Algebraic Decoupling and Nilpotent Scission over the Chrysene Tensor Space: A Geometric Framework for Cryptographic Information Containment

Abstract

Software-defined and probabilistic methods of state validation leave non-compliant configurations as well-defined objects of the ambient space; rejection is an external decision rather than an algebraic annihilation. This paper constructs a discrete non-commutative framework in which containment becomes an intrinsic geometric relation. The ambient geometry is the Chrysene Tensor Space, a fibrated manifold with orthogonal connectivity. States are valued in the Galois field, so that information is represented natively in base four. Complementary projections determine an admissible sector (a geometric key) and a hazard sector. Encoding embeds a message into the admissible coordinates selected by the key; recovery is the corresponding projection. A nilpotent scission operator sends every state that violates the governing orthogonality conditions into the absolute null ideal, from which no admissible morphism can extract residual information. The resulting theory expresses hard containment and selective accessibility as algebraic properties of the geometry. It is offered as a complementary topological language rather than as a replacement for existing cryptographic primitives.