Stochastic Population Bottlenecks in Gaucher Disease (GBA1), Elimination of the Age-18 Pediatric Subsidy Cliff, and Deterministic Civic-Legislative Governance for Orphan Drug Budgeting

Rural depopulation and historical demographic isolation induce genetic bottlenecks that elevate the incidence of autosomal recessive lysosomal storage disorders, notably Gaucher disease (GBA1 deficiency), in stark contrast to de novo chromosomal nondisjunction events (such as Trisomy 21) which remain invariant to parental kinship (F_IS). Beyond genetic etiology, ultra-rare patient cohorts face catastrophic institutional failures in healthcare resource allocation. Drawing upon empirical civic-legislative intervention in Japan—at a historical juncture when the total national cohort of Gaucher disease patients numbered only N = 90—this monograph analyzes the elimination of the "Age-18 Pediatric Subsidy Cliff" (18歳の壁). Prior to intervention, state-funded macrophage-targeted Enzyme Replacement Therapy (ERT, Genzyme Corp.; administered f = 4 times monthly at a base unit threshold of c_0 = 40,000 JPY per vial/infusion tier, requiring multiple vials scaled by adult body weight) was abruptly terminated upon a patient's 18th birthday due to expiration of pediatric chronic disease coverage (Shōni Mansei Tokutei Shikkan). While conventional bureaucratic budgeting projections required τ_std = 4.0 years (48 months) for parliamentary appropriation into the adult intractable disease framework (Tokutei Shikkan), a direct Human-in-Command (HIC) civic-legislative relay—initiated via a formal written petition (Chinjō-sho, 陳情書) drafted by an anonymized affected friend and family at the direction of the primary civic advocate (Yoko Hasebe), validated through a Municipal Assembly Councillor (Uncle), and escalated to National Diet Member Hon. Keigo Masuya (桝屋敬悟元衆議院議員)—compressed the statutory authorization and national budgetary allocation to τ_HIC = 0.5 years (6 months). This historic reform was subsequently chronicled on the front page of the Kōmei Shimbun (公明新聞一面) while strictly preserving the affected family's requested anonymity. We formalize the mathematical dynamics of recessive allele amplification, legislative latency compression (η_HIC = 8.0x), and zero-knowledge identity shielding within the QFS-zkVM architecture over the 64-bit Goldilocks prime field (F_p, p = 2^64 - 2^32 + 1).