Beyond Eight: ABC Conjecture and Neutron Drip Line — A Structural Analogy at the Boundary of Existence

This essay proposes a structural analogy between the ABC conjecture in number theory and the neutron drip line in nuclear physics. The ABC conjecture concerns the residue E = log(c/rad(abc)) that cannot be eliminated when additive and multiplicative structures interact. Similarly, the neutron drip line marks where atomic nuclei can no longer bind additional neutrons—Hydrogen-7 exists at this boundary with an extremely narrow resonance width (Γ ≈ 0.09 MeV), while Hydrogen-8 cannot exist at all. Both phenomena exhibit a "rarefaction then cutoff" pattern at their structural boundaries. This is not a proof but a map for future investigation. The author records the intuition: "When eight is confirmed, ABC is proven."

"This essay was written after the author's retirement from ABC conjecture research in December 2025, as a final record of fifty years of observation."