Cosmic Coherence and the Emergence of the Large-Scale Web

Large-scale filamentary organization is a ubiquitous feature of complex systems with finite information capacity, most notably in cosmological structure. While commonly attributed to dynamical gravitational processes, the structural origin of such morphology remains largely unexplored. In cosmology, this structural question isolates filamentary structure as a privileged carrier of coherence in the large-scale distribution of matter. In this work we show that filamentary connectivity arises as a structurally selected outcome once informational coherence is finite, hierarchically constrained, and subjected to coarse-graining. We formulate a minimal framework in which degrees of freedom are organized ultrametrically, coherence costs are hierarchical, and coarse-graining acts as a spectral filter. Within this setting, configurations requiring coherence to be maintained across many independent directions are intrinsically fragile, while configurations supported along minimal connectivity channels persist. Filamentary organization emerges as the unique robust carrier of extended coherence, without invoking dynamical equations, metric evolution, or background expansion. An explicit finite ultrametric toy model demonstrates this selection mechanism concretely: under spectral coarse-graining, only low-band hierarchical modes survive, yielding intrinsically one-dimensional coherence patterns. A minimal spatial projection shows how these structural survivors naturally translate into node–filament–void morphologies. Our results do not propose a new dynamical model of structure formation. Rather, they identify a prior structural constraint: once coherence is finite and hierarchically organized, filamentary connectivity is not an assumption but an inevitable outcome. This establishes filamentary structure as a generic feature of admissible coherence organization, rather than a contingent product of specific dynamics.