Information Entropy and Structural Isomorphism in Arithmetic Systems

We investigate a deterministic arithmetic system defined by the polynomial Q(n) = n⁴⁷ - (n-1)⁴⁷ as a toy model for constraint-driven structure formation. Central Result: The distribution of 46 forbidden residue classes modulo 283 imposes a sharp upper bound of k_max = 28 on consecutive admissible sequences. This bound emerges purely from arithmetic geometry and represents an intrinsic "channel capacity" of the system. Structural Isomorphism: The numerical coincidence between this arithmetic bound (28) and the nuclear magic number governing shell closure in atomic nuclei suggests a structural isomorphism: both systems exhibit discrete stability thresholds arising from constraint accumulation rather than fine-tuning. Numerical Evidence:- 2,597,698 prime-producing values identified (n ≤ 3×10⁸)- 3 quadruplets observed vs 3.52 predicted (Hardy-Littlewood ratio: 0.85)- Zero primes in all 46 forbidden residue classes (verified) Related Resources:Companion mathematical paper and complete dataset: https://github.com/Ruqing1963/prime-polynomial-Q47