RQGP Paper S - Structural Neutron Drip Line for Alpha-Cluster Nuclei within RQGP

In the Refined Quantum Geometric Physics (RQGP) framework, nucleons are modelled as flow networks — protons act as pressure sources and neutrons as sinks, connected by structural pathways called pistons, with the surrounding vacuum providing an ambient redistribution reservoir. For a composite nucleus to remain bound, every neutron must receive enough flux through its internal routing to remain in a stable state. When that routing fails, the neutron starves structurally, and the nucleus becomes unstable. Paper S addresses a specific question: at what neutron number does starvation onset occur for nuclei built from alpha-cluster units — groups of two protons and two neutrons arranged in a compact lattice structure? These are the even-proton nuclei from oxygen through to tin whose internal geometry is reasonably approximated as a body-centred cubic arrangement of alpha modules. The first finding is a negative result, which forms the genuine scientific motivation for everything that follows. When the standard RQGP network is run without any capacity restriction, local neutron starvation is mathematically impossible before the point of global vacuum inversion — the threshold where total proton surplus no longer exceeds total neutron demand across the nucleus as a whole. This was confirmed computationally across six different internal wiring configurations. The implication is that something additional to the basic network topology is required to explain why nuclei become neutron-unbound well before that global threshold. That additional element is the bounded vacuum postulate. Rather than treating the vacuum reservoir as unlimited, the paper introduces a structural postulate that the pool of vacuum redistribution capacity available to surface neutrons is proportional to the nucleus's current proton surplus. As more neutrons are added and the surplus shrinks, the pool contracts. Eventually the surface neutrons — those on the outer shell of the alpha lattice — can no longer draw enough from the shrinking pool to compensate for the growing demand, and starvation fires. The number of surface alphas that participate in this starvation process is called the active module count. Two independent geometric arguments — one based on counting oxygen-16 tetrahedral sub-units within the lattice, the other based on the solid-angle fraction of the nuclear surface accessible from outside — both converge on the same answer: approximately one quarter of the surface alpha modules are active, giving a value that steps upward in discrete increments as the nucleus grows. Combining the bounded vacuum postulate with this geometric result yields a closed-form expression for the starvation-onset neutron number that depends only on the proton number. The formula contains no fitted numerical parameters — all inputs come from the locked boundary conditions of the RQGP axis law and the BCC geometric rule. The formula is compared against three elements. Oxygen is the only experimentally established case: the model predicts onset one neutron before the experimentally confirmed last-bound oxygen isotope, a one-neutron offset consistent with the distinction between starvation onset and actual unbinding. For calcium and iron, where experimental data does not exist, comparison is made against AME2020 mass-model reference zones, and both predictions fall within those zones. Three elements near neutron magic numbers — sulfur, nickel, and krypton — fall outside the model's scope, and their deviations are characterised and explained. A prospective prediction is made for magnesium, not used in the derivation, which sits at the lower bound of theoretical estimates for that region. The paper is explicit throughout about what it does and does not claim. It is not a universal drip-line formula. It is a structural capacity mechanism that recovers the correct onset scale for alpha-cluster nuclei in the regime between neutron shell closures, derived from geometric and flow-network principles without reference to binding energy or fitted mass parameters.