Cosmic Rays as Probes of Effective Galactic Texture and Structural Admissibility

This paper develops an astrophysical module of the Fractal Consistency Law (FCL) motivated by the 2026 DAMPE result on charge-dependent spectral softenings of primary cosmic rays below the knee. The central observational point is that protons, helium, carbon, oxygen, and iron exhibit a common softening scale when their spectra are expressed as functions of magnetic rigidity, with a characteristic break rigidity, denoted Rbr, approximately given by Rbr ≃ 15 TV, whereas a primary scaling controlled by nuclear mass is strongly disfavored. The present work does not interpret that result as a direct detection of fundamental fractal spacetime texture. Instead, it treats the result as high-value bridge evidence for the FCL program: cosmic rays appear to respond to a common relational variable that encodes their interaction with the magnetized structure of the Galactic medium. The paper introduces the concept of effective galactic texture, operationally defined by the Galactic magnetic field Bgal(x), the magnetic coherence length Lc(x), the effective diffusion tensor Dij(x,R), the arrival-direction anisotropy Aani(n,R), and the source distribution Qi(x,R). It further proposes a dynamic admissibility functional, ACR, intended to quantify the structural probability that a charged trajectory remains observationally persistent while crossing a magnetized medium. The FCL claim developed here is not that cosmic-ray propagation is independent of energy or composition, but that the relevant organizing variable is not mass in isolation. It is the composite rigidity variable Ri = pi c/(Zi e), which summarizes the negotiation between momentum, charge, and the magnetic structure of the propagation environment. The paper formulates an empirical audit program: model comparison between rigidity-dependent and mass-dependent spectral break hypotheses; fitting of smoothly broken spectra; construction of an effective texture roughness index Θtex(R); correlation of spectral residuals with independent magnetic and anisotropy maps; and multi-mission testing with DAMPE, AMS-02, CALET, ISS-CREAM, LHAASO, and future high-energy cosmic-ray datasets. The result is classified within the FCL program as high/very-high bridge-gold: it does not validate the theory by itself, but it strengthens the strategic hypothesis that propagation physics is governed by structural admissibility variables.