The Reverse Fragmentation Principle (RFP): Geometry, Stress Fields, Cohesion, and Rheological Regimes of Architectural Selection / Zasada odwrotnej fragmentacji (RFP): geometria, pola naprężeń, kohezja i reżimy reologiczne selekcji architektury

Abstrakt In this paper, I analyze the physical conditions of realizability of multiscale architectures consistent with the Reverse Fragmentation Principle (RFP). In contrast to earlier parts of the series, which focused on the formal and energetic structure of the architecture selection problem, I concentrate here on the role of geometry, stress fields, material rheology, and cohesion as passive physical constraints that restrict the space of solutions admissible in real material systems. I show that neither geometry, nor rheology, nor cohesion generates heavy-tailed architectures; instead, they act as realizability filters that eliminate configurations incompatible with scale continuity, local stability conditions, or the capacity for physical adaptation. In particular, I demonstrate that a hierarchical organization of scales enables stress redistribution, localization of degradation, and avoidance of abrupt global loss of integrity, provided that a minimal, distributed cohesion exists to prevent material dispersion. I introduce the concept of regimes of validity of heavy-tail architecture selection, defined by the coupling between geometry, force fields, rheology, and cohesion, and I identify the conditions leading to the breakdown of these regimes. The paper provides a coherent interpretative framework for multiscale architectures in real material systems and clarifies the limits of applicability of the Reverse Fragmentation Principle (RFP). Keywords: Reverse Fragmentation Principle (RFP), multiscale architectures, architectural selection, heavy-tail distributions, physical realizability, structural stability, force field geometry, stress fields, local stability conditions, material rheology, rheological adaptation, cohesion, maintenance of aggregation, fragmentation, material dispersion, degradation localization, hierarchical scale organization, structural brittleness, global integrity loss, realizability regimes, physical regime map, passive selection filters, long-term stability