Living braided nematics

Braided matter is ubiquitous across lengths scales, from flagella and fungal filaments to plant tendrils and worm balls. Understanding the topological design space of these braided and tangled collectives continues to present fundamental challenges. Here we introduce a topological framework to classify and characterize braided nematic structures, using the floating braids made by California blackworms (Lumbriculus Variegatus) as a model system. By combining experimental and theoretical approaches, we demonstrate the existence of braid-ordered states in which mechanical stability emerges from braid topology. We further establish a correspondence between the structure of a 2d braid cross-section and its 3d topological state, which explains the assembly rules through which living systems organize into topologically stable braids. By applying our theoretical framework to blackworm braids, we demonstrate that braid-order enables emergent collective motions, including vertical lift and horizontal locomotion of filamentous collectives. These results provide general principles for building and designing functional topological materials.