We introduce the Arithmetic Orbit Trajectory (AOT) framework, grounded in the GF (2⁸) algebraic structure of AES-128, to characterize continuous glucose monitoring (CGM) time series. CGM values are classified into arithmetic equilibrium states (Z/15Z subgroup, no Sylow-17 component; 80-93 mg/dL in the normoglycemic range) and arithmetic transition states (Sylow-17 component present). The Sylow-17 algebraic critical point 99 mg/dL (0x63=SBOX0x00, multiplicative order 17) coincides with the ADA prediabetes threshold. In 16 subjects from the BIG IDEAs Lab Glycemic Variability dataset (PhysioNet, 37, 080 readings), the AOT Oscillation Index (mean Sylow-17 run length) strongly predicted hyperglycemic area above 100 mg/dL (Spearman rho=0. 818, p=0. 0001, R²=0. 600), while HbA1c did not (rho=0. 208, p=0. 44). In the matched HbA1c 5. 5-5. 7 subgroup (n=9), AOTOI vs HAA100 rho=0. 867 (p=0. 003). Subjects in the highest AOTOI tertile had 2. 6x higher HAA100 despite identical TIR (97. 7% vs 97. 7%), demonstrating AOT captures glycemic stress invisible to standard metrics. These findings constitute a proof-of-concept for the IGCI-AOT framework combining cumulative glycation exposure with algebraic trajectory structure.
Yao-Kai Kao (Sun,) studied this question.