Unified Biliary Hydrodynamics, Non-Newtonian Biopolymer Hydrogel Micro-Encapsulation, and Portal-Routed Medium-Chain Lipid Governance: A Deterministic Cholecystokinin (CCK)-Silent Framework over 64-Bit Goldilocks Prime Fields

This unified monograph establishes an end-to-end bio-physical, hydrodynamic, thermodynamic, and cryptographic governance framework for managing multiple biliary micro-calculi (dₛ ∈ [1.0, 5.0] mm) through deterministic dietary lipid routing and non-Newtonian biopolymer hydrogel micro-encapsulation. Drawing upon thin-slice multi-planar abdominal computed tomography (1.00 mm and 3.00 mm axial and coronal reconstructions acquired on October 25, 2026), we first prove via modified Hagen-Poiseuille mechanics why clusters of sub-ductal micro-calculi (rₛ < RCD) exhibit a substantially higher probability of cystic duct entrainment, obstructive choledocholithiasis, and acute biliary pancreatitis than solitary macro-calculi (dₛ > 15 mm). Second, we model duodenal enteroendocrine I-cell receptor gating across transmembrane free fatty acid receptors GPR40 (FFAR1), GPR120 (FFAR4), and CD36, demonstrating how unbuffered Long-Chain Triglyceride (LCT) boluses—specifically pure liquid flaxseed oil (Linum usitatissimum, rich in ω-3 α-linolenic acid, C18:3n-3)—trigger steep Cholecystokinin (CCK) wavefronts and high-amplitude gallbladder ejection pressure spikes (Δ PGB > Pcrit), whereas Medium-Chain Triglycerides (MCTs, C₈–C₁₀) bypass chylomicron assembly via direct mesenteric portal venous transport (Δ[CCK] ≈ 0). Third, to preserve essential ω-3 bioavailability and intestinal lubrication while eliminating biliary contractile hazard, we formulate a Non-Newtonian Biopolymer Hydrogel Micro-Encapsulated Lipid Matrix (HHIC) integrating poly-γ-glutamic acid (γ-PGA from fermented natto mucilage), marine sodium alginate-fucoidan, chia seed polysaccharide, and coagulated egg albumin. By Stokes-Einstein-Obstruction diffusion theory and coupled gastric emptying kinetics, HHIC attenuates luminal LCT flux by an order of magnitude (maxₜ JLCT(t) < 0.15\,Kₘ Kₘ) while sequestering ileal bile acids to upregulate hepatic CYP7A1 and reduce the biliary Cholesterol Saturation Index (CSI < 1.0). Finally, we encode these physiological state constraints and four-tier clinical interlocks into the QFS-zkVM over the 64-bit Goldilocks prime field (Fₚ, p = 2⁶⁴ - 2³² + 1) under Human-in-Command (HIC) sovereign governance and the Strict No-Learn Covenant (NLL-v1.0-2026).