Winged Radio Galaxies as Geometric Archives of Fractal-Consistency Discharge

We develop a Fractal Consistency Law (FCL/LCF) working paper that interprets winged radio galaxies in LoTSS DR2 as candidate geometric archives of structural processing around active supermassive black holes. The empirical anchor is the LoTSS DR2 winged radio galaxy sample: 621 confirmed winged radio galaxies and 403 candidates, including 382 X-shaped and 239 Z-shaped systems, with predominantly FR-II morphology, steep low-frequency spectra, a median projected size near 498 kpc, and a substantial giant-radio-galaxy tail. We formulate six tests: contour fractality, axis memory, spectral aging, X/Z regime separation, giantness coupling, and multi-channel synchrony. We then map these tests onto the FCL claim that persistent astrophysical structures are not arbitrary anomalies but admissible coarse-grained records of local, relational, and inter-scale inconsistency minimization. The conclusion is deliberately conservative: present evidence does not prove fundamental fractal spacetime texture, but it provides a high-value bridge dataset for testing whether black-hole jet systems encode residual structural syntax across morphology, spectrum, environment, and time.