Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Semenov, Stanislav
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417523331
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