Structural Admissibility and Recurrent Geometry Across Scales

Across natural and engineered systems, similar structural forms recur despite vast differences in scale, material, and dynamics. These recurrences are often misinterpreted as evidence of universal numerical scaling laws. Here we propose instead a Structural Admissibility Principle, in which repetition arises from shared geometric and constraint conditions rather than fixed scale ratios. We show that systems ranging from biological organisms and human-built structures to astrophysical formations exhibit recurrent architectures because geometry governs load, transport, coordination, and failure. Absolute size emerges from local constraint balances and environmental conditions, while admissible structure remains invariant. This framework explains both cross-scale similarity and observed diversity without invoking universal metric hierarchies.