Processual Memory Architecture: A Transformation-Based Framework for Verifiable Computation and Safety-by-Construction AGI

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 round
trip 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 local
node 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.