Semantic Computational Architecture (SCA): A Dynamical Systems Approach to Adaptive Semantic Virtual Memory

Every computational substrate is organized around an atomic primitive. Seman-

tic Computational Architecture (SCA) proposes canonicalized semantic state as this

primitive, organizing knowledge into a dynamic graph grouped into adaptively-sized

“packets” and paged through a multi-resolution memory hierarchy. This report for-

malizes SCA as a semantic dynamical system, defining a global state-space, an aug-

mented Markov transition operator, and a unified global optimization objective. We

establish a rigorous measure-theoretic foundation for semantic volume, define explicit

topological and logical invariants, and formalize a set of standing assumptions (A1–

A9) under which the system’s guarantees hold. Memory governance is formulated as

a bilevel optimization problem with proven boundedness guarantees, and we give a

formal approximation-ratio guarantee for the discrete packet-selection heuristic that

realizes it in practice. We define the algebraic axioms of the Semantic Abstraction

Operator A(P, r) and prove a theorem on monotone volume reduction, with an ex-

plicit account of the operational (iterative) semantics under which the theorem holds.

Furthermore, we propose an approximation conjecture bounding activated workspace

relative to a theoretical oracle, motivated by spectral partitioning theory and ran-

dom walk mixing properties. Finally, we provide a formal complexity analysis, an

evaluation protocol distinguishing between exact and reference oracles, and an explicit

statement of the primary open problem—convergence and stability of the online packet

dynamics—identified as the central target of future work.

jason.crowe@alumni.com

Mosaic Systems Architecture 

2026.