Access-algebra separation between global information and public objectivity in quantum many-body environments

Quantum Darwinism and related objectivity frameworks study how information about a quantum system is redundantly recorded in its environment. This preprint studies a downstream selection problem: when several candidate records coexist, which one is public under a specified access channel? The problem is formulated as access-limited quantum hypothesis testing. The global Chernoff distinguishability of a candidate record is compared with the public Chernoff distinguishability after a declared sequence of completely positive trace-preserving access maps. The main result is a sufficient access-algebra separation mechanism: if a broadcast record has extensive distinguishability inside the public access algebra, while a globally stronger encoded record is hidden from that algebra at subextensive rate, then global information density and public distinguishability density have opposite thermodynamic orderings. This is not a definition of objectivity in the sense of Spectrum Broadcast Structure or Strong Quantum Darwinism; it is an operational separation theorem for a declared public decision problem. The preprint gives a random-linear access-algebra construction and controlled realizations based on code distance, local circuits, operator spreading, and protected Hamiltonian access algebras.