An answer can be enormously hard to find, yet easy to check.

The solve takes an engine; the check takes moments, on your machine.

The certificate

Specimen
certificate.json
{
"certificate_id": "QC-2026-003535",
"issued_utc": "2026-01-01T00:00:00Z",
"engine": { "name": "QUADI", "version": "x.y.z", "run_id": "sha256:91bd…e07a" },
"problem": {
"domain": "quadratic",
"instance_digest": "sha256:763e959543cc4ebd2a554079aa4068265a5ecd6c8e0d289eca9c525a1c4196a3",
"units": "binary",
"variables": 35
},
"result": {
"solution_digest": "sha256:b7d3…044a",
"objective_value": 0.0184,
"feasible": true
},
"evidence": {
"class": "bound",
"certified_bound": 0.0184,
"gap": 0.0,
"certificate_digest": "sha256:f312de6679137c064752f27c0b4c4b3702665d620d3ec532b91f839f559c16f7"
},
"verification": {
"verifier": "standalone",
"inputs": ["certificate", "result"],
"recomputation": "match",
"status": "VERIFIED"
}
}
problem Pins exactly what was solved: a cryptographic digest of the instance, its true units, its size. A certificate cannot be reattached to a different problem.
result Fingerprints the delivered answer itself and records its measured value. Swap the answer, and the certificate fails.
evidence The mathematical claim: the class states the guarantee — proven optimal, or a certified bound with its exact gap. This is the quantity a checker recomputes.
verification From the files alone, a standalone verifier recomputes the evidence and must reproduce it. A match reads VERIFIED; anything else fails loudly.

Digests in a certificate identify real objects; that is what makes them checkable.

Working certificates and the standalone verifier accompany engagements.

Independent verification available on request.