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 ($d_s \in [1.0, 5.0]\text{ mm}$) through deterministic dietary lipid routing and non-Newtonian biopolymer hydrogel micro-encapsulation. Drawing upon thin-slice multi-planar abdominal computed tomography ($1.00\text{ mm}$ and $3.00\text{ mm}$ axial and coronal reconstructions acquired on October 25, 2026), we first prove via modified Hagen-Poiseuille mechanics why clusters of sub-ductal micro-calculi ($r_s < R_{\text{CD}}$) exhibit a substantially higher probability of cystic duct entrainment, obstructive choledocholithiasis, and acute biliary pancreatitis than solitary macro-calculi ($d_s > 15\text{ mm}$). 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 $\omega$-3 $\alpha$-linolenic acid, $\text{C}_{18:3\text{n-}3}$)—trigger steep Cholecystokinin (CCK) wavefronts and high-amplitude gallbladder ejection pressure spikes ($\Delta P_{\text{GB}} > P_{\text{crit}}$), whereas Medium-Chain Triglycerides (MCTs, $\text{C}_8$–$\text{C}_{10}$) bypass chylomicron assembly via direct mesenteric portal venous transport ($\Delta[\text{CCK}] \approx 0$). Third, to preserve essential $\omega$-3 bioavailability and intestinal lubrication while eliminating biliary contractile hazard, we formulate a Non-Newtonian Biopolymer Hydrogel Micro-Encapsulated Lipid Matrix ($\mathcal{H}_{\text{HIC}}$) integrating poly-$\gamma$-glutamic acid ($\gamma$-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, $\mathcal{H}_{\text{HIC}}$ attenuates luminal LCT flux by an order of magnitude ($\max_t J_{\text{LCT}}(t) < 0.15\,K_m \ll K_m$) while sequestering ileal bile acids to upregulate hepatic CYP7A1 and reduce the biliary Cholesterol Saturation Index ($\text{CSI} < 1.0$). Finally, we encode these physiological state constraints and four-tier clinical interlocks into the QFS-zkVM over the 64-bit Goldilocks prime field ($\mathbb{F}_p, p = 2^{64} - 2^{32} + 1$) under Human-in-Command (HIC) sovereign governance and the Strict No-Learn Covenant (NLL-v1.0-2026).