This paper presents SV-TGD 4.5, an upgraded semi-classical framework that reconstructs fundamental physics based on the statistical mechanics of a granular vacuum medium (Deep-Vacuum Queues, DVQ). The central contribution of this version is a Z-dependent Vacuum Phase Transition mechanism derived from Ginzburg-Landau theory combined with Jamming scaling laws, which provides a unified quantitative explanation for the long-standing contradiction between the Proton Radius Puzzle (anomaly in muonic hydrogen) and the null result in muonic helium. Numerical simulations demonstrate that the vacuum acts as a non-linear medium with a critical field threshold determined by the nuclear charge number Z. For weak sources like the Proton (Z=1), the vacuum remains in a fluid state, allowing standard vacuum polarization to manifest as the observed "anomaly." Conversely, for stronger sources like the Helium nucleus (Z=2), the local vacuum undergoes a phase transition into a rigid "crystalline" state (Jamming), which mechanically suppresses the short-range Uehling potential and eliminates the anomaly. Beyond resolving this specific puzzle, SV-TGD 4.5 continues to establish a unified foundation where gravity arises from entropy gradients and electromagnetism emerges from topological defects (solitons) within the granular lattice. This work challenges the geometric continuity of spacetime, proposing instead that physical laws are emergent properties of a discrete, mechanical vacuum substrate.
Shichao Tang (Mon,) studied this question.