Pan-Archipelagic Tripartite Genomic Stratification, Multi-Locus Hierarchical Wahlund Amplification across Autosomal Recessive Founder Diseases, and Zero-Knowledge Deterministic Governance for National Orphan Drug Budgeting

Building upon our prior monographs on stochastic population bottlenecks and civic-legislative governance in Gaucher disease (DOI: 10.5281/zenodo.23581227) and coalescent haplotype dynamics of GBA1/GBAP1 recombination with mating network orthogonality (DOI: 10.5281/zenodo.23581971), this third treatise generalizes the hierarchical Wahlund amplification framework across the pan-archipelagic genomic structure of the Japanese archipelago and a multi-locus spectrum of rare autosomal recessive and founder-effect disorders. Integrating the tripartite ancestral admixture model—comprising Paleolithic Jomon hunter-gatherers (K1, peaking at 28.5% in Okinawa and 18.9% in Tohoku), Northeast Asian Yayoi agriculturalists (K2), and East Asian Kofun state-formation migrants (K3, concentrated in Kansai)—we construct a multi-scale coalescent tensor across 47 macro-prefectural regions and isolated micro-topographic demes. We derive exact homozygosity inflation operators for five canonical disease classes in Japan: (1) non-allelic homologous recombination in Gaucher disease (GBA1 L444P / RecNciI / F213I), (2) the ancestral 3-kb SVA retrotransposon founder insertion in Fukuyama Congenital Muscular Dystrophy (FKTN), (3) truncating founder haplotypes (p.S1653Kfs2 and p.Y2935) in EYS-associated autosomal recessive retinitis pigmentosa, (4) regional clustering across adult and infantile lysosomal storage disorders (GLB1, GAA, HEXA), and (5) endemic geographic foci of hereditary transthyretin amyloidosis (TTR V30M in Arao/Kumamoto and Ogawa/Nagano). Finally, to permanently eradicate institutional healthcare rationing and the "Age-18 Pediatric Subsidy Cliff" across all statutory intractable diseases (Shitei Nanbyo), we architect a privacy-preserving, deterministic fiscal state machine over the 64-bit Goldilocks prime field (F_p, p = 2^64 - 2^32 + 1) utilizing QFS-zkVM, RTO P2.0, Q-SAFA, PHOENIX_ROUTER, and Human-in-Command (HIC) cryptographic interlocks.