We present Processual Memory Architecture (PMA), a computational framework that unifies data storage and computation by representing all information as transformation functions rather than static state, rendering the traditional ontological distinction between them architecturally unnecessary. In PMA, storing information means encoding it as a mathematical transformation that produces the data when applied to a standardized canonical input; reading means applying the transformation; and computing means composing transformations. This inversion of the conventional von Neumann paradigm yields five emergent architectural properties—structural auditability, transparent reasoning, enforced constraints, tamper evidence, and reversibility—that collectively enable verifiable computation: systems that can mathematically verify the integrity and correctness of their own reasoning chains. We provide a complete mathematical specification of PMA over Galois fields GF(2k) with roundtrip exactness guarantees, constructive algorithms for both invertible and non-invertible encoding modes, and a reference permutation-based embodiment with explicit bit-level storage formats. We analyze thermodynamic properties under reversible logic implementation, demonstrating that PMA operations on adiabatic substrates can approach within 10× of the Landauer limit at the localnode level. We then present the integration architecture for PMA with artificial general intelligence (AGI) safety frameworks, showing how transformation-based reasoning enables safety constraints that are structural rather than advisory—creating systems where unsafe behavior is computationally undefined rather than merely prohibited. We discuss applications to financial auditing, medical AI verification, and autonomous systems governance, and compare PMA's approach to verifiable computation with existing paradigms including blockchain, zero-knowledge proofs, and mechanistic interpretability.