Paper 143: EHT Photon Ring Fractal Dimension ---\\ Astrophysical Test of the VCML G\"{o

The Viability--Causal Machine Learning (VCML) framework predicts that the boundary of any self-referential dynamical system traces the G\"{o}del diagonal with fractal dimension $d_H = 2/ = 1.2361$, where $ = (1+5)/2$ is the golden ratio. We develop a pipeline to test this prediction against the photon ring of M87$^*$ as imaged by the Event Horizon Telescope (EHT): a bright, nearly circular ring at $ $43~$ $as believed to trace the photon capture radius near the event horizon. We validate the pipeline on synthetic rings spanning $d_H \{1.0, 1.236, 1.5\}$ using medial-axis skeletonization followed by box-counting. For a perfect circle the pipeline recovers $d_H = 0.987$ (1.3\% below unity); for a ring with prescribed $2/ $ boundary the pipeline recovers $d_H = 1.243$ (0.6\% above target). Application to EHT FITS data is pending public access to the CyVerse data commons archive.