      "type": "array"
                    }
                  },
                  "required": [
                    "capacity",
                    "items"
                  ],
                  "type": "object"
                },
                "bodyType": {
                  "enum": [
                    "json",
                    "form-data",
                    "text"
                  ],
                  "type": "string"
                },
                "method": {
                  "enum": [
                    "POST"
                  ],
                  "type": "string"
                },
                "type": {
                  "const": "http",
                  "type": "string"
                }
              },
              "required": [
                "type",
                "method",
                "bodyType",
                "body"
              ],
              "type": "object"
            },
            "output": {
              "properties": {
                "example": {
                  "additionalProperties": false,
                  "properties": {
                    "_atlas": {
                      "additionalProperties": false,
                      "description": "Atlas documentation and related-route metadata added after deployment",
                      "properties": {
                        "docs": {
                          "description": "Documentation URL for this bridge",
                          "format": "uri",
                          "maxLength": 512,
                          "type": "string"
                        },
                        "related": {
                          "description": "Bounded related Atlas routes",
                          "items": {
                            "additionalProperties": false,
                            "description": "One related Atlas route",
                            "properties": {
                              "bridge": {
                                "description": "Related bridge name",
                                "maxLength": 64,
                                "type": "string"
                              },
                              "docs": {
                                "description": "Related bridge documentation URL",
                                "format": "uri",
                                "maxLength": 512,
                                "type": "string"
                              },
                              "summary": {
                                "description": "Short capability summary",
                                "maxLength": 256,
                                "type": "string"
                              },
                              "url": {
                                "description": "Related route URL",
                                "format": "uri",
                                "maxLength": 512,
                                "type": "string"
                              }
                            },
                            "required": [
                              "bridge",
                              "url",
                              "docs",
                              "summary"
                            ],
                            "type": "object"
                          },
                          "maxItems": 3,
                          "type": "array"
                        }
                      },
                      "required": [
                        "docs"
                      ],
                      "type": "object"
                    },
                    "algorithm_version": {
                      "const": "knapsack-01-dp-v1",
                      "description": "Pinned deterministic algorithm and transcript contract",
                      "type": "string"
                    },
                    "evidence": {
                      "additionalProperties": false,
                      "description": "Reproducible transcript evidence that detects final-DP drift but does not prove optimality",
                      "properties": {
                        "dp_capacity": {
                          "description": "Maximum capacity index in the final DP transcript",
                          "maximum": 100000,
                          "minimum": 0,
                          "type": "integer"
                        },
                        "dp_items": {
                          "description": "Number of item rows incorporated into the final dynamic program",
                          "maximum": 512,
                          "minimum": 0,
                          "type": "integer"
                        },
                        "optimality_proof": {
                          "const": false,
                          "description": "Always false: the digest alone is not an optimality proof",
                          "type": "boolean"
                        },
                        "transcript_encoding": {
                          "const": "dpValue[0..capacity] as signed int64 two's-complement, 8-byte big-endian, no prefix",
                          "description": "Exact byte encoding hashed; dimensions are carried separately and are not part of the digest",
                          "type": "string"
                        },
                        "transcript_sha256": {
                          "description": "Lowercase SHA-256 digest of the encoded final DP values; this is non-proof evidence",
                          "maxLength": 64,
                          "minLength": 64,
                          "pattern": "^[0-9a-f]{64}$",
                          "type": "string"
                        },
                        "verification": {
                          "const": "recompute the bounded dynamic program; the digest detects transcript drift but is not an optimality proof",
                          "description": "Independent verification instruction; recomputation is required to verify optimality",
                          "type": "string"
                        }
                      },
                      "required": [
                        "dp_items",
                        "dp_capacity",
                        "transcript_encoding",
                        "transcript_sha256",
                        "optimality_proof",
                        "verification"
                      ],
                      "type": "object"
                    },
                    "objective": {
                      "const": "maximum_total_value",
                      "description": "The solver maximizes total selected value within capacity",
                      "type": "string"
                    },
                    "objective_value": {
                      "description": "Proven maximum total value",
                      "maximum": 512000000000,
                      "minimum": 0,
                      "type": "integer"
                    },
                    "operation": {
                      "const": "knapsack",
                      "description": "Stable route operation name",
                      "type": "string"
                    },
                    "optimal": {
                      "const": true,
                      "description": "True because the bounded dynamic program computes the exact optimum",
                      "type": "boolean"
                    },
                    "solution": {
                      "additionalProperties": false,
                      "description": "Selected item set and capacity accounting",
                      "properties": {
                        "remaining_capacity": {
                          "description": "Capacity minus selected weight",
                          "maximum": 100000,
                          "minimum": 0,
                          "type": "integer"
                        },
                        "selected": {
                          "description": "Selected items in input order; [] is valid when no positive-value item fits",
                          "items": {
                            "additionalProperties": false,
                            "description": "One selected item",
                            "properties": {
                              "id": {
                                "description": "Input item identifier",
                                "maxLength": 64,
                                "minLength": 1,
                                "pattern": "^[ -~]+$",
                                "type": "string"
                              },
                              "original_index": {
                                "description": "Zero-based input index",
                                "maximum": 511,
                                "minimum": 0,
                                "type": "integer"
                              },
                              "value": {
                                "description": "Input item value",
                                "maximum": 1000000000,
                                "minimum": 0,
                                "type": "integer"
                              },
                              "weight": {
                                "description": "Input item weight",
                                "maximum": 1000000000,
                                "minimum": 0,
                                "type": "integer"
                              }
                            },
                            "required": [
                              "id",
                              "original_index",
                              "weight",
                              "value"
                            ],
                            "type": "object"
                          },
                          "maxItems": 512,
                          "type": "array"
                        },
                        "used_capacity": {
                          "description": "Total selected weight",
                          "maximum": 100000,
                          "minimum": 0,
                          "type": "integer"
                        }
                      },
                      "required": [
                        "selected",
                        "used_capacity",
                        "remaining_capacity"
                      ],
                      "type": "object"
                    },
                    "warnings": {
                      "description": "Always empty for this exact solver; non-proof semantics are carried in evidence",
                      "items": {
                        "description": "Human-readable warning",
                        "type": "string"
                      },
                      "maxItems": 0,
                      "type": "array"
                    },
                    "work_units": {
                      "description": "Item count times (capacity+1), the declared dynamic-program work units",
                      "maximum": 2000000,
                      "minimum": 0,
                      "type": "integer"
                    }
                  },
                  "required": [
                    "operation",
                    "algorithm_version",
                    "objective",
                    "objective_value",
                    "optimal",
                    "solution",
                    "work_units",
                    "evidence",
                    "warnings"
                  ],
                  "type": "object"
                },
                "type": {
                  "type": "string"
                }
              },
              "required": [
                "type"
              ],
              "type": "object"
            }
          },
          "required": [
            "input"
          ],
          "type": "object"
        },
        "tags": [
          "0-1-knapsack-solver",
          "optimization",
          "operations-research",
          "bounded-computation",
          "deterministic"
        ]
      }
    }
  },
  "liveness": {
    "reliability": null
  },
  "verified": false,
  "featured": false,
  "provider": {
    "host": "decision-solver.use.x402atlas.com",
    "manifest_name": "decision-solver.use.x402atlas.com",
    "source": "cdp-mirror",
    "source_manifest_url": "https://api.cdp.coinbase.com/platform/v2/x402/discovery/resources",
    "submitted_at": "2026-10-14T01:15:01.050Z"
  },
  "exampleResponse": {
    "example": {
      "_atlas": {
        "docs": "https://example.com",
        "related": [
          {
            "bridge": "string",
            "docs": "https://example.com",
            "summary": "string",
            "url": "https://example.com"
          }
        ]
      },
      "algorithm_version": "string",
      "evidence": {
        "dp_capacity": 0,
        "dp_items": 0,
        "optimality_proof": true,
        "transcript_encoding": "string",
        "transcript_sha256": "string",
        "verification": "string"
      },
      "objective": "string",
      "objective_value": 0,
      "operation": "string",
      "optimal": true,
      "solution": {
        "remaining_capacity": 0,
        "selected": [
          {
            "id": "string",
            "original_index": 0,
            "value": 0,
            "weight": 0
          }
        ],
        "used_capacity": 0
      },
      "warnings": [
        "string"
      ],
      "work_units": 0
    },
    "type": "string"
  }
}