BU50 Appearance-Side Minimal Admissible Structure under B_U First Lawful Nonzero Retention, Finite Projection Audit, and the Reclassification of Formal Divergence / Finite Energy

Abstract This paper develops BU50 as a structural account of the appearance-side minimal admissible structure under Single-Universe Boundary Consistency, B_U. Its central claim is that the first lawful “nonzero” item on the appearance side is not a minimal object, particle, or epistemic observation limit, but the smallest admissible retained structure that survives microscopic zeroing, finite projection, coherence audit, and settlement. Total reality cannot enter the phenomenal ledger as an unfiltered ontic intensity. It must pass through B_U, the fixed boundary B_0, the dynamically complete interface D(M), and the fast-slow decomposition in which microscopic fast variables are projected into a zero-mean…