Structural Inaccessibility of the ABC Conjecture: A No-Go Theorem for Finite Local Observation Methods / ABC予想の構造的到達不能性 — 有限局所観測型手法に対するNo-Go定理

We prove a no-go theorem (Main Theorem R [A]) for the ABC conjecture: no method in method class C (finite local observation-based methods, encompassing sieves, Baker bounds, Buium arithmetic differential geometry, cyclotomic valuations, and room decomposition) can prove the finiteness of super-Wieferich primes. We also prove a density theorem: at least 21% of bases possess a super-Wieferich prime, with an expected density of approximately 25% by inclusion-exclusion. The paper identifies five structural properties (inter-prime independence, Buium flat connection, K-theory vacuity, simultaneous vanishing of all observables, and finite locality) that motivate the axioms of method class C, and formulates the null geometry of Spec Z as an indefinite bilinear form whose null cone precisely captures the super-Wieferich condition. Bilingual: Japanese + English.

ABC予想の核心であるHigher Wieferich Bound (HW_q)に対し、方法クラスC(有限局所観測型手法)のno-go定理(主定理R [A])を証明する。密度定理(底の21%以上にsuper-Wieferich素数が存在)[A]、5つの構造的性質による公理の動機づけ、Spec Z上のnull幾何の定式化を含む6部構成の統合論文。日英バイリンガル。