{
  "x402Version": 2,
  "id": 28630,
  "slug": "28630",
  "resource": "https://decision-solver.use.x402atlas.com/assignment",
  "description": "Assignment solver — exact minimum-cost worker-to-task matching for resource allocation, with deterministic choices and a primal/dual optimality certificate.",
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  "serviceName": "Bounded Decision Solver",
  "resourceType": "Blockchain Data",
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            "properties": {
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                "description": "Documentation URL for this bridge",
                "format": "uri",
                "maxLength": 512,
                "type": "string"
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                "description": "Bounded related Atlas routes",
                "items": {
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                  "minimum": 0,
                  "type": "integer"
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                "description": "Signed row dual potentials",
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                  "description": "Signed dual potential value",
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            "description": "Proven minimum total cost",
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            "items": {
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            "description": "Counted Hungarian inner comparisons",
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                1,
                3
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                2,
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                0
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                    "items": {
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                      "items": {
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                "properties": {
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                    "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"
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                      "related": {
                        "description": "Bounded related Atlas routes",
                        "items": {
                          "additionalProperties": false,
                          "description": "One related Atlas route",
                          "properties": {
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                              "description": "Related bridge name",
                              "maxLength": 64,
                              "type": "string"
                            },
                            "docs": {
                              "description": "Related bridge documentation URL",
                              "format": "uri",
                              "maxLength": 512,
                              "type": "string"
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                            "summary": {
                              "description": "Short capability summary",
                              "maxLength": 256,
                              "type": "string"
                            },
                            "url": {
                              "description": "Related route URL",
                              "format": "uri",
                              "maxLength": 512,
                              "type": "string"
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                          "required": [
                            "bridge",
                            "url",
                            "docs",
                            "summary"
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                          "type": "object"
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                        "maxItems": 3,
                        "type": "array"
                      }
                    },
                    "required": [
                      "docs"
                    ],
                    "type": "object"
                  },
                  "algorithm_version": {
                    "const": "hungarian-min-v1",
                    "description": "Pinned deterministic algorithm and certificate contract",
                    "type": "string"
                  },
                  "certificate": {
                    "additionalProperties": false,
                    "description": "Independently checkable primal/dual certificate for the padded square matrix",
                    "properties": {
                      "column_potentials": {
                        "description": "Signed column dual potentials",
                        "items": {
                          "description": "Signed dual potential value",
                          "type": "integer"
                        },
                        "maxItems": 64,
                        "minItems": 1,
                        "type": "array"
                      },
                      "padded_assignment": {
                        "description": "Task index matched to each padded worker",
                        "items": {
                          "description": "Zero-based padded task index",
                          "maximum": 63,
                          "minimum": 0,
                          "type": "integer"
                        },
                        "maxItems": 64,
                        "minItems": 1,
                        "type": "array"
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                      "row_potentials": {
                        "description": "Signed row dual potentials",
                        "items": {
                          "description": "Signed dual potential value",
                          "type": "integer"
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                        "minItems": 1,
                        "type": "array"
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                    "required": [
                      "padded_assignment",
                      "row_potentials",
                      "column_potentials"
                    ],
                    "type": "object"
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                  "objective": {
                    "const": "minimum_total_cost",
                    "description": "The solver minimizes the sum of selected assignment costs",
                    "type": "string"
                  },
                  "objective_value": {
                    "description": "Proven minimum total cost",
                    "maximum": 64000000000,
                    "minimum": -64000000000,
                    "type": "integer"
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                  "operation": {
                    "const": "assignment",
                    "description": "Stable route operation name",
                    "type": "string"
                  },
                  "optimal": {
                    "const": true,
                    "description": "True because the primal/dual certificate proves this exact optimum",
                    "type": "boolean"
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                  "solution": {
                    "additionalProperties": false,
                    "description": "Customer assignment excluding padded dummy workers",
                    "properties": {
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                        "description": "Exactly one assignment per input worker, ordered by worker index",
                        "items": {
                          "additionalProperties": false,
                          "description": "One chosen worker-to-task edge",
                          "properties": {
                            "cost": {
                              "description": "Input cost on the chosen edge",
                              "maximum": 1000000000,
                              "minimum": -1000000000,
                              "type": "integer"
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                              "description": "Zero-based input task index",
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                        "minItems": 1,
                        "type": "array"
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                  "warnings": {
                    "description": "Always empty for this exact solver",
                    "items": {
                      "description": "Human-readable warning",
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                    "maxItems": 0,
                    "type": "array"
                  },
                  "work_units": {
                    "description": "Counted Hungarian inner comparisons",
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                  "optimal",
                  "solution",
                  "work_units",
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                  "warnings"
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                "type": "string"
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        "optimization",
        "operations-research",
        "bounded-computation",
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    "operations-research",
    "bounded-computation",
    "deterministic",
    "bazaar"
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  "lastUpdated": "2026-10-06T04:21:29.9Z",
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    "extensions": {
      "bazaar": {
        "category": "utilities",
        "info": {
          "input": {
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                  2,
                  2
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            "bodyType": "json",
            "method": "POST",
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                "column_potentials": [
                  0,
                  -2,
                  0
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                "padded_assignment": [
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                  0,
                  2
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                "row_potentials": [
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                          "description": "Documentation URL for this bridge",
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                          "maxLength": 512,
                          "type": "string"
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                          "description": "Bounded related Atlas routes",
                          "items": {
                            "additionalProperties": false,
                            "description": "One related Atlas route",
                            "properties": {
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                                "maxLength": 64,
                                "type": "string"
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                              "docs": {
                                "description": "Related bridge documentation URL",
                                "format": "uri",
                                "maxLength": 512,
                                "type": "string"
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                              "summary": {
                                "description": "Short capability summary",
                                "maxLength": 256,
                                "type": "string"
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                              "url": {
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                                "format": "uri",
                                "maxLength": 512,
                                "type": "string"
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                            "required": [
                              "bridge",
                              "url",
                              "docs",
                              "summary"
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                          "type": "array"
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                      "required": [
                        "docs"
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                      "type": "object"
                    },
                    "algorithm_version": {
                      "const": "hungarian-min-v1",
                      "description": "Pinned deterministic algorithm and certificate contract",
                      "type": "string"
                    },
                    "certificate": {
                      "additionalProperties": false,
                      "description": "Independently checkable primal/dual certificate for the padded square matrix",
                      "properties": {
                        "column_potentials": {
                          "description": "Signed column dual potentials",
                          "items": {
                            "description": "Signed dual potential value",
                            "type": "integer"
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                          "maxItems": 64,
                          "minItems": 1,
                          "type": "array"
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                        "padded_assignment": {
                          "description": "Task index matched to each padded worker",
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                            "description": "Zero-based padded task index",
                            "maximum": 63,
                            "minimum": 0,
                            "type": "integer"
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                          "minItems": 1,
                          "type": "array"
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                        "row_potentials": {
                          "description": "Signed row dual potentials",
                          "items": {
                            "description": "Signed dual potential value",
                            "type": "integer"
                          },
                          "maxItems": 64,
                          "minItems": 1,
                          "type": "array"
                        }
                      },
                      "required": [
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                        "row_potentials",
                        "column_potentials"
                      ],
                      "type": "object"
                    },
                    "objective": {
                      "const": "minimum_total_cost",
                      "description": "The solver minimizes the sum of selected assignment costs",
                      "type": "string"
                    },
                    "objective_value": {
                      "description": "Proven minimum total cost",
                      "maximum": 64000000000,
                      "minimum": -64000000000,
                      "type": "integer"
                    },
                    "operation": {
                      "const": "assignment",
                      "description": "Stable route operation name",
                      "type": "string"
                    },
                    "optimal": {
                      "const": true,
                      "description": "True because the primal/dual certificate proves this exact optimum",
                      "type": "boolean"
                    },
                    "solution": {
                      "additionalProperties": false,
                      "description": "Customer assignment excluding padded dummy workers",
                      "properties": {
                        "assignments": {
                          "description": "Exactly one assignment per input worker, ordered by worker index",
                          "items": {
                            "additionalProperties": false,
                            "description": "One chosen worker-to-task edge",
                            "properties": {
                              "cost": {
                                "description": "Input cost on the chosen edge",
                                "maximum": 1000000000,
                                "minimum": -1000000000,
                                "type": "integer"
                              },
                              "task_index": {
                                "description": "Zero-based input task index",
                                "maximum": 63,
                                "minimum": 0,
                                "type": "integer"
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                              "worker_index": {
                                "description": "Zero-based input worker index",
                                "maximum": 63,
                                "minimum": 0,
                                "type": "integer"
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                            "required": [
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                          "maxItems": 64,
                          "minItems": 1,
                          "type": "array"
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                      },
                      "required": [
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                      "type": "object"
                    },
                    "warnings": {
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