Substrate-Invariant Safety Enforcement: A Categorical Framework for Formal Verification Across Electronic, Photonic, and Quantum Computational Architectures

We introduce the Substrate-Invariant Safety Functor, a category-theoretic formalism defining the necessary and sufficient properties a physical enforcement layer must satisfy to guarantee deterministic safety constraints independent of the computational substrate. We instantiate this functor across electronic FPGA, photonic integrated circuits, and quantum-classical hybrid architectures, deriving substrate-specific enforcement mechanisms (gate-level interdiction, coherent signal annihilation, and measurement-based statistical attestation) and identifying failure modes unique to each domain. We prove that the no-cloning theorem and measurement collapse jointly necessitate a classical safety mediator for quantum substrates as a mathematical consequence of the axioms. We further specify cross-substrate attestation via an Attestation Aggregation Functor with post-quantum soundness. This work completes a three-paper theoretical arc establishing hardware-enforced AI safety across heterogeneous computational fabrics.