The first representation obstruction occurs at six vertices.
Within the studied class, structures on up to five vertices that satisfy the recognition condition admit a representation as a nonnegative sum of directed hyperedges on their original vertices. At six vertices, structures satisfying the same condition can fall outside that representation.
We established the minimality of the existing six-vertex construction through an exhaustive classification of the target class on up to five vertices, verifying 8,675 instances.
The result is supported by a computer-assisted proof and an independent verification program. It identifies the minimum size at which this representation fails to capture shared source failures.
Certify the safety of the evidence configuration—and its cost.
Execution verification requires a choice of observation sources and a decision about how much evidence to collect. Those choices affect both assurance and operating cost.
Our new method takes a catalogue of candidate sources, their costs, and the required fault tolerance, then finds a minimum-cost evidence configuration meeting those requirements.
It certifies that the selected configuration satisfies the safety requirements and establishes a lower bound on the expenditure needed to meet the same requirements. When the configuration cost matches that bound, global optimality within the candidate catalogue is established.
The same requirements. Configuration cost reduced from 10 to 7.
In a construction with ten candidate sources, the method preserved the same fault-tolerance requirements while reducing configuration cost from ten, using the full catalogue, to seven.
The cost of seven was also certified as optimal. No cheaper configuration within the same candidate catalogue can meet the same requirements.
This research supports both execution assurance and the economics of the evidence needed to establish it with checkable results.
Make the basis for trust independently checkable.
ChoiceProof’s research is grounded in mathematical proofs and independent verification implementations. Its conclusions can be rechecked from the same inputs.
We are building infrastructure that enables third parties to verify AI-agent execution. We strengthen that foundation through computable criteria and checkable proofs.