MA-RDAM - Relative Displacement Access Memory (RDAM) and Multi-Access RDAM (MA-RDAM): A Hierarchical Variational Discrete Framework

This work introduces a complete mathematical framework termed Relative Displacement Access Memory (RDAM) together with its multi-focal extension MA-RDAM. The model defines a hierarchical discrete dynamical system based on relative displacement addressing over a locally Hilbertian metric space. The geometry of the state space is not assumed a priori but induced by admissible transitions themselves. The framework relies on six independent axioms: locality of transitions, discrete relative addressing, occupation exclusion, hierarchical self-similarity, multi-scale variational coherence, and involutive spectral duality. The model establishes attractor theory, spectral classification, invariant measures, bounded topological entropy, operator formulation with non-abelian displacement structure, and structural universality for local discrete dynamics. The RDAM/MA-RDAM framework defines a new class of hierarchical variational dynamical systems with relative addressing and global spectral symmetry. Email: cordierfr@wanadoo.fr or frederic.cordier@alcahest-quantique.frORCID: 0009-0001-8661-3275Project page: https://www.alcahest-quantique.fr