Cage-Constrained Chemical Reachability in π-Stacked Chrysene-Adenosine Systems: Existence, Stereochemical Selection, and Local Transformation Invariance

Abstract

We develop a mathematical existence theory for constrained chemical transformation in a π-stacked chrysene-adenosine molecular architecture. Starting from a fixed chrysene molecular anchor and a saturated local tether of the form C6-O-CαH2-CβH2-OPO3RA, we define persistent-atom typed molecular states, local chemical graph-rewrite rules, cage-admissible configuration spaces, and a free reaction category whose morphisms are finite sequences of chemically admissible, geometrically liftable transformations. An explicit conditional witness reaches the target connectivity C5-Cα(H)(NH2)-Cβ(=O)-O2'Ado while preserving the inherited chrysene C5-C6 carbon-framework bond and complete atom provenance. A separate oriented-cage condition yields stereochemical selection χ(cα)=χ*.

We prove local transformation invariance across the {6,12}, {3,6,12}, and {3,6,9,12} substitution contexts. Chemical rewrite transport is exact under local concordance and reaction-inert external context; cage-level persistence additionally requires corresponding candidate geometric lifts whose hard-constraint deviation satisfies Δ_F^Λ < m_min. Alternative carbonyl factorizations, dual-cipher source-capture transport, and adenine-anchor variants are incorporated without requiring reaction-word or realization uniqueness. The resulting theory establishes conditional target reachability and stereochemically refined existence under explicit hypotheses, while a separate certification framework specifies how those hypotheses may be tested computationally and experimentally.