Stratified Algebra

We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms governing intra-layer and inter-layer interactions, study their implications for algebraic dynamics, and present concrete matrix-based models that satisfy different subsets of these axioms. Both associative and bracket-sensitive constructions are considered, with an emphasis on stratum-breaking propagation and permutation symmetry. This framework proposes a paradigm shift in the way algebraic structures are conceived: instead of enforcing uniform global rules, it introduces stratified layers with context-dependent interactions. Such a rethinking of algebraic organization allows for the modeling of systems where local consistency coexists with global asymmetry, non-associativity, and semantic transitions.