Open-System Corridor: Reduced Ledger Summaries, Density-Class States, and the Trace Slot

Entanglement forces mixed states: density-class reduction is not optional. This preprint derives the Open-System Corridor as the next forced step after tensor-class composition and entanglement. Composite systems immediately create partial-access cases: a joint ledger for AB may exist while only subsystem A is accessible at an interface, with B functioning as an environment or untracked ledger. Corridor admissibility therefore requires a reduction rule that preserves all A-outcome weights under any declared A-interface without retaining B. The paper shows that entanglement makes pure amplitude summaries on A insufficient for this role, forcing an enlarged reduced-state class. The minimal forced reduced object is a density-class state: a positive, coarse-graining additive, weight-normalized quadratic-functional object rho_A that generates Born-consistent outcome weights for any A-interface. The paper then forces a trace-slot reduction (partial trace analogue) from composite density-class objects to subsystem density-class states, establishing existence and minimality of a reduction map that preserves all local A-outcome weights (with uniqueness deferred until sequential reduction compatibilities are forced). Standard formulas using operators and trace pairing are presented only as representations of the corridor-forced role, not as axioms. The next forced papers are Open-System Update Corridor (Kraus-class update slot) and Effective Dynamics Corridor (interaction-induced open evolution and Lindblad-class pressure under added continuity/Markov assumptions).