Bounded Decision Solver
0/1 knapsack solver — exact work-bounded capacity planning and portfolio selection for maximum value, with deterministic ties and reproducible DP evidence.
Offering
- Provider
- decision-solver.use.x402atlas.com
- Method
- POST
- Offering type
- Api Endpoint
- Transport type
- http
- Category
- General Utilities
- Delivery
- Not provided
- Pricing model
- Not provided
- x402 version
- 2
Endpoint context
- URL
https://decision-solver.use.x402atlas.com/knapsack- MIME type
- Not provided
- First seen
- 2026-10-16T01:50:06.715Z
- Last seen
- Tags
- 0-1-knapsack-solver, optimization, operations-research, bounded-computation, deterministic
Payment pricing
x402 payment terms are the authoritative price for calling this endpoint.
- Payment option 1
- 0.005 USDC
Atomic price: 5000 · Network: eip155:8453 · Asset: USDC · Scheme: exact - Payment option 2
- 0.005 USDC
Atomic price: 5000 · Network: eip155:137 · Asset: USDC · Scheme: exact - Payment option 3
- 0.005 USDC
Atomic price: 5000 · Network: eip155:42161 · Asset: USDC · Scheme: exact - Payment option 4
- 0.005 USDC
Atomic price: 5000 · Network: solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp · Asset: USDC · Scheme: exact
Raw x402 terms
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]Observed health
- Status
- Reachable
- Latest latency
- 11 ms
- Average latency
- 81 ms
- HTTP status
- 405
- Last checked
- Reachability
- 100% over 12 checks
Latency is measured to the first response headers. A reachable result does not verify response accuracy or merchant identity.
Input schema
{
"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 schema
{
"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"
}