Omega Infinity: Recursive Meta-Markov Chain Compression A Novel Approach Using Adaptive Prediction with Self-Referential Encoding

We present Omega Infinity, a novel lossless data compression framework based on adaptive Markov chain prediction with recursive meta-level encoding. Our approach introduces two key innovations: (1) an adaptive Markov model that builds incrementally during both compression and decompression, eliminating the need to store the probability model explicitly, and (2) a recursive meta-compression scheme where the function f(m) = m is applied iteratively, compressing the output ranks of each level using the same Markov-based technique. Experimental results demonstrate compression ratios of up to 16.8x for structured data and 93.9% reduction for DNA sequences, significantly outperforming traditional methods on repetitive patterns while maintaining competitive performance on natural language text. The theoretical foundation rests on the observation that Markov prediction transforms high-entropy source symbols into low-entropy rank sequences, which themselves exhibit predictable patterns amenable to further compression.