2025/04/30 by Semenov, Stanislav · 2 citations
Computer Science · #03F60 #26E40 #Algorithms and Data Compression #Cellular Automata and Applications #Coding theory and cryptography #E.4 #F.4.1 #FOS: Mathematics #General Mathematics (math.GM)
paper · pdf · doi:10.48550/arxiv.2504.21473
openalex publication_date 2025/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a simple yet powerful invariant relation connecting four successive terms of a class of exponentially decaying alternating functions. Specifically, for the sequence defined by f(n) = ((1/2)n + (-1)n) / n, we prove that the combination [(n-2)f(n-2) + (n-3)f(n-3)] / [n f(n) + (n-1)f(n-1)] is universally equal to 4 for all integers n >= 4. This invariant bridge across four points opens new possibilities for predictive coding, data compression, and error detection. We demonstrate how the relation can be used to reconstruct missing data, verify data integrity, and reduce redundancy in data streams with minimal computational overhead. The simplicity and universality of this invariant make it a promising tool for a wide range of applications in information theory and coding systems.