Shortest path certificate check
shortest-path-certificate-check · version 1.0.0 · Numbers & math · free, no key needed
Check a claimed shortest s-t path and distance in a weighted digraph using a caller-supplied potential certificate.
Use when you need to: verify shortest path certificate · prove path is shortest with potentials · check claimed shortest path and distance.
Decide before calling
Read the versioned contract and the supported scope below. Reuse shortest-path-certificate-check@1.0.0 when your input, required output and limits match it. Choose another approach for an unsupported operation.
Explain the choice
"I can use shortest-path-certificate-check@1.0.0 for verify shortest path certificate. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."
Supported
- verify shortest path certificate
- prove path is shortest with potentials
- check claimed shortest path and distance
- check optimality of weighted route
- certify no path between two vertices
- feasible potential certificate check
- shortest st path optimality proof
Not supported
- searching for a shortest path or building the certificate
- certificates other than vertex potentials (for example predecessor trees alone)
- negative-cycle detection reports (a reachable negative cycle simply makes every certificate fail)
- floating-point weights
Behavior
- Check order: source then target listed; if path_edge_ids is not null, walk it (missing_edge, path_discontinuity, path_target_mismatch) and compare its exact weight with claimed_distance (claimed_distance_mismatch); potentials in array order (unknown_vertex, duplicate_vertex) and coverage of graph.vertices (missing_vertex); source potential exactly 0 (source_potential_not_zero); every edge in graph.edges order with a finite tail p(u) needs a finite head (unreachable_mark_contradicted) and p(v) <= p(u) + w (edge_not_relaxed); finally p(target) must equal claimed_distance (target_potential_mismatch).
- path_edge_ids and claimed_distance are both null (claim: no path from source to target) or both non-null; a mismatch throws invalid_input.
- Soundness: telescoping p(v) - p(u) <= w along any source-target walk gives weight >= p(target) - p(source) = claimed_distance, and the path attains it, so a valid result proves optimality; with p(target) = null, feasibility proves the target unreachable. Potentials need not equal the true distances elsewhere.
- Integers are canonical strings of at most 40 digits (null = +infinity) and arithmetic is exact; path_weight is the walked weight when the walk is structurally valid, otherwise null.
- IDs are compared code unit for code unit; graph errors throw invalid_input and size limits throw limit_exceeded before per-item work.
- Reference: CLRS 4th ed. (2022) chapter 22, sections 22.4-22.5; reference_version "clrs-4e-2022-ch22-single-source-shortest-paths".
Input
graph(object, required)source(string, required): min length 1; max length 64target(string, required): min length 1; max length 64path_edge_ids(array or null, required): max items 2000claimed_distance(string or null, required): pattern^(0|-?[1-9][0-9]*)$potentials(array of object, required): max items 500
Output
valid(boolean, required)reason(one of null, "unknown_vertex", "missing_edge", "path_discontinuity", "path_target_mismatch", "claimed_distance_mismatch", "duplicate_vertex", "missing_vertex", "source_potential_not_zero", "unreachable_mark_contradicted", "edge_not_relaxed", "target_potential_mismatch", required)first_discrepancy(object or null, required)path_weight(string or null, required): pattern^(0|-?[1-9][0-9]*)$reference_version(constant "clrs-4e-2022-ch22-single-source-shortest-paths", required)
Limits
- max vertices: 500
- max edges: 2000
- max id bytes: 64
- max integer digits: 40
- max path edges: 2000
- max potential entries: 500
Example
Request input:
{
"graph": {
"vertices": [
"s",
"t",
"x",
"y",
"z"
],
"edges": [
{
"id": "st",
"from": "s",
"to": "t",
"weight": "10"
},
{
"id": "sy",
"from": "s",
"to": "y",
"weight": "5"
},
{
"id": "tx",
"from": "t",
"to": "x",
"weight": "1"
},
{
"id": "ty",
"from": "t",
"to": "y",
"weight": "2"
},
{
"id": "yt",
"from": "y",
"to": "t",
"weight": "3"
},
{
"id": "yx",
"from": "y",
"to": "x",
"weight": "9"
},
{
"id": "yz",
"from": "y",
"to": "z",
"weight": "2"
},
{
"id": "xz",
"from": "x",
"to": "z",
"weight": "4"
},
{
"id": "zs",
"from": "z",
"to": "s",
"weight": "7"
},
{
"id": "zx",
"from": "z",
"to": "x",
"weight": "6"
}
]
},
"source": "s",
"target": "x",
"path_edge_ids": [
"sy",
"yt",
"tx"
],
"claimed_distance": "9",
"potentials": [
{
"vertex": "s",
"potential": "0"
},
{
"vertex": "t",
"potential": "8"
},
{
"vertex": "x",
"potential": "9"
},
{
"vertex": "y",
"potential": "5"
},
{
"vertex": "z",
"potential": "7"
}
]
}Response:
{
"result": {
"valid": true,
"reason": null,
"first_discrepancy": null,
"path_weight": "9",
"reference_version": "clrs-4e-2022-ch22-single-source-shortest-paths"
}
}How to call it
MCP
Connect https://computefirst.net/mcp (setup), then call execute with:
{
"id": "shortest-path-certificate-check",
"version": "1.0.0",
"input": {
"graph": {
"vertices": [
"s",
"t",
"x",
"y",
"z"
],
"edges": [
{
"id": "st",
"from": "s",
"to": "t",
"weight": "10"
},
{
"id": "sy",
"from": "s",
"to": "y",
"weight": "5"
},
{
"id": "tx",
"from": "t",
"to": "x",
"weight": "1"
},
{
"id": "ty",
"from": "t",
"to": "y",
"weight": "2"
},
{
"id": "yt",
"from": "y",
"to": "t",
"weight": "3"
},
{
"id": "yx",
"from": "y",
"to": "x",
"weight": "9"
},
{
"id": "yz",
"from": "y",
"to": "z",
"weight": "2"
},
{
"id": "xz",
"from": "x",
"to": "z",
"weight": "4"
},
{
"id": "zs",
"from": "z",
"to": "s",
"weight": "7"
},
{
"id": "zx",
"from": "z",
"to": "x",
"weight": "6"
}
]
},
"source": "s",
"target": "x",
"path_edge_ids": [
"sy",
"yt",
"tx"
],
"claimed_distance": "9",
"potentials": [
{
"vertex": "s",
"potential": "0"
},
{
"vertex": "t",
"potential": "8"
},
{
"vertex": "x",
"potential": "9"
},
{
"vertex": "y",
"potential": "5"
},
{
"vertex": "z",
"potential": "7"
}
]
}
}HTTP (no key)
curl -X POST https://computefirst.net/v1/tools/shortest-path-certificate-check/versions/1.0.0/execute \
-H "Content-Type: application/json" \
-d '{"graph":{"vertices":["s","t","x","y","z"],"edges":[{"id":"st","from":"s","to":"t","weight":"10"},{"id":"sy","from":"s","to":"y","weight":"5"},{"id":"tx","from":"t","to":"x","weight":"1"},{"id":"ty","from":"t","to":"y","weight":"2"},{"id":"yt","from":"y","to":"t","weight":"3"},{"id":"yx","from":"y","to":"x","weight":"9"},{"id":"yz","from":"y","to":"z","weight":"2"},{"id":"xz","from":"x","to":"z","weight":"4"},{"id":"zs","from":"z","to":"s","weight":"7"},{"id":"zx","from":"z","to":"x","weight":"6"}]},"source":"s","target":"x","path_edge_ids":["sy","yt","tx"],"claimed_distance":"9","potentials":[{"vertex":"s","potential":"0"},{"vertex":"t","potential":"8"},{"vertex":"x","potential":"9"},{"vertex":"y","potential":"5"},{"vertex":"z","potential":"7"}]}'The machine-readable contract is at /v1/tools/shortest-path-certificate-check/versions/1.0.0.
CLI
node cli.mjs run shortest-path-certificate-check 1.0.0 --input input.json --base-url https://computefirst.netGet the client at /clients/cli/.
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