The Reverse Fragmentation Principle (RFP) as an Architectural Selection Problem / Zasada odwrotnej fragmentacji (RFP) jako problem selekcji architektury

Abstrakt In this paper, I present a formal, mathematical analysis of the Reverse Fragmentation Principle (RFP), treating it as an architecture-selection problem in the space of scale distributions. I define structural architecture as the density distribution of load-bearing elements, and I describe the degradation process by means of a global degradation-cost functional that aggregates the long-term consequences of local destructive events. In regimes lacking an imposed characteristic scale and assuming the existence of a load-redistribution mechanism, I show that heavy-tail distributions constitute selectively stable solutions within the space of realizable architectures, arising from the minimization of the global degradation cost under operative structural and selection constraints. In this perspective, power-law distributions are not a product of fracture mechanics or fragmentation dynamics, but instead follow from long-term structural optimality under the governing selection conditions. This work clarifies the relationship between the Reverse Fragmentation Principle and classical theories of fragmentation and self-organized criticality, and it provides a formal foundation for further extensions of the theory to include geometric and rheological effects. Keywords: Reverse Fragmentation Principle (RFP), RFP, architecture selection, selective stability, realizable architectures, heavy-tail distributions, power-law distributions, degradation-cost functional, variational stability, scale-free architectures, multiscale systems, load redistribution, long-term structural degradation, structural attractors, statistical mechanics of failure, theoretical geomechanics