Technical Supplement: Mathematical Models at Structural Boundaries — ABC Conjecture and Neutron Drip Line

Technical supplement to "Beyond Eight," providing the mathematical framework for the proposed structural analogy. Includes: (1) R-matrix theory and Breit-Wigner resonance formula for nuclear systems near the drip line, (2) Quality distribution theory for ABC triples, (3) Comparative analysis with figures showing the "rarefaction then cutoff" pattern in both systems. Appendix S contains speculative extensions generated through AI dialogue (Claude, Gemini), including penetrability-density correspondence, halo structure analogies, and the capacity limit hypothesis. These speculations are explicitly marked as unverified directions for future research.

"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."