BU99 Reality Evolution as Minimal Admissible Structure Recognition under B_U

BU99 develops the B_U account of reality evolution as the recognition, retention, amplification, and settlement of minimal admissible structures. Its central claim is that the real world does not evolve by exhaustively searching all possible states, nor by preserving formal identity at zero cost. Reality evolves by identifying the smallest structures that can pass boundary conditions, carry residual continuity, pay friction cost, receive feedback, and obtain standing on the settlement surface. This makes evolution a low-entropy process operating inside a high-dimensional candidate field: many possibilities appear, but only minimal admissible structures remain traceable, retainable, and settleable. The paper begins by correcting a long-standing backward-mirror assumption: formal systems often treat identity, equivalence, and transformation as costless. In reality, every state change and every information update carries non-zero cost. Perfect gluing belongs to formal idealization. Real continuity requires weak persistent morphism and a friction-cost functional. Whenever two states cannot be perfectly joined, a weak persistent morphism is needed to carry the minimum traceable continuity between them; whenever a structure changes, moves, persists, or returns through feedback, a non-zero cost is paid. BU99 therefore places weak persistent morphism not as a universal explanatory slogan, but as the continuity operator required by real transition. The main structural chain of BU99 is: U \rightarrow \Xi_{res} \rightarrow K_{min} \rightarrow R_H \rightarrow M_U \rightarrow p^w \rightarrow L_s \rightarrow G_{tl} \rightarrow C_{fric} \rightarrow Feedback \rightarrow Standing_{new} This chain identifies the total admissible domain, residual stratification, minimal admissible structure, higher-order retainable residue, universal co-admissive medium, weak persistent morphism, soft link, translinkage gradient flow, friction-cost functional, feedback, and new standing. Each term carries a distinct role. K_{min} is the smallest structure capable of entering settlement. R_H preserves retainable residual material. M_U provides the co-admissive medium for cross-domain connection. p^w maintains minimum continuity across transition. C_{fric} records the unavoidable cost of transformation. Feedback tests retainability, and settlement grants standing. BU99 also establishes why minimal admissible structure recognition is more efficient than high-dimensional exhaustive search. High-dimensional evolution does not run by fully unfolding all variables. It finds low-dimensional settleable sections inside a larger possibility space. This explains why weak signals, residues, anomalies, partial paths, and failed fragments should not be automatically discarded. Some are noise or removable friction; others carry future admissible structure. Reality evolution therefore requires residual stratification rather than blind pruning. The final judgment is direct: reality recognizes structure before it displays achievement. Standing is not granted to fluent readout, formal closure, local coherence, or temporary success. Standing is granted only after boundary compatibility, residual control, weak persistence, friction-cost payment, feedback, and settlement jointly hold. BU99 thus supplies the ontological ground for later files on weak persistent morphism, LLM reconstruction, and coherent quantum inference: the world itself operates through minimal admissible structure recognition.