AXIOM NSPE: A Dual Rail Proof Engine for Non Success Reasoning with Provenance Verification

When an autonomous system proposes an objective, how can we formally determine not only whether that objective will succeed, but precisely why and where it will fail? Existing verification approaches focus almost exclusively on proving that desired properties hold. They offer limited insight into the structure of failure, leaving engineers and auditors without the diagnostic clarity needed to understand, communicate, and resolve infeasibility in safety critical contexts.

AXIOM NSPE was designed to close this gap. It is a dual rail proof engine that compiles proposed objectives into machine checkable proof obligations and evaluates them through two independent reasoning processes running in parallel. The constructive rail works to establish that all success conditions are satisfiable. The non success rail, operating simultaneously, builds compositional negative proof certificates that pinpoint the exact constraints preventing satisfaction. The result is not merely a binary pass or fail verdict, but a structured explanation of feasibility or infeasibility grounded in formal proof artifacts.

When the non success rail determines that an objective cannot be met, a blocking core extraction algorithm isolates the minimal subset of constraints responsible for the failure. Each blocking core is paired with reopening frontiers that describe the specific relaxations under which feasibility could be restored. This diagnostic output transforms failure from an opaque signal into an actionable engineering artifact.

Provenance integrity across the proof pipeline is maintained through a falsification probe escrow mechanism that cryptographically binds every proof artifact to an attested chain of custody. Iterative cycle detection enforces structural validity over directed acyclic graph representations with fail closed resource limits, preventing unbounded computation. Deterministic SHA-256 graph digests enable any independent party to verify that a given decision trace has not been altered after the fact.

The complete system is implemented in pure Python with no external dependencies beyond the standard library, maximizing portability and auditability. The test suite comprises 15,960 automated cases that exercise every proof path, boundary condition, and adversarial input scenario. External validation has been performed against six reference graphs from the DAGBench dataset published by the University of Southern California Applied Networking Research Group. Alignment with established supply chain and provenance standards has been evaluated against SLSA Build Track levels 1 through 4, in toto attestation, and NIST SP 800-53, achieving full coverage across all 14 control mappings. Continuous integration reproduces every result across six platform and runtime combinations.